ArticlePDF Available

Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?


Abstract and Figures

We evaluate 179 classifiers arising from 17 families (discriminant analysis, Bayesian, neural networks, support vector machines, decision trees, rule-based classifi ers, boosting, bagging, stacking, random forests and other ensembles, generalized linear models, nearestneighbors, partial least squares and principal component regression, logistic and multinomial regression, multiple adaptive regression splines and other methods), implemented in Weka, R (with and without the caret package), C and Matlab, including all the relevant classifiers available today. We use 121 data sets, which represent the whole UCI data base (excluding the large-scale problems) and other own real problems, in order to achieve significant conclusions about the classifier behavior, not dependent on the data set collection. The classifiers most likely to be the bests are the random forest (RF) versions, the best of which (implemented in R and accessed via caret) achieves 94.1% of the maximum accuracy overcoming 90% in the 84.3% of the data sets. However, the difference is not statistically significant with the second best, the SVM with Gaussian kernel implemented in C using LibSVM, which achieves 92.3% of the maximum accuracy. A few models are clearly better than the remaining ones: random forest, SVM with Gaussian and polynomial kernels, extreme learning machine with Gaussian kernel, C5.0 and avNNet (a committee of multi-layer perceptrons implemented in R with the caret package). The random forest is clearly the best family of classifiers (3 out of 5 bests classi ers are RF), followed by SVM (4 classifiers in the top-10), neural networks and boosting ensembles (5 and 3 members in the top-20, respectively). © 2014 Manuel Fernández-Delgado, Eva Cernadas, Senén Barro and Dinani Amorim.
Content may be subject to copyright.
Journal of Machine Learning Research 15 (2014) 3133-3181 Submitted 11/13; Revised 4/14; Published 10/14
Do we Need Hundreds of Classifiers to Solve Real World
Classification Problems?
Manuel Fern´andez-Delgado
Eva Cernadas
Sen´en Barro
CITIUS: Centro de Investigaci´on en Tecnolox´ıas da Informaci´on da USC
University of Santiago de Compostela
Campus Vida, 15872, Santiago de Compostela, Spain
Dinani Amorim
Departamento de Tecnologia e Ciˆencias Sociais- DTCS
Universidade do Estado da Bahia
Av. Edgard Chastinet S/N - S˜ao Geraldo - Juazeiro-BA, CEP: 48.305-680, Brasil
Editor: Russ Greiner
We evaluate 179 classifiers arising from 17 families (discriminant analysis, Bayesian,
neural networks, support vector machines, decision trees, rule-based classifiers, boosting,
bagging, stacking, random forests and other ensembles, generalized linear models, nearest-
neighbors, partial least squares and principal component regression, logistic and multino-
mial regression, multiple adaptive regression splines and other methods), implemented in
Weka, R (with and without the caret package), C and Matlab, including all the relevant
classifiers available today. We use 121 data sets, which represent the whole UCI data
base (excluding the large-scale problems) and other own real problems, in order to achieve
significant conclusions about the classifier behavior, not dependent on the data set col-
lection. The classifiers most likely to be the bests are the random forest (RF)
versions, the best of which (implemented in R and accessed via caret) achieves 94.1% of
the maximum accuracy overcoming 90% in the 84.3% of the data sets. However, the dif-
ference is not statistically significant with the second best, the SVM with Gaussian kernel
implemented in C using LibSVM, which achieves 92.3% of the maximum accuracy. A few
models are clearly better than the remaining ones: random forest, SVM with Gaussian
and polynomial kernels, extreme learning machine with Gaussian kernel, C5.0 and avNNet
(a committee of multi-layer perceptrons implemented in R with the caret package). The
random forest is clearly the best family of classifiers (3 out of 5 bests classifiers are RF),
followed by SVM (4 classifiers in the top-10), neural networks and boosting ensembles (5
and 3 members in the top-20, respectively).
Keywords: classification, UCI data base, random forest, support vector machine, neural
networks, decision trees, ensembles, rule-based classifiers, discriminant analysis, Bayesian
classifiers, generalized linear models, partial least squares and principal component re-
gression, multiple adaptive regression splines, nearest-neighbors, logistic and multinomial
2014 Manuel Fern´andez-Delgado, Eva Cernadas, Sen´en Barro and Dinani Amorim.
andez-Delgado, Cernadas, Barro and Amorim
1. Introduction
When a researcher or data analyzer faces to the classification of a data set, he/she usually
applies the classifier which he/she expects to be “the best one”. This expectation is condi-
tioned by the (often partial) researcher knowledge about the available classifiers. One reason
is that they arise from different fields within computer science and mathematics, i.e., they
belong to different “classifier families”. For example, some classifiers (linear discriminant
analysis or generalized linear models) come from statistics, while others come from symbolic
artificial intelligence and data mining (rule-based classifiers or decision-trees), some others
are connectionist approaches (neural networks), and others are ensembles, use regression or
clustering approaches, etc. A researcher may not be able to use classifiers arising from areas
in which he/she is not an expert (for example, to develop parameter tuning), being often
limited to use the methods within his/her domain of expertise. However, there is no certainty
that they work better, for a given data set, than other classifiers, which seem more “exotic”
to him/her. The lack of available implementation for many classifiers is a major drawback,
although it has been partially reduced due to the large amount of classifiers implemented
in R1(mainly from Statistics), Weka2(from the data mining field) and, in a lesser extend,
in Matlab using the Neural Network Toolbox3. Besides, the R package caret (Kuhn, 2008)
provides a very easy interface for the execution of many classifiers, allowing automatic pa-
rameter tuning and reducing the requirements on the researcher’s knowledge (about the
tunable parameter values, among other issues). Of course, the researcher can review the
literature to know about classifiers in families outside his/her domain of expertise and, if
they work better, to use them instead of his/her preferred classifier. However, usually the
papers which propose a new classifier compare it only to classifiers within the same family,
excluding families outside the author’s area of expertise. Thus, the researcher does not know
whether these classifiers work better or not than the ones that he/she already knows. On the
other hand, these comparisons are usually developed over a few, although expectedly rele-
vant, data sets. Given that all the classifiers (even the “good” ones) show strong variations
in their results among data sets, the average accuracy (over all the data sets) might be of
limited significance if a reduced collection of data sets is used (Maci`a and Bernad´o-Mansilla,
2014). Specifically, some classifiers with a good average performance over a reduced data
set collection could achieve significantly worse results when the collection is extended, and
conversely classifiers with sub-optimal performance on the reduced data collection could be
not so bad when more data sets are included. There are useful guidelines (Hothorn et al.,
2005; Eugster et al., 2014) to analyze and design benchmark exploratory and inferential
experiments, giving also a very useful framework to inspect the relationship between data
sets and classifiers.
Each time we find a new classifier or family of classifiers from areas outside our domain
of expertise, we ask ourselves whether that classifier will work better than the ones that we
use routinely. In order to have a clear idea of the capabilities of each classifier and family, it
would be useful to develop a comparison of a high number of classifiers arising from many
different families and areas of knowledge over a large collection of data sets. The objective
1. See
2. See
3. See
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
is to select the classifier which more probably achieves the best performance for any data
set. In the current paper we use a large collection of classifiers with publicly available
implementations (in order to allow future comparisons), arising from a wide variety of
classifier families, in order to achieve significant conclusions not conditioned by the number
and variety of the classifiers considered. Using a high number of classifiers it is probable that
some of them will achieve the “highest” possible performance for each data set, which can
be used as reference (maximum accuracy) to evaluate the remaining classifiers. However,
according to the No-Free-Lunch theorem (Wolpert, 1996), the best classifier will not be the
same for all the data sets. Using classifiers from many families, we are not restricting the
significance of our comparison to one specific family among many available methods. Using
ahigh number of data sets, it is probable that each classifier will work well in some data
sets and not so well in others, increasing the evaluation significance. Finally, considering
the availability of several alternative implementations for the most popular classifiers, their
comparison may also be interesting. The current work pursues: 1) to select the globally
best classifier for the selected data set collection; 2) to rank each classifier and family
according to its accuracy; 3) to determine, for each classifier, its probability of achieving
the best accuracy, and the difference between its accuracy and the best one; 4) to evaluate
the classifier behavior varying the data set properties (complexity, #patterns, #classes and
Some recent papers have analyzed the comparison of classifiers over large collection of
data sets. OpenML (Vanschoren et al., 2012), is a complete web interface4to anonymously
access an experiment data base including 86 data sets from the UCI machine learning data
base (Bache and Lichman, 2013) and 93 classifiers implemented in Weka. Although plug-
ins for R, Knime and RapidMiner are under development, currently it only allows to use
Weka classifiers. This environment allows to send queries about the classifier behavior with
respect to tunable parameters, considering several common performance measures, feature
selection techniques and bias-variance analysis. There is also an interesting analysis (Maci`a
and Bernad´o-Mansilla, 2014) about the use of the UCI repository launching several inter-
esting criticisms about the usual practice in experimental comparisons. In the following,
we synthesize these criticisms (the italicized sentences are literal cites) and describe how we
tried to avoid them in our paper:
1. The criterion used to select the data set collection (which is usually reduced) may
bias the comparison results. The same authors stated (Maci`a et al., 2013) that the
superiority of a classifier may be restricted to a given domain characterized by some
complexity measures, studying why and how the data set selection may change the
results of classifier comparisons. Following these suggestions, we use all the data sets
in the UCI classification repository, in order to avoid that a small data collection
invalidate the conclusions of the comparison. This paper also emphasizes that the
UCI repository was not designed to be a complete, reliable framework composed of
standardized real samples.
2. The issue about (1) whether the selection of learners is representative enough and (2)
whether the selected learners are properly configured to work at their best performance
4. See
andez-Delgado, Cernadas, Barro and Amorim
suggests that proposals of new classifiers usually design and tune them carefully, while
the reference classifiers are run using a baseline configuration. This issue is also related
to the lack of deep knowledge and experience about the details of all the classifiers with
available implementations, so that the researchers usually do not pay much attention
about the selected reference algorithms, which may consequently bias the results in
favour of the proposed algorithm. With respect to this criticism, in the current paper
we do not propose any new classifier nor changes on existing approaches, so we are not
interested in favour any specific classifier, although we are more experienced with some
classifier than others (for example, with respect to the tunable parameter values). We
develop in this work a parameter tuning in the majority of the classifiers used (see
below), selecting the best available configuration over a training set. Specifically, the
classifiers implemented in R using caret automatically tune these parameters and,
even more important, using pre-defined (and supposedly meaningful) values. This
fact should compensate our lack of experience about some classifiers, and reduce its
relevance on the results.
3. It is still impossible to determine the maximum attainable accuracy for a data set,
so that it is difficult to evaluate the true quality of each classifier. In our paper, we
use a large amount of classifiers (179) from many different families, so we hypothesize
that the maximum accuracy achieved by some classifier is the maximum attainable
accuracy for that data set: i.e., we suppose that if no classifier in our collection is
able to reach higher accuracy, no one will reach. We can not test the validity of this
hypothesis, but it seems reasonable that, when the number of classifiers increases,
some of them will achieve the largest possible accuracy.
4. Since the data set complexity (measured somehow by the maximum attainable ac-
curacy) is unknown, we do not know if the classification error is caused by unfitted
classifier design (learner’s limitation) or by intrinsic difficulties of the problem (data
limitation). In our work, since we consider that the attainable accuracy is the maxi-
mum accuracy achieved by some classifier in our collection, we can consider that low
accuracies (with respect to this maximum accuracy) achieved by other classifiers are
always caused by classifier limitations.
5. The lack of standard data partitioning, defining training and testing data for cross-
validation trials. Simply the use of different data partitionings will eventually bias the
results, and make the comparison between experiments impossible, something which is
also emphasized by other researchers (Vanschoren et al., 2012). In the current paper,
each data set uses the same partitioning for all the classifiers, so that this issue can not
bias the results favouring any classifier. Besides, the partitions are publicly available
(see Section 2.1), in order to make possible the experiment replication.
The paper is organized as follows: the Section 2 describes the collection of data sets and
classifiers considered in this work; the Section 3 discusses the results of the experiments,
and the Section 4 compiles the conclusions of the research developed.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
2. Materials and Methods
In the following paragraphs we describe the materials (data sets) and methods (classifiers)
used to develop this comparison.
Data set #pat. #inp. #cl. %Ma j. Data set #pat. #inp. #cl. %Maj.
abalone 4177 8 3 34.6 energy-y1 768 8 3 46.9
ac-inflam 120 6 2 50.8 energy-y2 768 8 3 49.9
acute-nephritis 120 6 2 58.3 fertility 100 9 2 88.0
adult 48842 14 2 75.9 flags 194 28 8 30.9
annealing 798 38 6 76.2 glass 214 9 6 35.5
arrhythmia 452 262 13 54.2 haberman-survival 306 3 2 73.5
audiology-std 226 59 18 26.3 hayes-roth 132 3 3 38.6
balance-scale 625 4 3 46.1 heart-cleveland 303 13 5 54.1
balloons 16 4 2 56.2 heart-hungarian 294 12 2 63.9
bank 45211 17 2 88.5 heart-switzerland 123 12 2 39.0
blood 748 4 2 76.2 heart-va 200 12 5 28.0
breast-cancer 286 9 2 70.3 hepatitis 155 19 2 79.3
bc-wisc 699 9 2 65.5 hill-valley 606 100 2 50.7
bc-wisc-diag 569 30 2 62.7 horse-colic 300 25 2 63.7
bc-wisc-prog 198 33 2 76.3 ilpd-indian-liver 583 9 2 71.4
breast-tissue 106 9 6 20.7 image-segmentation 210 19 7 14.3
car 1728 6 4 70.0 ionosphere 351 33 2 64.1
ctg-10classes 2126 21 10 27.2 iris 150 4 3 33.3
ctg-3classes 2126 21 3 77.8 led-display 1000 7 10 11.1
chess-krvk 28056 6 18 16.2 lenses 24 4 3 62.5
chess-krvkp 3196 36 2 52.2 letter 20000 16 26 4.1
congress-voting 435 16 2 61.4 libras 360 90 15 6.7
conn-bench-sonar 208 60 2 53.4 low-res-spect 531 100 9 51.9
conn-bench-vowel 528 11 11 9.1 lung-cancer 32 56 3 40.6
connect-4 67557 42 2 75.4 lymphography 148 18 4 54.7
contrac 1473 9 3 42.7 magic 19020 10 2 64.8
credit-approval 690 15 2 55.5 mammographic 961 5 2 53.7
cylinder-bands 512 35 2 60.9 miniboone 130064 50 2 71.9
dermatology 366 34 6 30.6 molec-biol-promoter 106 57 2 50.0
echocardiogram 131 10 2 67.2 molec-biol-splice 3190 60 3 51.9
ecoli 336 7 8 42.6 monks-1 124 6 2 50.0
Table 1: Collection of 121 data sets from the UCI data base and our real prob-
lems. It shows the number of patterns (#pat.), inputs (#inp.), classes
(#cl.) and percentage of majority class (%Maj.) for each data set. Con-
tinued in Table 2. Some keys are: ac-inflam=acute-inflammation, bc=breast-
cancer, congress-vot= congressional-voting, ctg=cardiotocography, conn-bench-
sonar/vowel= connectionist-benchmark-sonar-mines-rocks/vowel-deterding, pb=
pittsburg-bridges, st=statlog, vc=vertebral-column.
andez-Delgado, Cernadas, Barro and Amorim
2.1 Data Sets
We use the whole UCI machine learning repository, the most widely used data base in the
classification literature, to develop the classifier comparison. The UCI website5specifies
a list of 165 data sets which can be used for classification tasks (March, 2013). We
discarded 57 data sets due to several reasons: 25 large-scale data sets (with very high
#patterns and/or #inputs, for which our classifier implementations are not designed), 27
data sets which are not in the “common UCI format”, and 5 data sets due to diverse
reasons (just one input, classes without patterns, classes with only one pattern and sets
not available). We also used 4 real-world data sets (Gonz´alez-Rufino et al., 2013) not
included in the UCI repository, about fecundity estimation for fisheries: they are denoted
as oocMerl4D (2-class classification according to the presence/absence of oocyte nucleus),
oocMerl2F (3-class classification according to the stage of development of the oocyte) for
fish species Merluccius; and oocTris2F (nucleus) and oocTris5B (stages) for fish species
Trisopterus. The inputs are texture features extracted from oocytes (cells) in histological
images of fish gonads, and its calculation is described in the page 2400 (Table 4) of the cited
Overall, we have 165 - 57 + 4 = 112 data sets. However, some UCI data sets provide
several “class” columns, so that actually they can be considered several classification prob-
lems. This is the case of data set cardiotocography, where the inputs can be classified into 3
or 10 classes, giving two classification problems (one additional data set); energy, where the
classes can be given by columns y1 or y2 (one additional data set); pittsburg-bridges, where
the classes can be material, rel-l, span, t-or-d and type (4 additional data sets); plant (whose
complete UCI name is One-hundred plant species), with inputs margin, shape or texture (2
extra data sets); and vertebral-column, with 2 or 3 classes (1 extra data set). Therefore, we
achieve a total of 112 + 1 + 1 + 4 + 2 + 1 = 121 data sets6, listed in the Tables 1 and 2
by alphabetic order (some data set names are reduced but significant versions of the UCI
official names, which are often too long). OpenML (Vanschoren et al., 2012) includes only
86 data sets, of which seven do not belong to the UCI database: baseball, braziltourism,
CoEPrA-2006 Classification 001/2/3, eucalyptus, labor, sick and solar-flare. In our work,
the #patterns range from 10 (data set trains) to 130,064 (miniboone), with #inputs ranging
from 3 (data set hayes-roth) to 262 (data set arrhythmia), and #classes between 2 and 100.
We used even tiny data sets (such as trains or balloons), in order to assess that each clas-
sifier is able to learn these (expected to be “easy”) data sets. In some data sets the classes
with only two patterns were removed because they are not enough for training/test sets.
The same data files were used for all the classifiers, excepting the ones provided by Weka,
which require the ARFF format. We converted the nominal (or discrete) inputs to numeric
values using a simple quantization: if an input xmay take discrete values {v1, . . . , vn}, when
it takes the discrete value viit is converted to the numeric value i∈ {1, . . . , n}. We are
conscious that this change in the representation may have a high impact in the results of
distance-based classifiers (Maci`a and Bernad´o-Mansilla, 2014), because contiguous discrete
values (viand vi+1) might not be nearer than non-contiguous values (v1and vn). Each input
5. See
6. The whole data set and partitions are available from:
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Data set #pat. #inp. #cl. %Maj. Data set #pat. #inp. #cl. %Ma j.
monks-2 169 6 2 62.1 soybean 307 35 18 13.0
monks-3 3190 6 2 50.8 spambase 4601 57 2 60.6
mushroom 8124 21 2 51.8 spect 80 22 2 67.1
musk-1 476 166 2 56.5 spectf 80 44 2 50.0
musk-2 6598 166 2 84.6 st-australian-credit 690 14 2 67.8
nursery 12960 8 5 33.3 st-german-credit 1000 24 2 70.0
oocMerl2F 1022 25 3 67.0 st-heart 270 13 2 55.6
oocMerl4D 1022 41 2 68.7 st-image 2310 18 7 14.3
oocTris2F 912 25 2 57.8 st-landsat 4435 36 6 24.2
oocTris5B 912 32 3 57.6 st-shuttle 43500 9 7 78.4
optical 3823 62 10 10.2 st-vehicle 846 18 4 25.8
ozone 2536 72 2 97.1 steel-plates 1941 27 7 34.7
page-blocks 5473 10 5 89.8 synthetic-control 600 60 6 16.7
parkinsons 195 22 2 75.4 teaching 151 5 3 34.4
pendigits 7494 16 10 10.4 thyroid 3772 21 3 92.5
pima 768 8 2 65.1 tic-tac-toe 958 9 2 65.3
pb-MATERIAL 106 4 3 74.5 titanic 2201 3 2 67.7
pb-REL-L 103 4 3 51.5 trains 10 28 2 50.0
pb-SPAN 92 4 3 52.2 twonorm 7400 20 2 50.0
pb-T-OR-D 102 4 2 86.3 vc-2classes 310 6 2 67.7
pb-TYPE 105 4 6 41.9 vc-3classes 310 6 3 48.4
planning 182 12 2 71.4 wall-following 5456 24 4 40.4
plant-margin 1600 64 100 1.0 waveform 5000 21 3 33.9
plant-shape 1600 64 100 1.0 waveform-noise 5000 40 3 33.8
plant-texture 1600 64 100 1.0 wine 179 13 3 39.9
post-operative 90 8 3 71.1 wine-quality-red 1599 11 6 42.6
primary-tumor 330 17 15 25.4 wine-quality-white 4898 11 7 44.9
ringnorm 7400 20 2 50.5 yeast 1484 8 10 31.2
seeds 210 7 3 33.3 zoo 101 16 7 40.6
semeion 1593 256 10 10.2
Table 2: Continuation of Table 1 (data set collection).
is pre-processed to have zero mean and standard deviation one, as is usual in the classifier
literature. We do not use further pre-processing, data transformation or feature selection.
The reasons are: 1) the impact of these transforms can be expected to be similar for all the
classifiers; however, our objective is not to achieve the best possible performance for each
data set (which eventually might require further pre-processing), but to compare classifiers
on each set; 2) if pre-processing favours some classifier(s) with respect to others, this impact
should be random, and therefore not statistically significant for the comparison; 3) in order
to avoid comparison bias due to pre-processing, it seems advisable to use the original data;
4) in order to enhance the classification results, further pre-processing eventually should be
specific to each data set, which would increase largely the present work; and 5) additional
transformations would require a knowledge which is outside the scope of this paper, and
should be explored in a different study. In those data sets with different training and test
sets (annealing or audiology-std, among others), both files were not merged to follow the
practice recommended by the data set creators, and to achieve “significant” accuracies on
the right test data, using the right training data. In those data sets where the class attribute
andez-Delgado, Cernadas, Barro and Amorim
must be defined grouping several values (in data set abalone) we follow the instructions in
the data set description (file data.names). Given that our classifiers are not oriented to
data with missing features, the missing inputs are treated as zero, which should not bias the
comparison results. For each data set (abalone) two data files are created: abalone R.dat,
designed to be read by the R, C and Matlab classifiers, and abalone.arff, designed to be
read by the Weka classifiers.
2.2 Classifiers
We use 179 classifiers implemented in C/C++, Matlab, R and Weka. Excepting the
Matlab classifiers, all of them are free software. We only developed own versions in C for
the classifiers proposed by us (see below). Some of the R programs use directly the package
that provides the classifier, but others use the classifier through the interface train provided
by the caret7package. This function develops the parameter tuning, selecting the values
which maximize the accuracy according to the validation selected (leave-one-out, k-fold,
etc.). The caret package also allows to define the number of values used for each tunable
parameter, although the specific values can not be selected. We used all the classifiers
provided by Weka, running the command-line version of the java class for each classifier.
OpenML uses 93 Weka classifiers, from which we included 84. We could not include
in our collection the remaining 9 classifiers: ADTree, alternating decision tree (Freund
and Mason, 1999); AODE, aggregating one-dependence estimators (Webb et al., 2005);
Id3 (Quinlan, 1986); LBR, lazy Bayesian rules (Zheng and Webb, 2000); M5Rules (Holmes
et al., 1999); Prism (Cendrowska, 1987); ThresholdSelector; VotedPerceptron (Freund and
Schapire, 1998) and Winnow (Littlestone, 1988). The reason is that they only accept
nominal (not numerical) inputs, while we converted all the inputs to numeric values. Be-
sides, we did not use classifiers ThresholdSelector, VotedPerceptron and Winnow, included
in openML, because they accept only two-class problems. Note that classifiers Locally-
WeightedLearning and RippleDownRuleLearner (Vanschoren et al., 2012) are included in
our collection as LWL and Ridor respectively. Furthermore, we also included other 36 clas-
sifiers implemented in R, 48 classifiers in R using the caret package, as well as 6 classifiers
implemented in C and other 5 in Matlab, summing up to 179 classifiers.
In the following, we briefly describe the 179 classifiers of the different families identi-
fied by acronyms (DA, BY, etc., see below), their names and implementations, coded as
name implementation, where implementation can be C,m(Matlab), R,t(in R using
caret) and w(Weka), and their tunable parameter values (the notation A:B:C means from
A to C step B). We found errors using several classifiers accessed via caret, but we used
the corresponding R packages directly. This is the case of lvq, bdk, gaussprLinear, glm-
net, kernelpls, widekernelpls, simpls, obliqueTree, spls, gpls, mars, multinom, lssvmRadial,
partDSA, PenalizedLDA, qda, QdaCov, mda, rda, rpart, rrlda, sddaLDA, sddaQDA and
sparseLDA. Some other classifiers as Linda, smda and xyf (not listed below) gave errors
(both with and without caret) and could not be included in this work. In the R and caret
implementations, we specify the function and, in typewriter font, the package which provide
that classifier (the function name is absent when it is is equal to the classifier).
7. See
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Discriminant analysis (DA): 20 classifiers.
1. lda R, linear discriminant analysis, with the function lda in the MASS package.
2. lda2 t, from the MASS package, which develops LDA tuning the number of components
to retain up to #classes 1.
3. rrlda R, robust regularized LDA, from the rrlda package, tunes the parameters
lambda (which controls the sparseness of the covariance matrix estimation) and alpha
(robustness, it controls the number of outliers) with values {0.1, 0.01, 0.001}and {0.5,
0.75, 1.0}respectively.
4. sda t, shrinkage discriminant analysis and CAT score variable selection (Ahdesm¨aki
and Strimmer, 2010) from the sda package. It performs LDA or diagonal discriminant
analysis (DDA) with variable selection using CAT (Correlation-Adjusted T) scores.
The best classifier (LDA or DDA) is selected. The James-Stein method is used for
shrinkage estimation.
5. slda t with function slda from the ipred package, which develops LDA based on
left-spherically distributed linear scores (Glimm et al., 1998).
6. stepLDA t uses the function train in the caret package as interface to the function
stepclass in the klaR package with method=lda. It develops classification by means of
forward/backward feature selection, without upper bounds in the number of features.
7. sddaLDA R, stepwise diagonal discriminant analysis, with function sdda in the SDDA
package with method=lda. It creates a diagonal discriminant rule adding one input
at a time using a forward stepwise strategy and LDA.
8. PenalizedLDA t from the penalizedLDA package: it solves the high-dimensional
discriminant problem using a diagonal covariance matrix and penalizing the discrimi-
nant vectors with lasso or fussed coefficients (Witten and Tibshirani, 2011). The lasso
penalty parameter (lambda) is tuned with values {0.1,0.0031,104}.
9. sparseLDA R, with function sda in the sparseLDA package, minimizing the SDA
criterion using an alternating method (Clemensen et al., 2011). The parameter
lambda is tuned with values 0,{10i}4
1. The number of components is tuned from
2 to #classes 1.
10. qda t, quadratic discriminant analysis (Venables and Ripley, 2002), with function
qda in the MASS package.
11. QdaCov t in the rrcov package, which develops Robust QDA (Todorov and Filz-
moser, 2009).
12. sddaQDA R uses the function sdda in the SDDA package with method=qda.
13. stepQDA t uses function stepclass in the klaR package with method=qda, forward
/ backward variable selection (parameter direction=both) and without limit in the
number of selected variables (maxvar=Inf).
andez-Delgado, Cernadas, Barro and Amorim
14. fda R, flexible discriminant analysis (Hastie et al., 1993), with function fda in the
mda package and the default linear regression method.
15. fda t is the same FDA, also with linear regression but tuning the parameter nprune
with values 2:3:15 (5 values).
16. mda R, mixture discriminant analysis (Hastie and Tibshirani, 1996), with function
mda in the mda package.
17. mda t uses the caret package as interface to function mda, tuning the parameter
subclasses between 2 and 11.
18. pda t, penalized discriminant analysis, uses the function gen.rigde in the mda package,
which develops PDA tuning the shrinkage penalty coefficient lambda with values from
1 to 10.
19. rda R, regularized discriminant analysis (Friedman, 1989), uses the function rda in
the klaR package. This method uses regularized group covariance matrix to avoid
the problems in LDA derived from collinearity in the data. The parameters lambda
and gamma (used in the calculation of the robust covariance matrices) are tuned with
values 0:0.25:1.
20. hdda R, high-dimensional discriminant analysis (Berg´e et al., 2012), assumes that
each class lives in a different Gaussian subspace much smaller than the input space,
calculating the subspace parameters in order to classify the test patterns. It uses the
hdda function in the HDclassif package, selecting the best of the 14 available models.
Bayesian (BY) approaches: 6 classifiers.
21. naiveBayes R uses the function NaiveBayes in R the klaR package, with Gaussian
kernel, bandwidth 1 and Laplace correction 2.
22. vbmpRadial t, variational Bayesian multinomial probit regression with Gaussian
process priors (Girolami and Rogers, 2006), uses the function vbmp from the vbmp
package, which fits a multinomial probit regression model with radial basis function
kernel and covariance parameters estimated from the training patterns.
23. NaiveBayes w (John and Langley, 1995) uses estimator precision values chosen from
the analysis of the training data.
24. NaiveBayesUpdateable w uses estimator precision values updated iteratively using
the training patterns and starting from the scratch.
25. BayesNet w is an ensemble of Bayes classifiers. It uses the K2 search method, which
develops hill climbing restricted by the input order, using one parent and scores of
type Bayes. It also uses the simpleEstimator method, which uses the training patterns
to estimate the conditional probability tables in a Bayesian network once it has been
learnt, which α= 0.5 (initial count).
26. NaiveBayesSimple w is a simple naive Bayes classifier (Duda et al., 2001) which
uses a normal distribution to model numeric features.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Neural networks (NNET): 21 classifiers.
27. rbf m, radial basis functions (RBF) neural network, uses the function newrb in the
Matlab Neural Network Toolbox, tuning the spread of the Gaussian basis function
with 19 values between 0.1 and 70. The network is created empty and new hidden
neurons are added incrementally.
28. rbf t uses caret as interface to the RSNNS package, tuning the size of the RBF network
(number of hidden neurons) with values in the range 11:2:29.
29. RBFNetwork w uses K-means to select the RBF centers and linear regression to
learn the classification function, with symmetric multivariate Gaussians and normal-
ized inputs. We use a number of clusters (or hidden neurons) equal to half the training
patterns, ridge=108for the linear regression and Gaussian minimum spread 0.1.
30. rbfDDA t (Berthold and Diamond, 1995) creates incrementally from the scratch a
RBF network with dynamic decay adjustment (DDA), using the RSNNS package and
tuning the negativeThreshold parameter with values {10i}10
1. The network grows
incrementally adding new hidden neurons, avoiding the tuning of the network size.
31. mlp m: multi-layer perceptron (MLP) implemented in Matlab (function newpr) tun-
ing the number of hidden neurons with 11 values from 3 to 30.
32. mlp C: MLP implemented in C using the fast artificial neural network (FANN) li-
brary8, tuning the training algorithm (resilient, batch and incremental backpropaga-
tion, and quickprop), and the number of hidden neurons with 11 values between 3
and 30.
33. mlp t uses the function mlp in the RSNNS package, tuning the network size with values
34. avNNet t, from the caret package, creates a committee of 5 MLPs (the number of
MLPs is given by parameter repeat) trained with different random weight initializa-
tions and bag=false. The tunable parameters are the #hidden neurons (size) in {1, 3,
5}and the weight decay (values {0, 0.1, 104}). This low number of hidden neurons
is to reduce the computational cost of the ensemble.
35. mlpWeightDecay t uses caret to access the RSNNS package tuning the parameters
size and weight decay of the MLP network with values 1:2:9 and {0, 0.1, 0.01, 0.001,
36. nnet t uses caret as interface to function nnet in the nnet package, training a MLP
network with the same parameter tuning as in mlpWeightDecay t.
37. pcaNNet t trains the MLP using caret and the nnet package, but running principal
component analysis (PCA) previously on the data set.
8. See
andez-Delgado, Cernadas, Barro and Amorim
38. MultilayerPerceptron w is a MLP network with sigmoid hidden neurons, unthresh-
olded linear output neurons, learning rate 0.3, momentum 0.2, 500 training epochs,
and #hidden neurons equal (#inputs and #classes)/2.
39. pnn m: probabilistic neural network (Specht, 1990) in Matlab (function newpnn),
tuning the Gaussian spread with 19 values in the range 0.01-10.
40. elm m, extreme learning machine (Huang et al., 2012) implemented in Matlab using
the code freely available9. We try 6 activation functions (sine, sign, sigmoid, hardlimit,
triangular basis and radial basis) and 20 values for #hidden neurons between 3 and
200. As recommended, the inputs are scaled between [-1,1].
41. elm kernel m is the ELM with Gaussian kernel, which uses the code available from
the previous site, tuning the regularization parameter and the kernel spread with
values 25..214 and 216..28respectively.
42. cascor C, cascade correlation neural network (Fahlman, 1988) implemented in C
using the FANN library (see classifier #32).
43. lvq R is the learning vector quantization (Ripley, 1996) implemented using the func-
tion lvq in the class package, with codebook of size 50, and k=5 nearest neighbors.
We selected the best results achieved using the functions lvq1, olvq2, lvq2 and lvq3.
44. lvq t uses caret as interface to function lvq1 in the class package tuning the pa-
rameters size and k (the values are specific for each data set).
45. bdk R, bi-directional Kohonen map (Melssen et al., 2006), with function bdk in the
kohonen package, a kind of supervised Self Organized Map for classification, which
maps high-dimensional patterns to 2D.
46. dkp C(direct kernel perceptron) is a very simple and fast kernel-based classifier
proposed by us (Fern´andez-Delgado et al., 2014) which achieves competitive results
compared to SVM. The DKP requires the tuning of the kernel spread in the same
range 216..28as the SVM.
47. dpp C (direct parallel perceptron) is a small and efficient Parallel Perceptron net-
work proposed by us (Fern´andez-Delgado et al., 2011), based in the parallel-delta
rule (Auer et al., 2008) with n= 3 perceptrons. The codes for DKP and DPP are
freely available10.
Support vector machines (SVM): 10 classifiers.
48. svm C is the support vector machine, implemented in C using LibSVM (Chang and
Lin, 2008) with Gaussian kernel. The regularization parameter C and kernel spread
gamma are tuned in the ranges 25..214 and 216..28respectively. LibSVM uses the
one-vs.-one approach for multi-class data sets.
9. See
10. See
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
49. svmlight C (Joachims, 1999) is a very popular implementation of the SVM in C. It
can only be used from the command-line and not as a library, so we could not use
it so efficiently as LibSVM, and this fact leads us to errors for some large data sets
(which are not taken into account in the calculation of the average accuracy). The
parameters C and gamma (spread of the Gaussian kernel) are tuned with the same
values as svm C.
50. LibSVM w uses the library LibSVM (Chang and Lin, 2008), calls from Weka for
classification with Gaussian kernel, using the values of C and gamma selected for
svm C and tolerance=0.001.
51. LibLINEAR w uses the library LibLinear (Fan et al., 2008) for large-scale linear
high-dimensional classification, with L2-loss (dual) solver and parameters C=1, toler-
ance=0.01 and bias=1.
52. svmRadial t is the SVM with Gaussian kernel (in the kernlab package), tuning C
and kernel spread with values 22..22and 102..102respectively.
53. svmRadialCost t (kernlab package) only tunes the cost C, while the spread of the
Gaussian kernel is calculated automatically.
54. svmLinear t uses the function ksvm (kernlab package) with linear kernel tuning C
in the range 22..27.
55. svmPoly t uses the kernlab package with linear, quadratic and cubic kernels (sxTy+
o)d, using scale s={0.001,0.01,0.1}, offset o= 1, degree d={1,2,3}and C=
56. lssvmRadial t implements the least squares SVM (Suykens and Vandewalle, 1999),
using the function lssvm in the kernlab package, with Gaussian kernel tuning the
kernel spread with values 102..107.
57. SMO w is a SVM trained using sequential minimal optimization (Platt, 1998) with
one-against-one approach for multi-class classification, C=1, tolerance L=0.001, round-
off error 1012, data normalization and quadratic kernel.
Decision trees (DT): 14 classifiers.
58. rpart R uses the function rpart in the rpart package, which develops recursive par-
titioning (Breiman et al., 1984).
59. rpart t uses the same function tuning the complexity parameter (threshold on the
accuracy increasing achieved by a tentative split in order to be accepted) with 10
values from 0.18 to 0.01.
60. rpart2 t uses the function rpart tuning the tree depth with values up to 10.
61. obliqueTree R uses the function obliqueTree in the oblique.tree package (Truong,
2009), with binary recursive partitioning, only oblique splits and linear combinations
of the inputs.
andez-Delgado, Cernadas, Barro and Amorim
62. C5.0Tree t creates a single C5.0 decision tree (Quinlan, 1993) using the function
C5.0 in the homonymous package without parameter tuning.
63. ctree t uses the function ctree in the party package, which creates conditional infer-
ence trees by recursively making binary splittings on the variables with the highest as-
sociation to the class (measured by a statistical test). The threshold in the association
measure is given by the parameter mincriterion, tuned with the values 0.1:0.11:0.99
(10 values).
64. ctree2 t uses the function ctree tuning the maximum tree depth with values up to
65. J48 w is a pruned C4.5 decision tree (Quinlan, 1993) with pruning confidence thresh-
old C=0.25 and at least 2 training patterns per leaf.
66. J48 t uses the function J48 in the RWeka package, which learns pruned or unpruned
C5.0 trees with C=0.25.
67. RandomSubSpace w (Ho, 1998) trains multiple REPTrees classifiers selecting ran-
domly subsets of inputs (random subspaces). Each REPTree is learnt using informa-
tion gain/variance and error-based pruning with backfitting. Each subspace includes
the 50% of the inputs. The minimum variance for splitting is 103, with at least 2
pattern per leaf.
68. NBTree w (Kohavi, 1996) is a decision tree with naive Bayes classifiers at the leafs.
69. RandomTree w is a non-pruned tree where each leaf tests blog2(#inputs + 1)cran-
domly chosen inputs, with at least 2 instances per leaf, unlimited tree depth, without
backfitting and allowing unclassified patterns.
70. REPTree w learns a pruned decision tree using information gain and reduced error
pruning (REP). It uses at least 2 training patterns per leaf, 3 folds for reduced error
pruning and unbounded tree depth. A split is executed when the class variance is
more than 0.001 times the train variance.
71. DecisionStump w is a one-node decision tree which develops classification or re-
gression based on just one input using entropy.
Rule-based methods (RL): 12 classifiers.
72. PART w builds a pruned partial C4.5 decision tree (Frank and Witten, 1999) in each
iteration, converting the best leaf into a rule. It uses at least 2 objects per leaf, 3-fold
REP (see classifier #70) and C=0.5.
73. PART t uses the function PART in the RWeka package, which learns a pruned PART
with C=0.25.
74. C5.0Rules t uses the same function C5.0 (in the C50 package) as classifiers C5.0Tree t,
but creating a collection of rules instead of a classification tree.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
75. JRip t uses the function JRip in the RWeka package, which learns a “repeated in-
cremental pruning to produce error reduction” (RIPPER) classifier (Cohen, 1995),
tuning the number of optimization runs (numOpt) from 1 to 5.
76. JRip w learns a RIPPER classifier with 2 optimization runs and minimal weights of
instances equal to 2.
77. OneR t (Holte, 1993) uses function OneR in the RWeka package, which classifies using
1-rules applied on the input with the lowest error.
78. OneR w creates a OneR classifier in Weka with at least 6 objects in a bucket.
79. DTNB w learns a decision table/naive-Bayes hybrid classifier (Hall and Frank, 2008),
using simultaneously both decision table and naive Bayes classifiers.
80. Ridor w implements the ripple-down rule learner (Gaines and Compton, 1995) with
at least 2 instance weights.
81. ZeroR w predicts the mean class (i.e., the most populated class in the training data)
for all the test patterns. Obviously, this classifier gives low accuracies, but it serves
to give a lower limit on the accuracy.
82. DecisionTable w (Kohavi, 1995) is a simple decision table majority classifier which
uses BestFirst as search method.
83. ConjunctiveRule w uses a single rule whose antecendent is the AND of several
antecedents, and whose consequent is the distribution of available classes. It uses
the antecedent information gain to classify each test pattern, and 3-fold REP (see
classifier #70) to remove unnecessary rule antecedents.
Boosting (BST): 20 classifiers.
84. adaboost R uses the function boosting in the adabag package (Alfaro et al., 2007),
which implements the adaboost.M1 method (Freund and Schapire, 1996) to create an
adaboost ensemble of classification trees.
85. logitboost R is an ensemble of DecisionStump base classifiers (see classifier #71),
using the function LogitBoost (Friedman et al., 1998) in the caTools package with
200 iterations.
86. LogitBoost w uses additive logistic regressors (DecisionStump) base learners, the
100% of weight mass to base training on, without cross-validation, one run for internal
cross-validation, threshold 1.79 on likelihood improvement, shrinkage parameter 1,
and 10 iterations.
87. RacedIncrementalLogitBoost w is a raced Logitboost committee (Frank et al.,
2002) with incremental learning and DecisionStump base classifiers, chunks of size
between 500 and 2000, validation set of size 1000 and log-likelihood pruning.
88. AdaBoostM1 DecisionStump w implements the same Adaboost.M1 method with
DecisionStump base classifiers.
andez-Delgado, Cernadas, Barro and Amorim
89. AdaBoostM1 J48 w is an Adaboost.M1 ensemble which combines J48 base classi-
90. C5.0 t creates a Boosting ensemble of C5.0 decision trees and rule models (func-
tion C5.0 in the hononymous package), with and without winnow (feature selection),
tuning the number of boosting trials in {1, 10, 20}.
91. MultiBoostAB DecisionStump w (Webb, 2000) is a MultiBoost ensemble, which
combines Adaboost and Wagging using DecisionStump base classifiers, 3 sub-committees,
10 training iterations and 100% of the weight mass to base training on. The same
options are used in the following MultiBoostAB ensembles.
92. MultiBoostAB DecisionTable w combines MultiBoost and DecisionTable, both
with the same options as above.
93. MultiBoostAB IBk w uses MultiBoostAB with IBk base classifiers (see classifier
94. MultiBoostAB J48 w trains an ensemble of J48 decision trees, using pruning con-
fidence C=0.25 and 2 training patterns per leaf.
95. MultiBoostAB LibSVM w uses LibSVM base classifiers with the optimal C and
Gaussian kernel spread selected by the svm C classifier (see classifier #48). We in-
cluded it for comparison with previous papers (Vanschoren et al., 2012), although a
strong classifier as LibSVM is in principle not recommended to use as base classifier.
96. MultiBoostAB Logistic w combines Logistic base classifiers (see classifier #86).
97. MultiBoostAB MultilayerPerceptron w uses MLP base classifiers with the same
options as MultilayerPerceptron w (which is another strong classifier).
98. MultiBoostAB NaiveBayes w uses NaiveBayes base classifiers.
99. MultiBoostAB OneR w uses OneR base classifiers.
100. MultiBoostAB PART w combines PART base classifiers.
101. MultiBoostAB RandomForest w combines RandomForest base classifiers. We
tried this classifier for comparison with previous papers (Vanschoren et al., 2012),
despite of RandomForest is itself an ensemble, so it seems not very useful to learn a
MultiBoostAB ensemble of RandomForest ensembles.
102. MultiBoostAB RandomTree w uses RandomTrees with the same options as above.
103. MultiBoostAB REPTree w uses REPTree base classifiers.
Bagging (BAG): 24 classifiers.
104. bagging R is a bagging (Breiman, 1996) ensemble of decision trees using the function
bagging (in the ipred package).
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
105. treebag t trains a bagging ensemble of classification trees using the caret interface
to function bagging in the ipred package.
106. ldaBag R creates a bagging ensemble of LDAs, using the function bag of the caret
package (instead of the function train) with option bagControl=ldaBag.
107. plsBag R is the previous one with bagControl=plsBag.
108. nbBag R creates a bagging of naive Bayes classifiers using the previous bag function
with bagControl=nbBag.
109. ctreeBag R uses the same function bag with bagControl=ctreeBag (conditional in-
ference tree base classifiers).
110. svmBag R trains a bagging of SVMs, with bagControl=svmBag.
111. nnetBag R learns a bagging of MLPs with bagControl=nnetBag.
112. MetaCost w (Domingos, 1999) is based on bagging but using cost-sensitive ZeroR
base classifiers and bags of the same size as the training set (the following bagging
ensembles use the same configuration). The diagonal of the cost matrix is null and
the remaining elements are one, so that each type of error is equally weighted.
113. Bagging DecisionStump w uses DecisionStump base classifiers with 10 bagging
114. Bagging DecisionTable w uses DecisionTable with BestFirst and forward search,
leave-one-out validation and accuracy maximization for the input selection.
115. Bagging HyperPipes w with HyperPipes base classifiers.
116. Bagging IBk w uses IBk base classifiers, which develop KNN classification tuning
K using cross-validation with linear neighbor search and Euclidean distance.
117. Bagging J48 w with J48 base classifiers.
118. Bagging LibSVM w, with Gaussian kernel for LibSVM and the same options as
the single LibSVM w classifier.
119. Bagging Logistic w, with unlimited iterations and log-likelihood ridge 108in the
Logistic base classifier.
120. Bagging LWL w uses LocallyWeightedLearning base classifiers (see classifier #148)
with linear weighted kernel shape and DecisionStump base classifiers.
121. Bagging MultilayerPerceptron w with the same configuration as the single Mul-
tilayerPerceptron w.
122. Bagging NaiveBayes w with NaiveBayes classifiers.
123. Bagging OneR w uses OneR base classifiers with at least 6 objects per bucket.
andez-Delgado, Cernadas, Barro and Amorim
124. Bagging PART w with at least 2 training patterns per leaf and pruning confidence
125. Bagging RandomForest w with forests of 500 trees, unlimited tree depth and
blog(#inputs + 1)cinputs.
126. Bagging RandomTree w with RandomTree base classifiers without backfitting, in-
vestigating blog2(#inputs)+1crandom inputs, with unlimited tree depth and 2 train-
ing patterns per leaf.
127. Bagging REPTree w use REPTree with 2 patterns per leaf, minimum class variance
0.001, 3-fold for reduced error pruning and unlimited tree depth.
Stacking (STC): 2 classifiers.
128. Stacking w is a stacking ensemble (Wolpert, 1992) using ZeroR as meta and base
129. StackingC w implements a more efficient stacking ensemble following (Seewald,
2002), with linear regression as meta-classifier.
Random Forests (RF): 8 classifiers.
130. rforest R creates a random forest (Breiman, 2001) ensemble, using the R function
randomForest in the randomForest package, with parameters ntree = 500 (number
of trees in the forest) and mtry=#inputs.
131. rf t creates a random forest using the caret interface to the function randomForest
in the randomForest package, with ntree = 500 and tuning the parameter mtry with
values 2:3:29.
132. RRF t learns a regularized random forest (Deng and Runger, 2012) using caret as
interface to the function RRF in the RRF package, with mtry=2 and tuning parameters
coefReg={0.01, 0.5, 1}and coefImp={0, 0.5, 1}.
133. cforest t is a random forest and bagging ensemble of conditional inference trees
(ctrees) aggregated by averaging observation weights extracted from each ctree. The
parameter mtry takes the values 2:2:8. It uses the caret package to access the party
134. parRF t uses a parallel implementation of random forest using the randomForest
package with mtry=2:2:8.
135. RRFglobal t creates a RRF using the hononymous package with parameters mtry=2
and coefReg=0.01:0.12:1.
136. RandomForest w implements a forest of RandomTree base classifiers with 500 trees,
using blog(#inputs + 1)cinputs and unlimited depth trees.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
137. RotationForest w (Rodr´ıguez et al., 2006) uses J48 as base classifier, principal com-
ponent analysis filter, groups of 3 inputs, pruning confidence C=0.25 and 2 patterns
per leaf.
Other ensembles (OEN): 11 classifiers.
138. RandomCommittee w is an ensemble of RandomTrees (each one built using a
different seed) whose output is the average of the base classifier outputs.
139. OrdinalClassClassifier w is an ensemble method designed for ordinal classification
problems (Frank and Hall, 2001) with J48 base classifiers, confidence threshold C=0.25
and 2 training patterns per leaf.
140. MultiScheme w selects a classifier among several ZeroR classifiers using cross vali-
dation on the training set.
141. MultiClassClassifier w solves multi-class problems with two-class Logistic w base
classifiers, combined with the One-Against-All approach, using multinomial logistic
142. CostSensitiveClassifier w combines ZeroR base classifiers on a training set where
each pattern is weighted depending on the cost assigned to each error type. Similarly
to MetaCost w (see classifier #112), all the error types are equally weighted.
143. Grading w is Grading ensemble (Seewald and Fuernkranz, 2001) with “graded” Ze-
roR base classifiers.
144. END w is an Ensemble of Nested Dichotomies (Frank and Kramer, 2004) which
classifies multi-class data sets with two-class J48 tree classifiers.
145. Decorate w learns an ensemble of fifteen J48 tree classifiers with high diversity
trained with specially constructed artificial training patterns (Melville and Mooney,
146. Vote w (Kittler et al., 1998) trains an ensemble of ZeroR base classifiers combined
using the average rule.
147. Dagging w (Ting and Witten, 1997) is an ensemble of SMO w (see classifier #57),
with the same configuration as the single SMO classifier, trained on 4 different folds
of the training data. The output is decided using the previous Vote w meta-classifier.
148. LWL w, Local Weighted Learning (Frank et al., 2003), is an ensemble of Decision-
Stump base classifiers. Each training pattern is weighted with a linear weighting
kernel, using the Euclidean distance for a linear search of the nearest neighbor.
Generalized Linear Models (GLM): 5 classifiers.
149. glm R (Dobson, 1990) uses the function glm in the stats package, with binomial
and Poisson families for two-class and multi-class problems respectively.
andez-Delgado, Cernadas, Barro and Amorim
150. glmnet R trains a GLM via penalized maximum likelihood, with Lasso or elasticnet
regularization parameter (Friedman et al., 2010) (function glmnet in the glmnet pack-
age). We use the binomial and multinomial distribution for two-class and multi-class
problems respectively.
151. mlm R (Multi-Log Linear Model) uses the function multinom in the nnet package,
fitting the multi-log model with MLP neural networks.
152. bayesglm t, Bayesian GLM (Gelman et al., 2009), with function bayesglm in the arm
package. It creates a GLM using Bayesian functions, an approximated expectation-
maximization method, and augmented regression to represent the prior probabilities.
153. glmStepAIC t performs model selection by Akaike information criterion (Venables
and Ripley, 2002) using the function stepAIC in the MASS package.
Nearest neighbor methods (NN): 5 classifiers.
154. knn Ruses the function knn in the class package, tuning the number of neighbors
with values 1:2:37 (13 values).
155. knn t uses function knn in the caret package with 10 number of neighbors in the
range 5:2:23.
156. NNge w is a NN classifier with non-nested generalized exemplars (Martin, 1995), us-
ing one folder for mutual information computation and 5 attempts for generalization.
157. IBk w (Aha et al., 1991) is a KNN classifier which tunes K using cross-validation
with linear neighbor search and Euclidean distance.
158. IB1 w is a simple 1-NN classifier.
Partial least squares and principal component regression (PLSR): 6
159. pls t uses the function mvr in the pls package to fit a PLSR (Martens, 1989) model
tuning the number of components from 1 to 10.
160. gpls R trains a generalized PLS (Ding and Gentleman, 2005) model using the function
gpls in the gpls package.
161. spls R uses the function spls in the spls package to fit a sparse partial least squares
(Chun and Keles, 2010) regression model tuning the parameters K and eta with values
{1, 2, 3}and {0.1, 0.5, 0.9}respectively.
162. simpls R fits a PLSR model using the SIMPLS (Jong, 1993) method, with the func-
tion plsr (in the pls package) and method=simpls.
163. kernelpls R (Dayal and MacGregor, 1997) uses the same function plsr with method
= kernelpls, with up to 8 principal components (always lower than #inputs1). This
method is faster when #patterns is much larger than #inputs.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
164. widekernelpls R fits a PLSR model with the function plsr and method = wideker-
nelpls, faster when #inputs is larger than #patterns.
Logistic and multinomial regression (LMR): 3 classifiers.
165. SimpleLogistic w learns linear logistic regression models (Landwehr et al., 2005) for
classification. The logistic models are fitted using LogitBoost with simple regression
functions as base classifiers.
166. Logistic w learns a multinomial logistic regression model (Cessie and Houwelingen,
1992) with a ridge estimator, using ridge in the log-likelihood R=108.
167. multinom t uses the function multinom in the nnet package, which trains a MLP
to learn a multinomial log-linear model. The parameter decay of the MLP is tuned
with 10 values between 0 and 0.1.
Multivariate adaptive regression splines (MARS): 2 classifiers.
168. mars R fits a MARS (Friedman, 1991) model using the function mars in the mda
169. gcvEarth t uses the function earth in the earth package. It builds an additive MARS
model without interaction terms using the fast MARS (Hastie et al., 2009) method.
Other Methods (OM): 10 classifiers.
170. pam t (nearest shrunken centroids) uses the function pamr in the pamr package (Tib-
shirani et al., 2002).
171. VFI w develops classification by voting feature intervals (Demiroz and Guvenir,
1997), with B=0.6 (exponential bias towards confident intervals).
172. HyperPipes w classifies each test pattern to the class which most contains the pat-
tern. Each class is defined by the bounds of each input in the patterns which belong
to that class.
173. FilteredClassifier w trains a J48 tree classifier on data filtered using the Discretize
filter, which discretizes numerical into nominal attributes.
174. CVParameterSelection w (Kohavi, 1995) selects the best parameters of classifier
ZeroR using 10-fold cross-validation.
175. ClassificationViaClustering w uses SimpleKmeans and EuclideanDistance to clus-
ter the data. Following the Weka documentation, the number of clusters is set to
176. AttributeSelectedClassifier w uses J48 trees to classify patterns reduced by at-
tribute selection. The CfsSubsetEval method (Hall, 1998) selects the best group of
attributes weighting their individual predictive ability and their degree of redundancy,
preferring groups with high correlation within classes and low inter-class correlation.
The BestFirst forward search method is used, stopping the search when five non-
improving nodes are found.
andez-Delgado, Cernadas, Barro and Amorim
177. ClassificationViaRegression w (Frank et al., 1998) binarizes each class and learns
its corresponding M5P tree/rule regression model (Quinlan, 1992), with at least 4
training patterns per leaf.
178. KStar w (Cleary and Trigg, 1995) is an instance-based classifier which uses entropy-
based similarity to assign a test pattern to the class of its nearest training patterns.
179. gaussprRadial t uses the function gausspr in the kernlab package, which trains a
Gaussian process-based classifier, with kernel= rbfdot and kernel spread (parameter
sigma) tuned with values {10i}7
3. Results and Discussion
In the experimental work we evaluate 179 classifiers over 121 data sets, giving 21,659 com-
binations classifier-data set. We use Weka v. 3.6.8, R v. 2.15.3 with caret v. 5.16-04,
Matlab v. 7.9.0 (R2009b) with Neural Network Toolbox v. 6.0.3, the C/C++ compiler v.
gcc/g++ 4.7.2 and fast artificial neural networks (FANN) library v. 2.2.0 on a computer
with Debian GNU/Linux v. 3.2.46-1 (64 bits). We found errors with some classifiers and
data sets caused by a variety of reasons. Some classifiers (lda R, qda t, QdaCov t, among
others) give errors in some data sets due to collinearity of data, singular covariance matrices,
and equal inputs for all the training patterns in some classes; rrlda R requires that all the
inputs must have different values in more than 50% of the training patterns; other errors
are caused by discrete inputs, classes with low populations (specially in data sets with many
classes), or too few classes (vbmpRadial requires 3 classes). Large data sets (miniboone and
connect-4) give some lack of memory errors, and few small data sets (trains and balloons)
give errors for some Weka classifiers requiring a minimum #patterns per class. Overall, we
found 449 errors, which represent 2.1% of the 21,659 cases. These error cases are excluded
from the average accuracy calculation for each classifier.
The validation methodology is the following. One training and one test set are generated
randomly (each with 50% of the available patterns), but imposing that each class has the
same number of training and test patterns (in order to have enough training and test
patterns of every class). This couple of sets is used only for parameter tuning (in those
classifiers which have tunable parameters), selecting the parameter values which provide
the best accuracy on the test set. The indexes of the training and test patterns (i.e., the
data partitioning) are given by the file conxuntos.dat for each data set, and are the same
for all the classifiers. Then, using the selected values for the tunable parameters, a 4-fold
cross validation is developed using the whole available data. The indexes of the training
and test patterns for each fold are the same for all the classifiers, and they are listed in
the file conxuntos kfold.dat for each data set. The test results is the average over the 4
test sets. However, for some data sets, which provide separate data for training and
testing (data sets annealing and audiology-std, among others), the classifier (with the
tuned parameter values) is trained and tested on the respective data sets. In this case,
the test result is calculated on the test set. We used this methodology in order to keep
low the computational cost of the experimental work. However, we are aware of that this
methodology may lead to poor bias and variance, and that the classifier results for each data
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Rank Acc. κClassifier Rank Acc. κClassifier
32.9 82.0 63.5 parRF t (RF) 67.3 77.7 55.6 pda t (DA)
33.1 82.3 63.6 rf t (RF) 67.6 78.7 55.2 elm m (NNET)
36.8 81.8 62.2 svm C (SVM) 67.6 77.8 54.2 SimpleLogistic w (LMR)
38.0 81.2 60.1 svmPoly t (SVM) 69.2 78.3 57.4 MAB J48 w (BST)
39.4 81.9 62.5 rforest R (RF) 69.8 78.8 56.7 BG REPTree w (BAG)
39.6 82.0 62.0 elm kernel m (NNET) 69.8 78.1 55.4 SMO w (SVM)
40.3 81.4 61.1 svmRadialCost t (SVM) 70.6 78.3 58.0 MLP w (NNET)
42.5 81.0 60.0 svmRadial t (SVM) 71.0 78.8 58.23 BG RandomTree w (BAG)
42.9 80.6 61.0 C5.0 t (BST) 71.0 77.1 55.1 mlm R (GLM)
44.1 79.4 60.5 avNNet t (NNET) 71.0 77.8 56.2 BG J48 w (BAG)
45.5 79.5 61.0 nnet t (NNET) 72.0 75.7 52.6 rbf t (NNET)
47.0 78.7 59.4 pcaNNet t (NNET) 72.1 77.1 54.8 fda R (DA)
47.1 80.8 53.0 BG LibSVM w (BAG) 72.4 77.0 54.7 lda R (DA)
47.3 80.3 62.0 mlp t (NNET) 72.4 79.1 55.6 svmlight C (NNET)
47.6 80.6 60.0 RotationForest w (RF) 72.6 78.4 57.9 AdaBoostM1 J48 w (BST)
50.1 80.9 61.6 RRF t (RF) 72.7 78.4 56.2 BG IBk w (BAG)
51.6 80.7 61.4 RRFglobal t (RF) 72.9 77.1 54.6 ldaBag R (BAG)
52.5 80.6 58.0 MAB LibSVM w (BST) 73.2 78.3 56.2 BG LWL w (BAG)
52.6 79.9 56.9 LibSVM w (SVM) 73.7 77.9 56.0 MAB REPTree w (BST)
57.6 79.1 59.3 adaboost R (BST) 74.0 77.4 52.6 RandomSubSpace w (DT)
58.5 79.7 57.2 pnn m (NNET) 74.4 76.9 54.2 lda2 t (DA)
58.9 78.5 54.7 cforest t (RF) 74.6 74.1 51.8 svmBag R (BAG)
59.9 79.7 42.6 dkp C (NNET) 74.6 77.5 55.2 LibLINEAR w (SVM)
60.4 80.1 55.8 gaussprRadial R (OM) 75.9 77.2 55.6 rbfDDA t (NNET)
60.5 80.0 57.4 RandomForest w (RF) 76.5 76.9 53.8 sda t (DA)
62.1 78.7 56.0 svmLinear t (SVM) 76.6 78.1 56.5 END w (OEN)
62.5 78.4 57.5 fda t (DA) 76.6 77.3 54.8 LogitBoost w (BST)
62.6 78.6 56.0 knn t (NN) 76.6 78.2 57.3 MAB RandomTree w (BST)
62.8 78.5 58.1 mlp C (NNET) 77.1 78.4 54.0 BG RandomForest w (BAG)
63.0 79.9 59.4 RandomCommittee w (OEN) 78.5 76.5 53.7 Logistic w (LMR)
63.4 78.7 58.4 Decorate w (OEN) 78.7 76.6 50.5 ctreeBag R (BAG)
63.6 76.9 56.0 mlpWeightDecay t (NNET) 79.0 76.8 53.5 BG Logistic w (BAG)
63.8 78.7 56.7 rda R (DA) 79.1 77.4 53.0 lvq t (NNET)
64.0 79.0 58.6 MAB MLP w (BST) 79.1 74.4 50.7 pls t (PLSR)
64.1 79.9 56.9 MAB RandomForest w (BST) 79.8 76.9 54.7 hdda R (DA)
65.0 79.0 56.8 knn R (NN) 80.6 75.9 53.3 MCC w (OEN)
65.2 77.9 56.2 multinom t (LMR) 80.9 76.9 54.5 mda R (DA)
65.5 77.4 56.6 gcvEarth t (MARS) 81.4 76.7 55.2 C5.0Rules t (RL)
65.5 77.8 55.7 glmnet R (GLM) 81.6 78.3 55.8 lssvmRadial t (SVM)
65.6 78.6 58.4 MAB PART w (BST) 81.7 75.6 50.9 JRip t (RL)
66.0 78.5 56.5 CVR w (OM) 82.0 76.1 53.3 MAB Logistic w (BST)
66.4 79.2 58.9 treebag t (BAG) 84.2 75.8 53.9 C5.0Tree t (DT)
66.6 78.2 56.8 BG PART w (BAG) 84.6 75.7 50.8 BG DecisionTable w (BAG)
66.7 75.5 55.2 mda t (DA) 84.9 76.5 53.4 NBTree w (DT)
Table 3: Friedman ranking, average accuracy and Cohen κ(both in %) for each classifier,
ordered by increasing Friedman ranking. Continued in the Table 4. BG = Bagging,
andez-Delgado, Cernadas, Barro and Amorim
Rank Acc. κClassifier Rank Acc. κClassifier
86.4 76.3 52.6 ASC w (OM) 110.4 71.6 46.5 BG NaiveBayes w (BAG)
87.2 77.1 54.2 KStar w (OM) 111.3 62.5 38.4 widekernelpls R (PLSR)
87.2 74.6 50.3 MAB DecisionTable w (BST) 111.9 63.3 43.7 mars R (MARS)
87.6 76.4 51.3 J48 t (DT) 111.9 62.2 39.6 simpls R (PLSR)
87.9 76.2 55.0 J48 w (DT) 112.6 70.1 38.0 sddaLDA R (DA)
88.0 76.0 51.7 PART t (DT) 113.1 61.0 38.2 kernelpls R (PLSR)
89.0 76.1 52.4 DTNB w (RL) 113.3 68.2 39.5 sparseLDA R (DA)
89.5 75.8 54.8 PART w (DT) 113.5 70.1 46.5 NBUpdateable w (BY)
90.2 76.6 48.5 RBFNetwork w (NNET) 113.5 70.7 39.9 stepLDA t (DA)
90.5 67.5 45.8 bagging R (BAG) 114.8 58.1 32.4 bayesglm t (GLM)
91.2 74.0 50.9 rpart t (DT) 115.8 70.6 46.4 QdaCov t (DA)
91.5 74.0 48.9 ctree t (DT) 116.0 69.5 39.6 stepQDA t (DA)
91.7 76.6 54.1 NNge w (NN) 118.3 67.5 34.3 sddaQDA R (DA)
92.4 72.8 48.5 ctree2 t (DT) 118.9 72.0 45.9 NaiveBayesSimple w (BY)
93.0 74.7 50.1 FilteredClassifier w (OM) 120.1 55.3 33.3 gpls R (PLSR)
93.1 74.8 51.4 JRip w (RL) 120.8 57.6 32.5 glmStepAIC t (GLM)
93.6 75.3 51.1 REPTree w (DT) 122.2 63.5 35.1 AdaBoostM1 w (BST)
93.6 74.7 52.3 rpart2 t (DT) 122.7 68.3 39.4 LWL w (OEN)
94.3 75.1 50.7 BayesNet w (BY) 126.1 50.8 30.5 glm R (GLM)
94.4 73.5 49.5 rpart R (DT) 126.2 65.7 44.7 dpp C (NNET)
94.5 76.4 54.5 IB1 w (NN) 129.6 62.3 31.8 MAB w (BST)
94.6 76.5 51.6 Ridor w (RL) 130.9 64.2 33.2 BG OneR w (BAG)
95.1 71.8 48.7 lvq R (NNET) 130.9 62.1 29.6 MAB IBk w (BST)
95.3 76.0 53.9 IBk w (NN) 132.1 63.3 36.2 OneR t (RL)
95.3 73.9 45.8 Dagging w (OEN) 133.2 64.2 34.3 MAB OneR w (BST)
96.0 74.4 50.7 qda t (DA) 133.4 63.3 33.3 OneR w (RL)
96.5 71.9 48.1 obliqueTree R (DT) 133.7 61.8 28.3 BG DecisionStump w (BAG)
97.0 68.9 42.0 plsBag R (BAG) 135.5 64.9 42.4 VFI w (OM)
97.2 73.9 52.1 OCC w (OEN) 136.6 60.4 27.7 ConjunctiveRule w (RL)
99.5 71.3 44.9 mlp m (NNET) 137.5 60.3 26.5 DecisionStump w (DT)
99.6 74.4 51.6 cascor C (NNET) 138.0 56.6 15.1 RILB w (BST)
99.8 75.3 52.7 bdk R (NNET) 138.6 60.3 26.1 BG HyperPipes w (BAG)
100.8 73.8 48.9 nbBag R (BAG) 143.3 53.2 17.9 spls R (PLSR)
101.6 73.6 49.3 naiveBayes R (BY) 143.8 57.8 24.3 HyperPipes w (OM)
103.2 72.2 44.5 slda t (DA) 145.8 53.9 15.3 BG MLP w (BAG)
103.6 72.8 41.3 pam t (OM) 154.0 49.3 3.2 Stacking w (STC)
104.5 62.6 33.1 nnetBag R (BAG) 154.0 49.3 3.2 Grading w (OEN)
105.5 72.1 46.7 DecisionTable w (RL) 154.0 49.3 3.2 CVPS w (OM)
106.2 72.7 48.0 MAB NaiveBayes w (BST) 154.1 49.3 3.2 StackingC w (STC)
106.6 59.3 71.7 logitboost R (BST) 154.5 49.2 7.6 MetaCost w (BAG)
106.8 68.1 41.5 PenalizedLDA R (DA) 154.6 49.2 2.7 ZeroR w (RL)
107.5 72.5 48.3 NaiveBayes w (BY) 154.6 49.2 2.7 MultiScheme w (OEN)
108.1 69.4 44.6 rbf m (NNET) 154.6 49.2 5.6 CSC w (OEN)
108.2 71.5 49.8 rrlda R (DA) 154.6 49.2 2.7 Vote w (OEN)
109.4 65.2 46.5 vbmpRadial t (BY) 157.4 52.1 25.13 CVC w (OM)
110.0 73.9 51.0 RandomTree w (DT)
Table 4: Continuation of Table 3. ASC = AttributeSelectedClassifier, BG = Bagging, CSC
= CostSensitiveClassifier, CVPS = CVParameterSelection, CVC = Classification-
ViaClustering, CVR = ClassificationViaRegression, MAB = MultiBoostAB, MCC
= MultiClassClassifier, MLP = MultilayerPerceptron, NBUpdeatable = Naive-
BayesUpdateable, OCC = OrdinalClassClassifier, RILB = RacedIncrementalLo-
set may vary with respect to previous papers in the literature due to resampling differences.
Although a leave-one-out validation might be more adequate (because it does not depend
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
0 20 40 60 80 100 120
Data set
Maximum accuracy / Majority class
10 20 30 40 50 60 70 80 90 100
#data set
% of the maximum accuracy
Figure 1: Left: Maximum accuracy (blue) and majority class (red), both in % ordered by
increasing %Maj. for each data set. Right: Histogram of the accuracy achieved
by parRF t (measured as percentage of the best accuracy for each data set).
on the data partitioning), specially for the small data sets, it would not be feasible for some
other larger data sets included in this study.
3.1 Average Accuracy and Friedman Ranking
Given its huge size (21,659 entries), the table with the complete results11 is not included
in the paper. Taking into account all the trials developed for parameter tuning in many
classifiers (number of tunable parameters and number of values used for tuning), the total
number of experiments is 241,637. The average accuracy for each classifier is calculated
excluding the data sets in which that classifier found errors (denoted as -- in the complete
table). The Figure 1 (left panel) plots, for each data set, the percentage of majority class
(see columns %Maj. in Tables 1 and 2) and the maximum accuracy achieved by some
classifier, ordered by increasing %Maj. Except for very few unbalanced data sets (with very
populated majority classes), the best accuracy is much higher than the %Maj. (which is
the accuracy achieved by classifier ZeroR w). The Friedman ranking (Sheskin, 2006) was
also computed to statistically sort the classifiers (this rank is increasing with the classifier
error) taking into account the whole data set collection. Given that this test requires the
same number of accuracy values for all the classifiers, in the error cases we use (only for
this test) the average accuracy for that data set over all the classifiers.
The Tables 3 and 4 report the Friedman ranking, the average accuracy and the Cohen
κ(Carletta, 1996), which excludes the probability of classifier success by chance, for the
179 classifiers, ordered following the Friedman ranking. The best classifier is parRF t
(parallel random forest implemented in R using the randomForest and caret
packages), with rank 32.9, average accuracy 82.0%(±16.3) and κ=63.5%(±30.6), followed
by rf t (random forest using the randomForest package and tuned with caret),
with rank 33.1 and the highest accuracy 82.3%(±15.3) and κ=63.6(±30.0). This result is
11. See
andez-Delgado, Cernadas, Barro and Amorim
0 10 20 30 40 50 60 70 80 90 100
% of the maximum accuracy
% of data sets
20 40 60 80 100 120
Data set
Accuracy (%)
Figure 2: Left: for each % of the maximum accuracy in the horizontal axis, the vertical
axis shows the percentage of data sets for which parRF t overcomes that % of the
maximum accuracy. Right: Accuracy (in %) achieved by parRF t (in red) and
maximum accuracy (in blue) for each data set (ordered by increasing maximum
somehow surprising, because Random Forest is an old method, but it works better than
other newer classifiers. The high deviations in accuracies and κare expected, due to the
large amount and variability of data sets. Since parRF t is a parallel version of rf t, us-
ing different random seeds, the difference between both can be considered not significant:
parRF t achieves better Friedman ranking, while rf t achieves better accuracy and κ. Simi-
lar situations arise with other couples of classifiers within the same family, which are slightly
different versions of the same classifier or versions with/without parameter tuning (svmRa-
dial t and svmRadialCost t, lda R and lda2 t, among others), with similar results, being
the difference between them caused by noise, random initializations, etc. The parRF t is
the best classifier in 12 out of 121 data sets, and its average accuracy is 4.9% below the
maximum average accuracy (i.e., the maximum accuracy over all the classifiers for each
data set, averaged over all the data sets), which is 86.9%. It is very significant (and it can
not be casual) that, among so many classifiers (179), the two bests ones (parRF t and rf t,
according both to average accuracy and Friedman rank) are random forests implemented
with the randomForest package and tuned with caret: this fact shows a clear superiority
with respect to the remaining classifiers. It is also interesting that an “old” classifier as RF
works better than many other, more recent, approaches. The Figure 1 (right panel) shows
that for the majority of the data sets (specifically for 102 out of 121, which represents the
84.3%), the parRF t achieves more than 90% of the maximum accuracy, being very near
to the best accuracy for almost all the data sets. The Figure 2 (left panel) plots, for each
% of the maximum accuracy in the horizontal axis, the % of data sets for which parRF
overcomes that percentage: for the 93% (resp. for 84.3%) of the data sets parRF achieves
more than 80% (resp. 90%) of the maximum accuracy. In this figure, the area under
curve (AUC) of the three bests classifiers (parRF t, rf t and svm C) are 0.9349, 0.9382 and
0.9312 respectively, being rf t slightly better than parRF t (as the accuracy in Table 3) and
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
svm C slightly worse. As we commented in the introduction, given the large number of
classifiers used in this work, it is reasonable to estimate the maximum attainable accuracy
for a data set as the maximum accuracy achieved by some classifier. Therefore, although
the No-Free-Lunch theorem states that no classifier can be always the best, in the practice,
parRF t is very near to the best attainable accuracy for almost all the data sets. Specifi-
cally, the Figure 2 (right panel) shows that parRF is very near to the maximum accuracy
for almost all the data sets, excepting three data sets: #41 (image-segmentation, 33.6%),
#70 (audiology-std, 13.0%) and #114 (balloons, 66.7%).
The third best classifier is svm C (LibSVM with Gaussian kernel), with rank (36.8, two
points above parRT t) and average accuracy 81.8%(±16.2). The following classifiers are:
svmPoly t (SVM with polynomial kernel, rank 38.0), rforest R (random forest without mtry
tuning, rank 39.4), elm kernel m (extreme learning machine, rank 39.6), svmRadialCost t
(40.3), svmRadial t (42.5), C5.0 t (42.9) and avNNet t (44.1). It may not be a casuality the
presence of three RF and two SVM among the five best classifiers, identifying both classifier
families as the best ones. Besides, there are also two neural networks and one boosting
ensemble (C5.0 t) among the top-10. The Figure 3 shows the 25 classifiers with the lowest
Friedman ranks (upper panel) and the classifiers with the highest average accuracies (lower
panel): parRF t and rf t have ranks clearly lower than svm C and the following classifiers.
In fact, the highest increment (3.7) between two classifier ranks is between rf t and svm C,
which shows that parRF t and rf t are clearly better than the remaining classifiers in the
plot. Besides, rf t, parRF, svm C, rforest R and elm kernel m have higher accuracies than
the others (the largest accuracy reduction, 0.37, is between svm C and svmRadialCost t).
Our proposal dkp C is in the 23th (resp. 21th) position according to the Friedman ranking
(resp. to the accuracy, 79.7%), but this apparently good result is somehow obscured by the
low value of κ(42.6%). It is caused by some data sets where dkp C assigns all the patterns
to the most populated class: for these data sets, κ= 0, which reduces the average κover
all the data sets.
We developed paired T-tests comparing the accuracies of parRF t and the following
9 classifiers in Table 3 (the null hypothesis is that the two accuracies compared are not
significantly different, so that, within a tolerance α= 0.05, when p < 0.05 parRF t is
significantly better than the other classifier. The Figure 4 (left panel) plots the T-statistic,
95%-limits and p-values, showing that parRF t is only significantly better (high T-statistic,
p < 0.05) than with C5.0 t and avNNet t. Although parRF t is better than svm C in 56
of 121 data sets, worse than svm C in 55 sets, and equal in 10 sets, the Figure 4 (right
panel) compares their percentages of the maximum accuracy for each data set (ordered
by increasing percentages): for the majority of the data sets they are almost 100% (i.e.,
parRF t and svm C are near to the maximum accuracy). Besides, svm C is never much
better than parRF t: when svm C outperforms parRF t, the difference is small, but when
parRF t outperforms svm C, the difference is higher (data sets 1-20). In fact, calculating
for each data set the difference between the accuracies of parRF t and svm C, the sum of
positive differences (parRF is better) is 193.8, while the negative ones (svm C better) sum
All the classifiers of the random forest and SVM families are included among the 25
best classifiers, with accuracies above 79% (while the best is 82.3%), which identify both
families as the best ones. Other classifiers included among the top-20, not belonging to RF
andez-Delgado, Cernadas, Barro and Amorim
parRF−t rf−t
Friedman rank
Accuracy (%)
Figure 3: Friedman rank (upper panel, increasing order) and average accuracies (lower
panel, decreasing order) for the 25 best classifiers.
and SVM families, are nnet t (MLP network, rank 45.5), pcaNNet t (MLP + PCA net-
work, rank 47.0), Bagging LibSVM w (ensemble of Gaussian LibSVMs, rank 47.1), mlp t
(RSNNS MLP with tunable network size, rank 38.0), MultiBoostAB LibSVM w (Multi-
BoostAB ensemble of Gaussian LibSVMs, rank 52.5) and adaboost R (Adaboost.M1 en-
semble of decision trees, rank 57.6). Beyond the 20th position are pnn m (Probabilistic
Neural Network with tunable Gaussian spread, rank 58.5), and our proposal dkp C (rank
59.9). Besides, note that 12 classifiers in the top-20 use caret, which might be due to the
automatic parameter tuning (only rforest R and adaboost R have no tunable parameter).
We must emphasize that, since parameter tuning and testing use different data sets, the fi-
nal result can not be biased by parameter optimization, because the set of parameter values
selected in the tuning stage is not necessarily the best on the test set. In some cases, the
tuning is not relevant: for C5.0 t the differences among the performances using different
parameter values are low, so it would work similarly without parameter tuning.
OpenML Vanschoren et al. (2012) uses only 86 data sets and 93 classifiers, while our
work is much wider (121 and 179, respectively), including Weka classifiers in a later version
(3.6.9), for example openML uses Bagging, while we use Bagging version 6502. Be-
sides, as we commented above, we do not use 9 of 93 classifiers included in the previous refer-
ence. The results in Figure 17 of that paper rank Bagging-NBayesTree as the best classifier,
followed by Bagging-PART, SVM-Polynomial, MultilayerPerceptron, Boosting-NBayesTree,
RandomForest, Boosting-PART, Bagging-C45, Boosting-C45 and SVM-RBF. However, in
our results the best Weka classifiers (in the top-20) are Baggging LibSVM w, RotationFor-
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
−1 0 1 2 3 4 5
T−statistic/confidence interval/p−value
0.457 0.128
20 40 60 80 100 120
#data set
% of the maximum accuracy
Figure 4: Left panel: T-statistics (point), confidence intervals and p-values (above upper
interval limits) of the T-tests comparing parRF T and the remaining 9 best clas-
sifiers. Right panel: Percentage of the maximum accuracy achieved by parRF t
(blue) and svm C (red) for the 121 data sets (ordered by increasing percentage)
est w, MultiBoostAB LibSVM w and LibSVM w, i.e., a Random Forest, a SVM and two
ensembles of SVMs. This is expected, because it is known that ensembles of strong classi-
fiers do not work better than the single classifier. Therefore, Bagging and MultiBoostAB of
LibSVM do not work better than LibSVM w, although the three are worse than svm C (the
same Gaussian LibSVM in C) and the caret SVM versions (svmPoly t, svmRadialCost t
and svmRadial t). Besides, similarly to openML, in our work svmPoly t (polynomial ker-
nel) is near to svm C (Gaussian kernel). However, in our results Bagging NaiveBayes w
works very bad (rank 110.4, Table 4), while other Baggging ensembles are better: Bag-
ging PART w (66.6), MultilayerPerceptron w (70.6), MultiBoostAB NaiveBayes w (equiv-
alent to Boosting-NaiveBayes in openML, rank 106.2) and MultiBoostAB PART w (65.6).
Therefore, in our experiments the bagging and multiBoostAB ensembles (except of Lib-
SVM w) do not work well. We use the same configurations for bagging (10 bagging iter-
ations, 100% of the training set for bag size, changing only the base learner) and Multi-
BoostAB (3 sub-committees, 10 boost iterations and 100% of build mass used to build
classifiers) as openML, so these bad results can not be caused by improper configuration
(or parameter tuning) of the ensemble or base classifier. Therefore, they might be caused
by the larger number of data sets, or by the inclusion in our collection of other classifiers
and implementations (in R, caret, C and Matlab), with better accuracies, not considered
by OpenML.
andez-Delgado, Cernadas, Barro and Amorim
No. Classifier PAMA No. Classifier PAMA
1 elm kernel m 13.2 11 mlp t 5.0
2 svm C 10.7 12 pnn m 5.0
3 parRF t 9.9 13 dkp C 5.0
4 C5.0 t 9.1 14 LibSVM w 5.0
5 adaboost R 9.1 15 svmPoly t 5.0
6 rforest R 8.3 16 treebag t 5.0
7 nnet t 6.6 17 RRFglobal t 5.0
8 svmRadialCost t 6.6 18 svmlight C 5.0
9 rf t 5.8 19 Bagging RandomForest w 4.1
10 RRF t 5.8 20 mda t 4.1
No. Classifier P95 No. Classifier P95
1 parRF t 71.1 11 elm kernel m 60.3
2 svm C 70.2 12 MAB-LibSVM w 60.3
3 rf t 68.6 13 RandomForest w 57.0
4 rforest R 65.3 14 RRF t 56.2
5 Bagging-LibSVM w 63.6 15 pcaNNet t 55.4
6 svmRadialCost t 63.6 16 RotationForest w 54.5
7 svmRadial t 62.8 17 avNNet t 53.7
8 svmPoly t 62.8 18 nnet t 53.7
9 LibSVM w 62.0 19 RRFglobal t 53.7
10 C5.0 t 61.2 20 mlp t 52.1
No. Classifier PMA No. Classifier PMA
1 parRF t 94.1 11 RandomCommittee w 91.4
2 rf t 93.6 12 nnet t 91.3
3 rforest R 93.3 13 avNNet t 91.1
4 C5.0 t 92.5 14 RRFglobal t 91.0
5 RotationForest w 92.5 15 knn R 90.5
6 svm C 92.3 16 Bagging-LibSVM w 90.5
7 mlp t 92.1 17 Bagging REPTree w 90.4
8 LibSVM w 91.7 18 MAB MLP w 90.4
9 RRF t 91.4 19 elm m 90.3
10 dkp C 91.4 20 rda R 90.3
Table 5: Up: list of the 20 classifiers with the highest Probabilities of Achieving the Max-
imum Accuracies (PAMA, in %). Middle: List of the 20 classifiers with the
highest probabilities of achieving 95% (P95) of the maximum accuracy over all
the data sets. Down: Classifiers sorted by its Percentage of the Maximum Ac-
curacy (PMA) for each data set, averaged over all the data sets. MAB means
3.2 Probability of Achieving the Best Accuracy
One of the objectives of this paper (Section 1) is to estimate, for each classifier, the Prob-
ability of Achieving the Maximum Accuracy (PAMA) for a given data set, as the
number of data sets for which it achieves the highest accuracy, divided by the number of
data sets. The Table 5 (upper part) shows the 20 classifiers with the highest values for
these probabilities (in %), being elm kernel m the best (for 13.2% of the data sets) followed
by svm C (10.7%) and parRF (9.9%). These values are very far from 100%, which confirms
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
that no classifier is the best for most data sets (following the No-Free-Lunch theorem). The
C5.0 t and adaboost R have about 9%. The remaining classifiers are about 4-8%, so that
many classifiers are the best for only few data sets. There are 5 classifiers of family RF, 5
SVM, 5 NNET and 4 ensembles among the 20 classifiers with the highest probabilities of
being the best. Our proposal dkp C achieves the 13th position.
The PAMA does not take into account that a classifier may be very near from the
best accuracy without being the best one. Therefore, an alternative, more significant,
measure is the probability of achieving more than 95% of the maximum accuracy
(P95) (middle part of Table 5 for the best 20 values). This probability (in %), for a given
classifier, is estimated dividing the number of data sets in which it achieves 95% or more of
the maximum accuracy (achieved by any other classifier on that data set), by the number of
data sets. The ten classifiers with the highest P95 are almost the same as in the Friedman
rank, with a different order. In this table, ParRF t achieves more than 95% of the maximum
accuracy for 71.1% of the data sets (again far from the 100%), followed by svm C (70.2%)
and rf t (68.6). The other classifiers have P95 below 65%. The low P95 of elm kernel w
(60.3%, 11th position), being the best for a highest number of data sets, shows a behavior
less stable than rf t, parRF t and svm C, because its accuracy in the other data sets is
lower in average.
Another interesting measurement is the Percentage of the Maximum Accuracy
(PMA) achieved by each classifier, averaged over the whole collection of data sets (the
20 first are shown in the lower part of the Table 5). Again, parRF t is the best achieving
94.1%(±11.3) of the maximum accuracy, followed by other two Random Forests: rf t and
rforest R (93.6% and 93.3% respectively). The svm C is in the 6th position, with PMA
92.3%(±15.9). Note that six out of eight Random Forest classifiers are in the top-20. The
PMA values are high, very near to, but below, the threshold of 95% used in the middle part
of Table 5. This explains the low values of P95: the bests classifiers have PMA about 94%,
so their probability of achieving 95% or more of the maximum accuracy is low (about 70%).
Setting the threshold in 90% of the maximum accuracies, the corresponding probabilities
would be much higher. The elm kernel m is not included in this table: this confirms its
unstable behavior, because in average it does not achieve PAM above 90.3% (even elm m,
without kernels, has better PMA). The mlp t (92.2%) has also a good value. The dkp C is
the 10th position, achieving in average the 91.4%, only 2.7 below the best. The 20 classifiers
are in a narrow margin between 90%-94% of the maximum accuracy, so that there are many
classifiers which a high percentage of the maximum accuracy. The Figure 5 shows that the
three Random Forests (parRT t, rf t and rforest R ) achieve PMAs clearly higher than the
remaining classifiers (including svm C), being the greatest gap (0.8) between rforest R and
C5.0 t.
3.3 Discussion by Classifier Family
The Figure 6 compares the classifier families showing in the upper panel the error bars with
the mean (blue square), minimum and maximum values of the Friedman ranks for each
family. The lower panel shows the minimum rank (corresponding to the best classifier) for
each family, by ascending order. The family RF has the lowest minimum rank (32.9) and
mean (46.7), and also a narrow interval (up to 60.5), which means that all the RF classifiers
andez-Delgado, Cernadas, Barro and Amorim
% of the maximum accuracy
Figure 5: Twenty classifiers with the highest percentages of the maximum accuracy. MAB
means MultiBoostAB, BG means Bagging.
work very well. The SVM has the following minimum (36.8), but the mean is much higher
(55.4), and the interval is also much wider (up to 81.6). The third best type is NNET, whose
minimum and mean rank are 39.6 (elm kernel m) and 73.8 respectively. The DTs have
the following minimum (42.9), followed by BAG (47.1), BST (52.5), OM (other methods,
specifically gaussprRadial, 60.4), DA (62.5), NN (62.6), OEN (other ensembles, specifically
RandomCommittee w, 63.0), LMR (65.2), MARS and GLM (65.5), PLSR (79.1), RL (81.4),
BY (94.3) and STC (154.0). We can make three family groups in the lower panel of Figure 6:
a) the best ones (RF, SVM, NNET, DT, BAG and BST), with the lowest ranks (about 30-
50); b) the intermediate families (OM, DA, NN, OEN, LMR, MARS and GLM), about
60-70; and c) the worst families (PLSR, RL, BY and STC), with ranks above 80.
Now, we discuss the results for each classifier family (see Tables 6 and 7). The discrim-
inant analysis (DA) classifiers work relatively well, being fda t the best one, followed
by rda R, mda t and pda t. The lda R works better than the caret version lda2 t (74.4),
which however tunes of the number of retained components. In other DA classifiers (fda
and mda) the parameter tuning developed in the caret versions allows to achieve better
accuracies than their R counterparts (without tuning). It is surprising that sophisticated
versions of LDA are worse: slda t, PenalizedLDA t, rrlda R, sddaLDA R, sparseLDA R and
stepLDA t. Finally, the QDA classifiers are very bad, achieving again the classical qda t the
best results compared to more advanced versions (QdaCov t, stepQDA t and sddaQDA R).
The Bayesian methods (BY) are clearly worse than DA, and they are not competitive
at all to the globally best classifiers, achieving the best (BayesNet w) a high rank (94.3).
Among the neural networks (NNET), the elm kernel m is the best one, followed by
several caret MLP implementations (avNNet t, nnet t, pcaNNet t and mlp t), included in
the top-20, better than other MLP implementations: mlp C (LibFANN), MultilayerPercep-
tron w (Weka) and mlp m (Matlab). The good result of avNNet (an ensemble of 4 small
MLPs with up to 9 hidden neurons whose weights are randomly initialized), compared to
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Classifier family
Friedman rank
Classifier family
Minimum Friedman rank
Figure 6: Friedman rank interval for the classifiers of each family (upper panel) and mini-
mum rank (by ascending order) for each family (lower panel).
greater MLPs, as mlp C and mlp m (up to 30 hidden neurons), is due to its ensemble na-
ture, because mlpWeightDecay t also has up to 9 hidden neurons, with worse results. The
rule used for size selection by MultilayerPerceptron w (#inputs + #classes)/2 does not
achieve good results. The pnn m (probabilistic neural network) and our proposal dkp C
(direct kernel perceptron) are very near to the top-20. The bad results of elm m (67.6)
are surprising taking into account the good behavior of the Gaussian elm kernel w. Simi-
larly, the LVQ versions are not good: lvq t, which tunes the size and k, works much better
than lvq R, being bdk R (99.8) the worst one. The cascor C (cascade correlation), which
uses LibFANN, is also worse (99.6) than the best MLP version (avNNet t). Finally, the
RBF networks are also bad, although the caret versions outperform the Weka and Matlab
versions. The dpp C is not competitive at all with the other networks.
The svm C, with Gaussian kernel using LibSVM is the best Support vector machine
(SVM), followed by the caret versions svmPoly t (polynomial kernel), svmRadialCost t and
svmRadial t (Gaussian kernel), better than the Weka versions LibSVM w and SMO w and
that svmlight C. The linear kernel versions (svmLinear t and LibLINEAR w) are clearly
worse, and lssvmRadial t is the worst one. Overall, the ten SVM classifiers achieve very
good results, with ranks in the (relatively narrow) interval 36.8—72.4 (excluding linear
RandomSubSpace w is the best decision tree (DT), with a bad rank (74.0); both
J48 t and J48 w achieve similar results (the former runs the latter in the RWeka package
tuned with caret). The best Rule-based (RL) classifiers are C5.0Rules t and JRip t,
andez-Delgado, Cernadas, Barro and Amorim
Discriminant analysis (DA)
1 fda t 62.5 11 qda t 96.0
2 rda R 63.8 12 slda t 103.2
3 mda t 66.7 13 PenalizedLDA t 106.8
4 pda t 67.3 14 rrlda R 108.2
5 fda R 72.1 15 sddaLDA R 112.6
6 lda R 72.4 16 sparseLDA R 113.3
7 lda2 t 74.4 17 stepLDA t 113.5
8 sda t 76.5 18 QdaCov t 115.8
9 hdda R 79.8 19 stepQDA t 116.0
10 mda R 80.9 20 sddaQDA R 118.3
Bayesian methods (BY)
1 BayesNet w 94.3 4 vbmpRadial t 109.4
2 naiveBayes R 101.6 5 NBUpdateable w 113.5
3 NaiveBayes w 107.5
Neural networks (NNET)
1 elm kernel m 39.6 12 rbf t 72.0
2 avNNet t 44.1 13 rbfDDA t 75.9
3 nnet t 45.5 14 lvq t 79.1
4 pcaNNet t 47.0 15 RBFNetwork w 90.2
5 mlp t 47.3 16 lvq R 95.1
6 pnn m 58.5 17 mlp m 99.5
7 dkp C 59.9 18 cascor C 99.6
8 mlp C 62.8 19 bdk R 99.8
9 mlpWeightDecay 63.6 20 rbf m 108.1
10 elm m 67.6 21 dpp C 126.2
11 MultilayerPerceptron w 70.6
Support vector machines (SVM)
1 svm C 36.8 6 svmLinear t 62.1
2 svmPoly t 38.0 7 SMO w 62.8
3 svmRadialCost t 40.3 8 svmlight C 72.4
4 svmRadial t 42.5 9 LibLINEAR w 74.6
5 LibSVM w 52.6 19 lssvmRadial t 81.6
Table 6: Friedman ranks of the classifiers in each family (continued in Table 7).
slightly worse than the best DT. The difference between JRip t and JRip w suggests that
the tuning of the number of optimization runs developed in the caret version, but not with
Weka, is important. ZeroR w is among the worst ones, because it only predicts the same
mean class for every test pattern: we included it to define the “zero-level” for the accuracy
(49.2%, there is no classifier with lower accuracy).
Among the boosting (BST) ensembles, C5.0 t is the best (position 9), followed by
MultiBoostAB LibSVM (position 18), adaboost R (position 19) and other MultiBoostAB
ensembles with strong base classifiers (MultilayerPerceptron, RandomForest, PART and
J48), while the ones with weak classifiers (OneR, IBk, DecisionStump, NaiveBayes, among
others) are worse. The Figure 7 (upper panel, only Weka ensembles and base classifiers
are plotted) shows that MultiBoostAB ensembles achieves much lower ranks than their
corresponding base classifiers, excepting LibSVM, RandomForest and Logistic, where both
are similar, and IBk, where the base classifier works much better. The same happens with
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Decision trees (DT)
1 RandomSubSpace w 74.0 9 ctree2 t 92.4
2 C5.0Tree t 84.2 10 REPTree w 93.6
3 11 rpart2 t 93.6
4 NBTree w 84.6 12 rpart R 94.4
5 J48 t 87.6 13 obliqueTree R 96.5
6 J48 w 87.9 14 RandomTree w 110.0
7 rpart t 91.2 15 DecisionStump w 137.5
8 ctree t 91.5
Rule-based classifiers (RL)
1 C5.0Rules t 81.4 7 Ridor w 94.6
2 JRip t 81.7 8 DecisionTable w 105.5
3 PART t 88.0 9 OneR t 132.1
4 DTNB w 89.0 10 OneR w 133.4
5 PART w 89.5 11 ConjunctiveRule w 136.6
6 JRip w 93.1 12 ZeroR w 154.6
Boosting (BST)
1 C5.0 t 42.9 11 MAB RandomTree w 76.6
2 MAB LibSVM w 52.5 12 MAB Logistic w 82.0
3 adaboost R 57.9 13 MAB DecisionTable w 87.2
4 MAB MultilayerPerceptron w 64.0 14 MAB NaiveBayes w 106.2
5 MAB RandomForest w 64.1 15 logitboost R 106.6
6 MAB PART w 65.6 16 AdaBoostM1 DecisionStump w 122.2
7 MAB J48 w 69.2 17 MAB DecisionStump w 129.6
8 AdaBoostM1 J48 w 72.6 18 MAB IBk w 130.9
9 MAB REPTree w 73.7 19 MAB OneR w 133.2
10 LogitBoost w 76.6 20 RILB w 138.0
Bagging (BAG)
1 BG LibSVM w 47.1 13 BG Logistic w 79.0
2 treebag t 66.4 14 BG DecisionTable w 84.6
3 BG PART w 66.6 15 bagging R 90.5
4 Bagging REPTree w 69.8 16 plsBag R 97.0
5 BG RandomTree w 71.0 17 nbBag R 100.8
6 BG J48 w 71.0 18 nnetBag R 104.5
7 BG IBk w 72.7 19 BG NaiveBayes w 110.4
8 ldaBag R 72.9 20 BG OneR w 130.9
9 BG LWL w 73.2 21 BG DecisionStump w 133.7
10 svmBag R 74.6 22 BG HyperPipes w 143.8
11 BG RandomForest w 77.1 23 BG MLP w 145.8
12 ctreeBag R 78.7 24 MetaCost w 154.5
Table 7: Continuation of Table 6. MAB means MultiBoostAB. RILB means RacedIncre-
mentalLogitBoost. BG means Bagging. Continued in Table 8.
AdaBoostM1 (J48 much better than DecisionStump). The adaboost R (AdaboostM1 with
classification trees) works very well (included in the top-20), while AdaBoostM1 J48 w
and AdaBoostM1 DecisionStump w work much worse: this big difference might be in the
AdaboostM1 implementation or in the base classifiers. There is also difference between
LogitBoost w and logitboost R, despite of using the same base classifier (DecisionStump):
andez-Delgado, Cernadas, Barro and Amorim
Friedman rank
Friedman rank
Figure 7: Upper panel: Friedman rank (ordered increasingly) of each Weka MultiBoostAB
ensemble (blue squares) and its corresponding Weka base classifier (red circles).
Lower panel: the same for Weka bagging ensembles (blue squares) and base
classifiers (red circles).
the Weka implementation is clearly better. The RacedIncrementalLogitBoost w is the worst
one, despite of being a committee of LogitBoost.
The best bagging (BG) ensemble is also the Baggging LibSVM w (included in the
top-20), although the svmBag R is not so good, revealing big differences between imple-
mentations. The Figure 7 (lower panel) compares 15 Bagging ensembles to their respective
base classifiers (both implemented in Weka), being the ensembles better except for Random-
Forest, NaiveBayes and MultilayerPerceptron. This means that RandomForest works bet-
ter than in MultiBoostAB and Baggging ensembles. The remaining Bagging classifiers are
not good: The ldaBag R, ctreeBag R, nbBag R and nnetBag R work also bad, similarly to
their Weka correspondents (Bagging NaiveBayes w and Baggging MultilayerPerceptron w).
Both stacking classifiers Stacking w and StackingC w work equally bad. The eight ran-
dom forest classifiers are included among the 25 best classifiers having all of them low
ranks, so this is clearly the best family of classifiers. Although one could think that there
is a redundancy in RF models that might over-emphasize some results (parRF t and rf t
are very similar classifiers), we must note that RRF t (Regularized RF), RRFglobal t (for
which the caret documentation does not give differences with RRF t, except in the tunable
parameters) and cforest t are different classifiers. Besides, the Weka RF implementations
(RandomForest w and RotationForest w) are also among the 25 best classifiers, confirming
that good positions of RF classifiers are not due to redundancy. Finally, none of the other
ensembles (OEN) achieves good results, being RandomCommittee w and Decorate w the
bests, but many of them are at the end of the list (rank 154.0).
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Stacking (STC)
1 Stacking w 154.0 2 StackingC w 154.1
Random forests (RF)
1 parRF t 32.9 5 RRF t 50.1
2 rf t 33.1 6 RRFglobal t 51.6
3 rforest R 39.4 7 cforest t 58.9
4 RotationForest w 47.6 8 RandomForest w 60.5
Other ensembles (OEN)
1 RandomCommittee w 63.0 7 LWL w 122.7
2 Decorate w 63.4 8 Grading w 154.0
3 END w 76.6 9 MultiScheme w 154.6
4 MultiClassClassifier w 80.6 10 CostSensitiveClassifier w 154.6
5 Dagging w 95.3 11 Vote w 154.6
6 OrdinalClassClassifier w 97.2
Generalized linear models (GLM)
1 gmlnet R 65.5 4 glmStepAIC t 120.8
2 mlm R 71.0 5 glm R 126.1
3 bayesglm t 114.8
Nearest neighbors (NN)
1 knn t 62.6 4 IBk w 94.5
2 knn R 65.0 5 IB1 w 95.3
3 NNge w 91.7
Partial least squares and principal component regression (PLSR)
1 pls t 79.1 4 kernelpls R 113.1
2 widekernelpls R 111.3 5 gpls R 120.1
3 simpls R 111.9 6 spls R 143.3
Logistic and multinomial regression(LMR)
1 multinom t 65.2 3 Logistic w 78.5
2 SimpleLogistic w 67.6
Multivariate adaptive regression splines (MARS)
1 gcvEarth t 65.5 2 mars R 111.9
Other methods (OM)
1 gaussprRadial 60.4 6 pam t 103.6
2 ClassificationViaRegression w 66.0 7 VFI w 135.5
3 AttributeSelectedClassifier w 86.4 8 HyperPipes w 143.8
4 KStar w 87.2 9 CVParameterSelection 154.0
5 FilteredClassifier w 93.0 10 ClassificationViaClustering w 157.4
Table 8: Continuation of Tables 6 and 7.
The GLM classifiers are divided in two groups: gmlnet R and mlm R, with relatively
good ranks (60-70), and the others, with much worse results. Something similar happens
with NN, where the R and caret versions (knn t and knn R) are about 70, while the Weka
variants NNge w, IBk w and IB1 w are much worse (about 90). With respect to the PLSR
classifiers, the simplest one (pls t) is the best, while the remaining, more sophisticated,
versions are much worse. The three LMR classifiers achieve ranks about 65-75, being
multinom t the best one. The original MARS classifier (mars R) is very bad, while the
fast MARS version (gcvEarth t) works much better. Finally, only the gaussprRadial R and
andez-Delgado, Cernadas, Barro and Amorim
ClassificationViaRegression w achieve good results among the Other methods, while the
remaining ones have ranks about 90 (AttributeSelectedClassifier w, KStar w and Filtered-
Classifier w), and more, being some of the worse classifiers in the collection (Classification-
ViaClustering w).
Rank Classifier Acc. (%) Rank Classifier Acc (%)
36.2 avNNet t 83.0 50.0 mlp t 82.2
39.9 svmPoly t 79.9 51.4 elm kernel m 77.5
41.0 pcaNNet t 82.9 54.1 RotationForest w 82.0
42.2 svmRadialCost t 80.0 54.9 rforest R 80.9
44.2 parRF t 82.6 57.6 mlpWeightDecay t 79.7
44.7 rf t 81.2 57.7 svmBag R 78.8
47.1 C5.0 t 82.0 59.7 fda t 81.0
47.2 svm C 79.0 60.8 cforest t 74.7
47.5 nnet t 82.1 61.5 Bagging LibSVM w 77.9
48.0 svmRadial t 79.4 62.9 knn t 80.4
No. Classifier P95 No. Classifier P95
1 svmRadialCost t 78.2 11 MultiBoostAB LibSVM w 65.5
2 svm C 74.5 12 pcaNNet t 63.6
3 svmPoly t 74.5 13 svmBag R 63.6
4 svmRadial t 72.7 14 elm kernel m 61.8
5 Bagging LibSVM w 70.9 15 nnet t 61.8
6 avNNet t 69.1 16 RotationForest w 61.8
7 parRF t 69.1 17 fda t 60.0
8 LibSVM w 67.3 18 mlp t 60.0
9 C5.0 t 67.3 19 MultiBoostAB REPTree w 58.2
10 rf t 67.3 20 RandomForest w 58.2
No. Classifier PMA No. Classifier PMA
1 avNNet t 95.0 11 pda t 92.8
2 pcaNNet t 94.9 12 mlm R 92.7
3 parRF t 94.3 13 fda t 92.7
4 nnet t 94.1 14 MAB MLP w 92.7
5 mlp t 94.1 15 bayesglm t 92.6
6 C5.0 t 93.8 16 simpls R 92.5
7 RotationForest w 93.7 17 rforest R 92.5
8 glmnet R 93.5 18 MultiBoostAB PART w 92.5
9 rda R 93.2 19 fda R 92.3
10 rf t 92.8 20 nnetBag R 92.2
Table 9: Results for two class data sets. Up: Friedman rank and average accuracies
for the 20 best classifiers. RF w = RotationForest w. MWD t = mlpWeightDe-
cay t. Middle: Probability (in %) of achieving 95% or more of the maximum
accuracy. Down: 20 classifiers with the highest average Percentage of the Maxi-
mum Accuracy (PMA) over the two-class data sets. MAB MLP w means Multi-
BoostAB MultilayerPerceptron w.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
3.4 Two-Class Data Sets
Since 45.4% of the data sets (55 out of 121) have only two classes, it is interesting to see
what happens when only 2-class data sets are considered. We repeated our analysis of the
Subsections 3.1 and 3.2, calculating the Friedman rank and the average accuracy, alongside
with the P95 and PMA, for all the classifiers and two-class data sets. Although it should be
recommendable, we did not use the area under ROC curve as quality measure, nor develop
cutoff tuning (Kuhn and Johnson, 2013), because some classifiers do not give probabilistic
output. The Table 9 reports the results:
The upper part shows the 20 classifiers with the best Friedman rank (calculated
using only 2-class data sets), alongside with their average accuracies. The classifiers
in this new list are approximately the same as in the top-20 of Table 3, but the order
is different: avNNet t (rank 36.2) is now the best, while the parRF t, rf t and svm C
(the three bests ones in Table 3) are now the 5th, 6th and 8th respectively. Besides,
the best average accuracy (83.0%) is almost the same as in Table 3 (82.3%), so the
classification results are not globally better for two class problems. Except the C5.0 t,
all the classifiers in the top-10 are NMP neural networks, SVMs and Random Forests.
As well, these families occupy 6 places in positions 11-20. Besides, 14 of 20 classifiers
use caret. The elm kernel m is worse than in Table 3.
The middle part reports the probabilities (in %) of achieving 95% or more of the
maximum accuracy (P95). The best one is 78.2% (svmRadialCost), higher than in
Table 3 (71.1%, parRF t). The first four classifiers are SVMs, while parRF t and rf t
are in 7th and 10th positions. The avNNet t, Baggging LibSVM w, LibSVM w and
C5.0 t also are in the top-10. In positions 11-20 there are two MultiBoostAB ensembles
(LibSVM and REPTree), svmBag R and fda t, alongside with several neural networks
(pcaNNet t, elm kernel m, nnet t and mlp t) and Random Forests (RotationForest w
and RandomForest w).
The lower part shows the 20 classifiers with the highest average Percentage of the
Maximum Accuracy (PMA). The maximum value (95.0%, avNNet t) is similar to the
multi-class value (94.1%, lower part of Table 5), being parRF t in the 3th position
(94.3%). Other NNET classifiers also achieve good PMAs: pcaNNet t, nnet t and
mlp t. The C5.0 t keeps its good results, while rf t falls to the 10th position. The
table also includes some classifiers with bad multi-class results: glmnet R, rda R,
pda t, fda t, bayesglm t and simpls R (both with bad multi-class rank), belonging to
families GLM, DA and PLSR, which behave well for two-class problems. The best
ensembles, apart from Random Forests, are MultiBoostAB MultilayerPerceptron w,
MultiBoostAB PART w and nnetBag R. Overall, the 20 classifiers are in a narrow
range between 92.2%-95% of accuracy.
3.5 Discussion by Data Set Properties
In this section we study the classifier behavior in function of five data set properties: its
“complexity”, increasing and decreasing #patterns, #inputs and #classes. This study will
be developed by calculating a modified average accuracy µj(in %) for each classifier j, in
andez-Delgado, Cernadas, Barro and Amorim
which each data set is “weighted” according to each property as µj=1
i=1 wiAij , j =
1, . . . , Nc, being wiis the weight measuring the property for data set i(0 wiNd),
defined in the following subsections; Nd= 121 is the number of data sets; Aij is the
accuracy (in %) achieved by classifier jin data set i; and Nc= 179 is the number of
classifiers. The classifier behavior with the data complexity is difficult to evaluate,
because the own data set complexity is hard to define (Ho and Basu, 2002), and it may be
relative to the classifier used. In our case, since we are trying a large number of classifiers,
we can suppose that some of them achieves the highest possible accuracy for each data
set. Since this maximum accuracy is higher for some data sets than for others, we can
believe that some data sets are harder, independently of the classifier used. Therefore, we
can calculate the weighted average accuracy µC
j(the Csuperscript denotes “complexity”)
of classifier jusing the weights wC
i(which evaluate the complexity of data set i) defined
as wC
k=1 Mk
, i = 1, . . . , Nd, being Mi= maxj=1,...,Nc{Aij /100}, the maximum
accuracy for data set idivided by 100. Note that PNd
i=1 wC
i=Nd. The weighted accuracy
j(see below) with wC
idefined above weights more the data sets iwith maximum accuracy
Milow, which are expected to be more complex. The Table 10 (upper panel) shows the
20 classifiers with the highest µC, which exhibit the best behavior when the hardest data
sets have stronger weight (data sets with maximum accuracy Milow). The parRF t is
the best one, and the three best classifiers (5 in the top-10) belong to the family RF.
Other two classifiers are neural networks (mlp t and avNNet t), C5.0 t is the 4th, and two
SVMs (svm C and LibSVM w) are 6th and 9th respectively. Our proposal dkp C exhibits
a good behavior (12th position), while other classifiers in the top-20 of Table 3 as nnet t,
Bagging LibSVM w and RRFglobal t are also included. The 20 classifiers are in a narrow
range between 70.0% and 66.9% (3.1 points), so the differences among them are not too high.
In order to study the classifier behavior increasing #patterns, the weighted accuracy
µPuses the following weights wP
k=1 Nk
, i = 1, . . . , Nd, where Niis the #patterns
(population) of data set i. The middle part of the Table 10 shows the weighted accuracy µP
(the two largest data sets, connect-4 and miniboone, give errors for some classifiers which
disturb this measure, so that they are excluded). Although the range is narrow (89.4%-
91.1%), again the rf t and parRF t are the bests, and svm C is the 3rd. There are six
random forests in the top-10. The and treebag t are also in the top-10. The positions 11-20
are completely filled by ensembles: Bagging, MultiBoostAB and AdaboostM1.
The classifier behavior decreasing #patterns in the data set can be analyzed cal-
culating the weighted accuracy using weights wD
idecreasing with the #patterns (Nmis
the maximum #patterns for all the data sets) wD
k=1 Nk
, i = 1, . . . , Nd;Nm=
maxj=1,...,Nd{Nj}, i = 1, . . . , Nd. The lower part of Table 10 shows the accuracies µD
weighting each data set decreasingly with the #patterns. The rf t is the best, followed
by rforest R, svm C and parRF t, which are only slightly worse than rf t. Again, there
are 6 random forests in the top-10. The positions 11-20 include dkp C, elm kernel m, and
MultiBoostAB ensembles of LibSVM and MultilayerPerceptron. The dependence of the
results with the #classes Nc
iof the data set ican be analyzed calculating the weighted
accuracy µLwith data set weights wL
igiven by wL
k=1 Nc
, i = 1, . . . , Nd. The Table 11
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
No. Classifier µCNo. Classifier µC
1 parRF t 69.9 11 nnet t 67.7
2 rf t 69.6 12 dkp C 67.6
3 rforest R 69.3 13 RRFglobal t 67.4
4 C5.0 t 69.0 14 Bagging LibSVM w 67.3
5 RotationForest w 68.6 15 Decorate w 67.1
6 svm C 68.4 16 knn t 67.1
7 mlp t 68.4 17 Bagging REPTree w 67.0
8 RRF t 68.1 18 elm m 67.0
9 LibSVM w 67.8 19 pda t 67.0
10 avNNet t 67.8 20 RandomCommittee w 66.9
No. Classifier µPNo. Classifier µP
1 rf t 91.1 11 Bagging LibSVM w 89.9
2 parRF t 91.1 12 RandomCommittee w 89.9
3 svm C 90.7 13 Bagging RandomTree w 89.8
4 RRF t 90.6 14 MultiBoostAB RandomTree w 89.8
5 RRFglobal t 90.6 15 MultiBoostAB LibSVM w 89.8
6 LibSVM w 90.6 16 MultiBoostAB PART w 89.7
7 RotationForest w 90.5 17 Bagging PART w 89.7
8 C5.0 t 90.5 18 AdaBoostM1 J48 w 89.5
9 rforest R 90.3 19 Bagging REPTree w 89.5
10 treebag t 90.2 20 MultiBoostAB J48 w 89.4
No. Classifier µDNo. Classifier µD
1 rf t 82.1 11 MultiBoostAB LibSVM w 79.7
2 rforest R 81.8 12 LibSVM w 79.6
3 svm C 81.6 13 RandomCommittee w 79.5
4 parRF t 81.6 14 dkp C 79.5
5 RRF t 80.8 15 nnet t 79.3
6 RotationForest w 80.3 16 elm kernel m 79.2
7 C5.0 t 80.2 17 avNNet t 79.2
8 mlp t 80.0 18 treebag t 79.0
9 Bagging LibSVM w 80.0 19 MAB MLP w 78.8
10 RRFglobal t 79.8 20 knn R 78.7
Table 10: Twenty best classifiers depending on the data set complexity and population.
Up: average accuracy µC(in %) weighting each data set decreasingly with its
complexity. Middle: accuracy µPweighting the data sets increasingly with
#patterns. Down: average accuracy µDweighted decreasingly with #patterns.
(upper part) shows the accuracy µLfor the 20 best classifiers. The best classifiers are svm C
and rf t (with the same accuracy), followed by rforest t, Bagging LibSVM w, parRF t and
others, only 1% below the bests. There are 4 Random Forests and 2 SVMs in the top-10.
The Bagging LibSVM w, MultiBoostAB LibSVM w and MultiBoostAB Multilayer Percep-
tron w ensembles are also included in the top-10. The best neural networks are dkp C (9th
position), MultilayerPerceptron w and elm m. Two DA classifiers (rda R and hdda R) and
two NN classifiers (knn R and IBk w) are included. With respect to the number of in-
puts, the weighted average accuracy µIaccording to the #inputs NI
ican be calculated
andez-Delgado, Cernadas, Barro and Amorim
No. Classifier µLNo. Classifier µL
1 svm C 80.5 11 RotationForest w 76.6
2 rf t 80.5 12 RRFglobal t 76.1
3 rforest R 79.8 13 MultilayerPerceptron w 76.1
4 Bagging LibSVM w 79.7 14 rda R 76.0
5 parRF t 79.5 15 knn R 75.9
6 MultiBoostAB LibSVM w 79.5 16 SMO w 75.6
7 LibSVM w 79.5 17 hdda R 75.4
8 RRF t 77.9 18 KStar w 75.3
9 dkp C 77.7 19 elm m 75.1
10 MAB MLP w 76.9 20 RandomCommittee w 75.1
No. Classifier µINo. Classifier µI
1 parRF t 84.0 11 mlp t 81.5
2 rf t 83.3 12 SMO w 81.3
3 rforest R 82.9 13 Bagging RandomTree w 81.3
4 RotationForest w 82.8 14 elm kernel m 81.1
5 MAB MLP w 82.5 15 mlp C 81.0
6 LibSVM w 82.4 16 dkp C 80.8
7 MultilayerPerceptron w 82.0 17 fda t 80.8
8 svm C 82.0 18 rda R 80.8
9 RandomCommittee w 81.8 19 SimpleLogistic w 80.7
10 C5.0 t 81.6 20 RRF t 80.4
Table 11: Up: average accuracy µLweighted using the #classes wL(only 20 first classi-
fiers). Down: average accuracy µIweighted with the #inputs wI.
defining the weights wIas wI
k=1 NI
, i = 1, . . . , Nd. The lower part of the Table 11
shows µIfor the 20 best classifiers: parRF t and rf t are the bests, with 4 random forests
among the top-5 (the other is MultiBoostAB Multilayer Perceptron w), while the svm C
falls to the 8th position, below LibSVM w (6th). The MultilayerPerceptron w and mlp t are
also included in the top-10. The dkp C is again in the top-20. Considering jointly the
four dependencies (complexity, population, #classes and #inputs), parRF t and rf t are
always in the first positions, while the svm C is not so regular: good behavior with #classes
and #patterns, but not so good with complexity and #inputs (6th and 8th positions). The
svm C and parRF t are worse than rf t with decreasing #patterns. Besides, the averages
of µC, µP, µD, µL, µIare 81.3%, 81.2% and 80.8% for rf t, parRF t and svm C respectively,
which shows the similarity between rf t and parRF t, and their difference to svm C. Most
of the random forest versions (rforest R, RotationForest w, RRF t and RRFglobal t), and
LibSVM w, are in the five tables. Apart from the RF and SVM classifiers, which fill most
of the 10 best positions in the five tables, it is remarkable the good behavior of C5.0 t
(family DT), included in the four tables and three times in the top-10. Among the neural
networks, the dkp C appears more often (in four of five tables): in fact, the µPtable does
not include any neural network, showing a bad behavior for populated data sets. The Bag-
ging LibSVM w is also the first bagging classifier in four tables, while MultiBoostAB of
LibSVM or MLP is the best boosting classifier, appearing in four tables. The Random-
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Committee w (the best classifier of family OEN) is also included in five tables, and in the
top-10 for µI. On the other hand, three of five tables include a classifier of family NN
(knn t or knn R). The DA classifiers show bad behavior with population, being included
only pda t in µC; rda R and hdda R in µL; fda t and rda R in µI.
4. Conclusion
This paper presents an exhaustive evaluation of 179 classifiers belonging to a wide collection
of 17 families over the whole UCI machine learning classification database, discarding the
large-scale data sets due to technical reasons, plus 4 own real sets, summing up to 121 data
sets from 10 to 130,064 patterns, from 3 to 262 inputs and from 2 to 100 classes. The
best results are achieved by the parallel random forest (parRF t), implemented in
R with caret, tuning the parameter mtry. The parRF t achieves in average 94.1% of the
maximum accuracy over all the data sets (Table 5, lower part), and overcomes the 90% of
the maximum accuracy in 102 out of 121 data sets. Its average accuracy over all the data
sets is 82.0%, while the maximum average accuracy (achieved by the best classifier for each
data set) is 86.9%. The random forest in R and tuned with caret (rf t) is slightly worse
(93.6% of the maximum accuracy), although it achieves slightly better average accuracy
(82.3%) than parRF t. The LibSVM implementation of SVM in C with Gaussian kernel
(svm C), tuning the regularization and kernel spread, achieves 92.3% of the maximum
accuracy. Six RFs and five SVMs are included among the 20 best classifiers, which are the
bests families. The parRF t may be considered as a reference (“gold-standard”) to compare
with new classifier proposals in order to assess their performance for general classification in
general (not requiring special features as large-scale, on-line learning, non-stationary data,
etc.). Other classifiers with good results are the extreme learning machine with Gaussian
kernel, the C5.0 decision tree and the multi-layer perceptron (avNNet t, a committee of
5 multi-layer perceptrons randomly initialized tuning the size and decay rate). The best
boosting and bagging ensembles use LibSVM as base classifiers (in Weka), being slightly
better than the single LibSVM classifier, and adaboost R (ensemble of decision trees trained
using Adaboost.M1). For two-class data sets, avNNet t is the best (95% of the maximum
accuracy), being the parRF t also very good (94.3%). It is also the best when the complexity,
#patterns and #inputs of the data set increase, being also good when #patterns decrease
(rf t is the best) and #classes increase (svm C is the best). The probabilistic neural network
in Matlab, tuning the Gaussian kernel spread (pnn m), and the direct kernel perceptron in C
(dkp C), a very simple and fast neural network proposed by us (Fern´andez-Delgado et al.,
2014), are also very near to the top-20. The remaining families of classifiers, including
other neural networks (radial basis functions, learning vector quantization and cascade
correlation), discriminant analysis, decision trees other than C5.0, rule-based classifiers,
other bagging and boosting ensembles, nearest neighbors, Bayesian, GLM, PLSR, MARS,
etc., are not competitive at all. Most of the best classifiers are implemented in R and tuned
using caret, which seems the best alternative to select a classifier implementation.
andez-Delgado, Cernadas, Barro and Amorim
We would like to acknowledge support from the Spanish Ministry of Science and Innovation
(MICINN), which supported this work under projects TIN2011-22935 and TIN2012-32262.
David W. Aha, Dennis Kibler, and Marc K. Albert. Instance-based learning algorithms.
Machine Learning, 6:37–66, 1991.
Miika Ahdesm¨aki and Korbinian Strimmer. Feature selection in omics prediction problems
using cat scores and false non-discovery rate control. Annals of Applied Stat., 4:503–519,
Esteban Alfaro, Mat´ıas G´amez, and Noelia Garc´ıa. Multiclass corporate failure prediction
by Adaboost.M1. Int. Advances in Economic Research, 13:301–312, 2007.
Peter Auer, Harald Burgsteiner, and Wolfang Maass. A learning rule for very simple uni-
versal approximators consisting of a single layer of perceptrons. Neural Networks, 1(21):
786–795, 2008.
Kevin Bache and Moshe Lichman. UCI machine learning repository, 2013. URL http:
Laurent Berg´e, Charles Bouveyron, and St´ephane Girard. HDclassif: an R package for
model-based clustering and discriminant analysis of high-dimensional data. J. Stat.
Softw., 46(6):1–29, 2012.
Michael R. Berthold and Jay Diamond. Boosting the performance of RBF networks with
dynamic decay adjustment. In Advances in Neural Information Processing Systems, pages
521–528. MIT Press, 1995.
Leo Breiman. Bagging predictors. Machine Learning, 24(2):123–140, 1996.
Leo Breiman. Random forests. Machine Learning, 45(1):5–32, 2001.
Leo Breiman, Jerome Friedman, R.A. Olshen, and Charles J. Stone. Classification and
Regression Trees. Wadsworth and Brooks, 1984.
Jean Carletta. Assessing agreement on classification tasks: The kappa statistic. Computa-
tional Linguistics, 22(2):249–254, 1996.
Jadzia Cendrowska. PRISM: An algorithm for inducing modular rules. Int. J. of Man-
Machine Studies, 27(4):349–370, 1987.
S. Le Cessie and J.C. Van Houwelingen. Ridge estimators in logistic regression. Applied
Stat., 41(1):191–201, 1992.
Chih-Chung Chang and Chih-Jen. Lin. Libsvm: a library for support vector machines,
2008. URL
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Hyonho Chun and Sunduz Keles. Sparse partial least squares for simultaneous dimension
reduction and variable selection. J. of the Royal Stat. Soc. - Series B, 72:3–25, 2010.
John G. Cleary and Leonard E. Trigg. K*: an instance-based learner using an entropic
distance measure. In Int. Conf. on Machine Learning, pages 108–114, 1995.
Line H. Clemensen, Trevor Hastie, Daniela Witten, and Bjarne Ersboll. Sparse discriminant
analysis. Technometrics, 53(4):406–413, 2011.
William W. Cohen. Fast effective rule induction. In Int. Conf. on Machine Learning, pages
115–123, 1995.
Bhupinder S. Dayal and John F. MacGregor. Improved PLS algorithms. J. of Chemometrics,
11:73–85, 1997.
ulsen Demiroz and H. Altay Guvenir. Classification by voting feature intervals. In Euro-
pean Conf. on Machine Learning, pages 85–92. Springer, 1997.
Houtao Deng and George Runger. Feature selection via regularized trees. In Int. Joint
Conf. on Neural Networks, pages 1–8, 2012.
Beijing Ding and Robert Gentleman. Classification using generalized partial least squares.
J. of Computational and Graphical Stat., 14(2):280–298, 2005.
Annette J. Dobson. An Introduction to Generalized Linear Models. Chapman and Hall,
Pedro Domingos. Metacost: A general method for making classifiers cost-sensitive. In Int.
Conf. on Knowledge Discovery and Data Mining, pages 155–164, 1999.
Richard Duda, Peter Hart, and David Stork. Pattern Classification. Wiley, 2001.
Manuel J.A. Eugster, Torsten Hothorn, and Friedrich Leisch. Domain-based benchmark
experiments: exploratory and inferential analysis. Austrian J. of Stat., 41:5–26, 2014.
Scott E. Fahlman. Faster-learning variations on back-propagation: an empirical study. In
1988 Connectionist Models Summer School, pages 38–50. Morgan-Kaufmann, 1988.
Rong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, Xiang-Rui Wang, and Chih-Jen Lin. LI-
BLINEAR: a library for large linear classification. J. Mach. Learn. Res., 9:1871–1874,
Manuel Fern´andez-Delgado, Jorge Ribeiro, Eva Cernadas, and Sen´en Barro. Direct parallel
perceptrons (DPPs): fast analytical calculation of the parallel perceptrons weights with
margin control for classification tasks. IEEE Trans. on Neural Networks, 22:1837–1848,
Manuel Fern´andez-Delgado, Eva Cernadas, Sen´en Barro, Jorge Ribeiro, and Jos´e Neves.
Direct kernel perceptron (DKP): ultra-fast kernel ELM-based classification with non-
iterative closed-form weight calculation. Neural Networks, 50:60–71, 2014.
andez-Delgado, Cernadas, Barro and Amorim
Eibe Frank and Mark Hall. A simple approach to ordinal classification. In European Conf.
on Machine Learning, pages 145–156, 2001.
Eibe Frank and Stefan Kramer. Ensembles of nested dichotomies for multi-class problems.
In Int. Conf. on Machine Learning, pages 305–312. ACM, 2004.
Eibe Frank and Ian H. Witten. Generating accurate rule sets without global optimization.
In Int. Conf. on Machine Learning, pages 144–151, 1999.
Eibe Frank, Yong Wang, Stuart Inglis, Geoffrey Holmes, and Ian H. Witten. Using model
trees for classification. Machine Learning, 32(1):63–76, 1998.
Eibe Frank, Geoffrey Holmes, Richard Kirkby, and Mark Hall. Racing committees for large
datasets. In Int. Conf. on Discovery Science, pages 153–164, 2002.
Eibe Frank, Mark Hall, and Bernhard Pfahringer. Locally weighted naive Bayes. In Conf.
on Uncertainty in Artificial Intelligence, pages 249–256, 2003.
Yoav Freund and Llew Mason. The alternating decision tree learning algorithm. In Int.
Conf. on Machine Learning, pages 124–133, 1999.
Yoav Freund and Robert E. Schapire. Experiments with a new boosting algorithm. In Int.
Conf. on Machine Learning, pages 148–156. Morgan Kaufmann, 1996.
Yoav Freund and Robert E. Schapire. Large margin classification using the perceptron
algorithm. In Conf. on Computational Learning Theory, pages 209–217, 1998.
Jerome Friedman. Regularized discriminant analysis. J. of the American Stat. Assoc., 84:
165–175, 1989.
Jerome Friedman. Multivariate adaptive regression splines. Annals of Stat., 19(1):1–141,
Jerome Friedman, Trevor Hastie, and Robert Tibshirani. Additive logistic regression: a
statistical view of boosting. Annals of Stat., 28:2000, 1998.
Jerome Friedman, Trevor Hastie, and Robert Tibshirani. Regularization paths for general-
ized linear models via coordinate descent. J. of Stat. Softw., 33(1):1–22, 2010.
Brian R. Gaines and Paul Compton. Induction of ripple-down rules applied to modeling
large databases. J. Intell. Inf. Syst., 5(3):211–228, 1995.
Andrew Gelman, Aleks Jakulin, Maria G. Pittau, and Yu-Sung Su. A weakly informative
default prior distribution for logistic and other regression models. The Annals of Applied
Stat., 2(4):1360–1383, 2009.
Mark Girolami and Simon Rogers. Variational bayesian multinomial probit regression with
Gaussian process priors. Neural Computation, 18:1790–1817, 2006.
Ekkehard Glimm, Siegfried Kropf, and J¨urgen L¨auter. Multivariate tests based on left-
spherically distributed linear scores. The Annals of Stat., 26(5):1972–1988, 1998.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Encarnaci´on Gonz´alez-Rufino, Pilar Carri´on, Eva Cernadas, Manuel Fern´andez-Delgado,
and Rosario Dom´ınguez-Petit. Exhaustive comparison of colour texture features and
classification methods to discriminate cells categories in histological images of fish ovary.
Pattern Recognition, 46:2391–2407, 2013.
Mark Hall. Correlation-Based Feature Subset Selection for Machine Learning. PhD thesis,
University of Waikato, 1998.
Mark Hall and Eibe Frank. Combining naive Bayes and decision tables. In Florida Artificial
Intel. Soc. Conf., pages 318–319. AAAI press, 2008.
Trevor Hastie and Robert Tibshirani. Discriminant analysis by Gaussian mixtures. J. of
the Royal Stat. Soc. series B, 58:158–176, 1996.
Trevor Hastie, Robert Tibshirani, and Andreas Buja. Flexible discriminant analysis by
optimal scoring. J. of the American Stat. Assoc., 89:1255–1270, 1993.
Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learn-
ing. Springer, 2009.
Tin Kam Ho. The random subspace method for constructing decision forests. IEEE Trans.
on Pattern Analysis and Machine Intelligence, 20(8):832–844, 1998.
Tin Kam Ho and Mitra Basu. Complexity measures of supervised classification problems.
IEEE Trans. on Pattern Analysis and Machine Intelligence, 24(3):289–300, 2002.
Geoffrey Holmes, Mark Hall, and Eibe Frank. Generating rule sets from model trees. In
Australian Joint Conf. on Artificial Intelligence, pages 1–12, 1999.
Robert C. Holte. Very simple classification rules perform well on most commonly used
datasets. Machine Learning, 11:63–91, 1993.
Torsten Hothorn, Friedrich Leisch, Achim Zeileis, and Kurt Hornik. The design and analysis
of benchmark experiments. J. Computational and Graphical Stat., 14:675–699, 2005.
Guang-Bin Huang, Hongming Zhou, Xiaojian Ding, and Rui Zhang. Extreme learning
machine for regression and multiclass classification. IEEE Trans. Syst. Man Cybern. -
Part B: Cybernetics, 42:513–529, 2012.
Torsten Joachims. Making Large-Scale Support Vector Machine Learning Practical. In
Bernhard Scholk¨opf, Cristopher J.C. Burges, and Alexander Smola, editors, Advances in
Kernel Methods - Support Vector Learning, pages 169–184. MIT-Press, 1999.
George H. John and Pat Langley. Estimating continuous distributions in Bayesian classifiers.
In Conf. on Uncertainty in Artificial Intelligence, pages 338–345, 1995.
Sijmen De Jong. SIMPLS: an alternative approach to partial least squares regression.
Chemometrics and Intelligent Laboratory Systems, 18:251–263, 1993.
Josef Kittler, Mohammad Hatef, Robert P.W. Duin, and Jiri Matas. On combining classi-
fiers. IEEE Trans. on Pat. Anal. and Machine Intel., 20:226–239, 1998.
andez-Delgado, Cernadas, Barro and Amorim
Ron Kohavi. The power of decision tables. In European Conf. on Machine Learning, pages
174–189. Springer, 1995.
Ron Kohavi. Scaling up the accuracy of naive-Bayes classifiers: a decision-tree hybrid. In
Int. Conf. on Knoledge Discovery and Data Mining, pages 202–207, 1996.
Max Kuhn. Building predictive models in R using the caret package. J. Stat. Softw., 28(5):
1–26, 2008.
Max Kuhn and Kjell Johnson. Applied Predictive Modeling. Springer, New York, 2013.
Niels Landwehr, Mark Hall, and Eibe Frank. Logistic model trees. Machine Learning, 95
(1-2):161–205, 2005.
Nick Littlestone. Learning quickly when irrelevant attributes are abound: a new linear
threshold algorithm. Machine Learning, 2:285–318, 1988.
Nuria Maci`a and Ester Bernad´o-Mansilla. Towards UCI+: a mindful repository design.
Information Sciences, 261(10):237–262, 2014.
Nuria Maci`a, Ester Bernad´o-Mansilla, Albert Orriols-Puig, and Tin Kam Ho. Learner
excellence biased by data set selection: a case for data characterisation and artificial data
sets. Pattern Recognition, 46:1054–1066, 2013.
Harald Martens. Multivariate Calibration. Wiley, 1989.
Brent Martin. Instance-Based Learning: Nearest Neighbor with Generalization. PhD thesis,
Univ. of Waikato, Hamilton, New Zealand, 1995.
Willem Melssen, Ron Wehrens, and Lutgarde Buydens. Supervised Kohonen networks for
classification problems. Chemom. Intell. Lab. Syst., 83:99–113, 2006.
Prem Melville and Raymond J. Mooney. Creating diversity in ensembles using artificial
data. Information Fusion: Special Issue on Diversity in Multiclassifier Systems, 6(1):
99–111, 2004.
John C. Platt. Fast training of support vector machines using sequential minimal opti-
mization. In Bernhard Scholk¨opf, Cristopher J.C. Burges, and Alexander Smola, editors,
Advances in Kernel Methods - Support Vector Learning, pages 185–208. MIT Press, 1998.
Ross Quinlan. Induction of decision trees. Machine Learning, 1(1):81–106, 1986.
Ross Quinlan. Learning with continuous classes. In Australian Joint Conf. on Artificial
Intelligence, pages 343–348, 1992.
Ross Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, 1993.
Brian D. Ripley. Pattern Recognition and Neural Networks. Cambridge Univ. Press, 1996.
Juan J. Rodr´ıguez, Ludmila I. Kuncheva, and Carlos J. Alonso. Rotation forest: a new
classifier ensemble method. IEEE Trans. on Pattern Analysis and Machine Intelligence,
28(10):1619–1630, 2006.
Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
Alexander K. Seewald. How to make stacking better and faster while also taking care
of an unknown weakness. In Int. Conf. on Machine Learning, pages 554–561. Morgan
Kaufmann Publishers, 2002.
Alexander K. Seewald and Johannes Fuernkranz. An evaluation of grading classifiers. In
Int. Conf. on Advances in Intelligent Data Analysis, pages 115–124, 2001.
David J. Sheskin. Handbook of Parametric and Nonparametric Statistical Procedures. CRC
Press, 2006.
Donald F. Specht. Probabilistic neural networks. Neural Networks, 3(1):109–118, 1990.
Johan A.K. Suykens and Joos Vandewalle. Least squares support vector machine classifiers.
Neural Processing Letters, 9(3):293–300, 1999.
Robert Tibshirani, Trevor Hastie, Balasubramanian Narasimhan, and Gilbert Chu. Diag-
nosis of multiple cancer types by shrunken centroids of gene expression. Proc. of the
National Academy of Sciences, 99(10):6567–6572, 2002.
Kai M. Ting and Ian H. Witten. Stacking bagged and dagged models. In Int. Conf. on
Machine Learning, pages 367–375, 1997.
Valentin Todorov and Peter Filzmoser. An object oriented framework for robust multivariate
analysis. J. Stat. Softw., 32(3):1–47, 2009.
Alfred Truong. Fast Growing and Interpretable Oblique Trees via Probabilistic Models. PhD
thesis, Univ. Oxford, 2009.
Joaquin Vanschoren, Hendrik Blockeel, Bernhard. Pfahringer, and Geoffrey Holmes. Ex-
periment databases. A new way to share, organize and learn from experiments. Machine
Learning, 87(2):127–158, 2012.
William N. Venables and Brian D. Ripley. Modern Applied Statistics with S. Springer, 2002.
Geoffrey Webb, Janice Boughton, and Zhihai Wang. Not so naive Bayes: aggregating
one-dependence estimators. Machine Learning, 58(1):5–24, 2005.
Geoffrey I. Webb. Multiboosting: a technique for combining boosting and wagging. Machine
Learning, 40(2):159–196, 2000.
Daniela M. Witten and Robert Tibshirani. Penalized classification using Fisher’s linear
discriminant. J. of the Royal Stat. Soc. Series B, 73(5):753–772, 2011.
David H. Wolpert. Stacked generalization. Neural Networks, 5:241–259, 1992.
David H. Wolpert. The lack of a priori distinctions between learning algorithms. Neural
Computation, 9:1341–1390, 1996.
Zijian Zheng and Goeffrey I. Webb. Lazy learning of Bayesian rules. Machine Learning, 4
(1):53–84, 2000.
... We compare our network against 187 neural and non-neural machine learning algorithms. Their configurations and performances are detailed in literatures 16,17,50 . See SI 1B.2 for dataset configuration details. ...
... Imbalanced data adaptation performance. We analyze the performance of MSNN for datasets with different levels of imbalance in terms of the percentage of majority class %Maj 17 . %Maj reflects the level of imbalance in the dataset, the higher the %Maj, the higher the imbalance. ...
Full-text available
Deep learning’s performance on the imbalanced small data is substantially degraded by overfitting. Recurrent neural networks retain better performance in such tasks by constructing dynamical systems for robustness. Synergetic neural network (SNN), a synergetic-based recurrent neural network, has superiorities in eliminating recall errors and pseudo memories, but is subject to frequent association errors. Since the cause remains unclear, most subsequent studies use genetic algorithms to adjust parameters for better accuracy, which occupies the parameter optimization space and hinders task-oriented tuning. To solve the problem and promote SNN’s application capability, we propose the modern synergetic neural network (MSNN) model. MSNN solves the association error by correcting the state initialization method in the working process, liberating the parameter optimization space. In addition, MSNN optimizes the attention parameter of the network with the error backpropagation algorithm and the gradient bypass technique to allow the network to be trained jointly with other network layers. The self-learning of the attention parameter empowers the adaptation to the imbalanced sample size, further improving the classification performance. In 75 classification tasks of small UC Irvine Machine Learning Datasets, the average rank of the MSNN achieves the best result compared to 187 neural and non-neural network machine learning methods.
... Results from each tree are then aggregated to give a predictive model with slightly higher levels of bias, allowing the model to generalize more broadly than a single tree (Speiser et al., 2015). Research indicates that random forest models consistently outperform other classification techniques in terms of prediction accuracy (Fernández-Delgado et al., 2014). ...
Full-text available
When specifying a predictive model for classification, variable selection (or subset selection) is one of the most important steps for researchers to consider. Reducing the necessary number of variables in a prediction model is vital for many reasons, including reducing the burden of data collection and increasing model efficiency and generalizability. The pool of variable selection methods from which to choose is large, and researchers often struggle to identify which method they should use given the specific features of their data set. Yet, there is a scarcity of literature available to guide researchers in their choice; the literature centers on comparing different implementations of a given method rather than comparing different methodologies under varying data features. Through the implementation of a large-scale Monte Carlo simulation and the application to one empirical dataset we evaluated the prediction error rates, area under the receiver operating curve, number of variables selected, computation times, and true positive rates of five different variable selection methods using R under varying parameterizations (i.e., default vs. grid tuning): the genetic algorithm (ga), LASSO (glmnet), Elastic Net (glmnet), Support Vector Machines (svmfs), and random forest (Boruta). Performance measures did not converge upon a single best method; as such, researchers should guide their method selection based on what measure of performance they deem most important. Results did show that the SVM approach performed worst and researchers are advised to use other methods. LASSO and Elastic Net performed well in most conditions, but researchers may face non-convergence problems if these methods are chosen. Random forest performed well across simulation conditions. Based on our study, the genetic algorithm is the most widely applicable method, exhibiting minimum error rates in hold-out samples when compared to other variable selection methods.