A Five Step Procedure for Outlier Analysis in Data Mining

Abstract

Nowadays, outlier detection is primarily studied as an independent knowledge discovery process merely because outliers might be indicators of interesting events that have never been known before. Despite the advances seen, many issues of outlier detection are left open or not yet completely resolved. Outlier detection is an important data mining task. It deserves more attention from data mining community. There are "good" outliers that provide useful information that can lead to the discovery of new knowledge and "bad" outliers that include noisy data points. Distinguishing between different types of outliers is an important issue in many applications. It requires not only an understanding of the mathematical properties of data but also relevant knowledge in the domain context in which the outliers occur. We propose a novel five step procedure for outlier analysis along with a comprehensive review of existing outlier detection techniques. The paper ends by addressing some important issues and open questions that can be subject of future research. This paper would be helpful in devising the choice of outlier analysis techniques for unsupervised machine learning research.

Full text

European Journal of Scientific Research
ISSN 1450-216X Vol.75 No.3 (2012), pp. 327-339
© EuroJournals Publishing, Inc. 2012
http://www.europeanjournalofscientificresearch.com
A Five Step Procedure for Outlier Analysis in Data Mining
V. Ilango
Department of Computer Applications
New Horizon College of Engineering, Bangalore-560103, India
E-mail: banalysist@yahoo.com
Tel: +91-080-6629777
R. Subramanian
Department of Computer Science, Pondicherry University, Pondicherry, India
E-mail: rsmanian.csc@pondiuni.edu.in
V. Vasudevan
Department of Information Technology, Kalasalingam University, Srivilliputtur, India
E-mail: v.vasudevan@klu.ac.in
Abstract
Nowadays, outlier detection is primarily studied as an independent knowledge
discovery process merely because outliers might be indicators of interesting events that
have never been known before. Despite the advances seen, many issues of outlier detection
are left open or not yet completely resolved. Outlier detection is an important data mining
task. It deserves more attention from data mining community. There are “good” outliers
that provide useful information that can lead to the discovery of new knowledge and “bad”
outliers that include noisy data points. Distinguishing between different types of outliers is
an important issue in many applications. It requires not only an understanding of the
mathematical properties of data but also relevant knowledge in the domain context in
which the outliers occur. We propose a novel five step procedure for outlier analysis along
with a comprehensive review of existing outlier detection techniques. The paper ends by
addressing some important issues and open questions that can be subject of future research.
This paper would be helpful in devising the choice of outlier analysis techniques for
unsupervised machine learning research.
Keywords: Univariate, Multivariate, Parametric, Nonparametric, detection rate, false
alarm and ROC curve
1. Introduction
Outliers are present in virtually every data set in any application domain, and the identification of
outliers has a hundred years long history. Number definition are compiled and expressed in [104]. The
important definitions are quoted here. “An observation (or subset of observations) which appears to be
inconsistent with the remainder of that set of data” [7]. An outlying observation, or 'outlier', is one that
appears to deviate markedly from other members of the sample in which it occurs [32]. An outlier is an
observation which deviates so much from other observations as to arouse suspicions that it was
generated by a different mechanism [38]. Outlier detection methods have been suggested for numerous

A Five Step Procedure for Outlier Analysis in Data Mining 328
applications, such as credit card fraud detection, clinical trials, voting irregularity analysis, data
cleansing, network intrusion, severe weather prediction, geographic information systems, athlete
performance analysis, and other data-mining tasks, fraud detection, medicine, public health, sports
statistics, detecting measurement errors, loan application processing ,intrusion detection, activity
monitoring , network performance ,fault diagnosis , structural defect detection , satellite image analysis
, time-series data analysis , medical condition monitoring and pharmaceutical research [43]. Outliers
may lead to the discovery of unexpected knowledge. In the 1880s when the English physicist Rayleigh
measured nitrogen from different sources, he found that there were small discrepancies among the
density measurements. After closer examination, he discovered that the density of nitrogen obtained
from the atmosphere was always greater than the nitrogen derived from its chemical compounds by a
small but definite margin. He reasoned from this anomaly that the aerial nitrogen must contain a small
amount of a denser gas. This discovery eventually led to the successful isolation of the gas argon, for
which he was awarded the Nobel Prize for Physics in 1904.which he considered as outlier that
produced good outcome [30]. [9] [17] [23] [92] [105] [34] [60] provide an extensive survey of outlier
detection techniques developed in machine learning and statistical domains. Our survey tries to provide
a structured and comprehensive overview of the outlier analysis techniques. Outlier will arise due to
natural variability of data set, measurement error as well as any recording error done by the users and
execution error [45]. Robust estimation to find the presence of outliers in the given sample is a critical
problem [100].
This study covers the answer for the following questions. a) How to define abnormality
detection, b) How to minimize computational cost (processing time, storage and I/O) c) How to
eliminate or minimize the impact of outlier in performance of information system, and to discover new
knowledge from hidden data. The important issues associated with outliers are detecting the outlier and
deciding what to do once it has been detected. Outlier detection involves identifying the time of
occurrence, which may not be known, as well as recognizing the type of outlier [57]. A key challenge
in outlier detection is that it involves exploring the unseen space. It is hard to enumerate all possible
normal behaviors in an application. Handling noise in outlier detection is a challenge. Noise may
distort the normal objects and blur the distinction between normal objects and outliers. It may help to
hide outliers and reduce the effectiveness of outlier detection [87]. The scope of this paper is modest to
provide bird’s eye view of outlier analysis techniques that focuses on unsupervised learning methods.
The contributions of this paper are listed below: Section two describes the five step procedures for
outlier analysis. Part (a) we have briefly explained different data sets and data cleaning measures. Part
(b) broadly describes various techniques for outlier detection based on unsupervised approach. Part (c)
discusses the methods of outlier representation. Part (d) narrates the techniques of how to profile and
describe the detected outlier. Part (e) explores the interesting measures for evaluation of outlier. Finally
paper concludes with suggestion for future research. To the best of our knowledge, this survey is an
attempt to provide a structured and a comprehensive-overview of outlier analysis techniques
Figure 1: Five Step Procedure of Outlier Analysis

Data
Sets
Data
Cleaning
Outlier
Detection
Representation
of Outlier
Outlier
Handling/Evaluation
Profiling of
Detected Outlier

329 V. Ilango, R. Subramanian and V. Vasudevan
2. Outlier Analysis Procedure
We have proposed in figure.1 five step outlier analysis procedures starting from data sets, data
cleaning, outlier detection, representation, profiling, handling and evaluation. Each step is explained in
detail as follows. a). Data sets are important for outlier analysis. There are different types of data set
such as: Nominal, ordinal, interval, ratio, binary, continuous, discrete, Transaction Data, Spatial Data,
Spatio-Temporal Data, and Sequence Data and Time Series data [70]. Data Cleaning: Indentifying
missing values is one of the data cleaning process. Missing values create difficulties for data analysis.
The following measures can be used to process the missing values such as: Ignoring the record, can fill
missing values manually, use global constant to fill in the missing values, use the attribute mean to fill
in the missing values, use the attribute mean for all samples belonging to the same class as the given
tuple [69] [76]. b). Outlier Detection Techniques: In the last decade numerous outlier detection
methods have been proposed. The layout of outlier mining techniques has been explained in figure.2.
The main focus is given on unsupervised outlier detection methods. Some of the outlier detection
techniques can be used for generic purpose and some of them can be used for specific purpose [11]
[41]. Outlier detection approaches can be classified into these three categories: supervised, semi-
supervised and unsupervised. Techniques trained in supervised mode assume the availability of a
training data set which has labeled instances for normal as well as anomaly class. Typical approach in
such cases is to build a predictive model for normal vs. anomaly classes [66]. The unsupervised
approach [86] of outlier detection does not require training data. This approach takes as input a set of
unlabelled data and attempts to find outlier within the data. Many semi-supervised [10][85] techniques,
assume that the training data has labeled instances for only the normal class, can be adapted to operate
in an unsupervised mode by using a sample of the unlabeled data set as training data. Table 1 explains
the advantages, drawback, techniques and tools for the above mentioned outlier detection methods.
Unsupervised learning approaches can be further grouped into ii).parametric and non-parametric
methods [28]. Parametric method: These methods assume that the whole data can be modeled to one
standard statistical (normal) distribution. A point that deviates significantly from the data model is
declared as an outlier. Non-parametric method: These methods make no assumption on the statistic
properties of data and instead identify outliers based on the full dimensional distance measure between
points.
Figure 2: Hierarchical Structure of Outlier Detection Methods

A Five Step Procedure for Outlier Analysis in Data Mining 330
Table 1: Machine Learning Outlier Techniques
Supervised Semi-supervised Unsupervised
Require knowledge of both
normal and anomaly
class.Build classifier to
distinguish between normal
and known anomalies
Require knowledge of normal
class only. Use modified
classification model to learn
the normal behavior and then
detect any deviations from
normal behavior as
anomalous
Assume the normal objects are somewhat ``clustered'‘
into multiple groups, each having some distinct
features .An outlier is expected to be far away from any
groups of normal objects
Advantages:
Models that can be easily
understood.High accuracy in
detecting many kinds of known
anomalies
Models that can be easily
understood. Normal behavior
can be accurately learned
The unsupervised techniques typically suffer from
higher false alarm rate, because often times the
underlying Assumptions do not hold true.
Drawbacks:
Require both labels from both
normal and anomaly class.
Cannot detect unknown and
emerging anomalies
Require labels from normal
class Possible high false
alarm rate - previously
unseen (yet legitimate) data
records may be recognized as
anomalies
Cannot detect collective outlier effectively. Normal
objects may not share any strong patterns, but the
collective outliers may share high similarity in a small
area
Techniques: K-mean,EM,
Wavecluster,CLAD,CBLOF,LOF,COF,DBSCAN,SNN
Artificial neural network,
Bayesian statistics ,Rule based
model, RBF,Ripper,SOM
Decision tree learning
One class SVM,Hidden
Markove Model
Software Tools :Weka ,SPSS,SAS,Tanagra, SYSTAT, MATLAB, Minitab, Liseral, MEDCALC,R-package
Table 2: Comparison Of Outlier Detection Techniques For Simple Data Sets
Outlier Property Outlier Detection Technique
Property Data Sets Property
Reference
Outlier Type Outlier Degree Technique
Based on
No of Outlier
Detected at Once Data Dimension Data Type
Global Local Scalar Outlierness One Multiple Univariate Multivariate
Moderate High
√ √ Distribution √ √ Numeric 32
√ √ Distribution √ √ Numeric 7
√ √ Distribution √ √ Numeric 27
√ √ Distribution √ √ Mixed-type 51
√ √ Depth √ √ Numeric 80
√ √ Graph √ √ Mixed-type 59
√ √ Clustering √ √ Numeric 22
√ √ Clustering √ √ Numeric 61
√ √ √ Clustering √ √ Numeric 102
√ √ Clustering √ √ Numeric 21
√ √ Distance √ √ Numeric 52
√ √ Distance √ √ Numeric 77
√ √ Distance √ √ Numeric 8
√ √ Density √ √ Numeric 14
√ √ Density √ √ Numeric 20
√ √ Density √ √ Numeric 50
√ √ Density √ √ Numeric 96
√ √ Density √ √ Numeric 95
√ √ Density √ √ Numeric 83
√ √ Density √ √ Numeric 81
√ √ Density √ √ Numeric 78
√ √ Density √ √ Numeric 28

331 V. Ilango, R. Subramanian and V. Vasudevan
Table 2: Comparison Of Outlier Detection Techniques For Simple Data Sets - continued
√ √ Density √ √ Numeric 53
√ √ NN √ √ Numeric 37
√ √ NN √ √ Numeric 29
√ √ SVM √ √ Numeric 63
√ √ SVM √ √ Numeric 62
Table 5: Comparison of univariate, bivariate and multivariate data
Univariate Bivariate Multivariate
Definition
Describes a case in terms of a
single variable - the distribution of
attributes that comprise it. Does
not deal with causes or
relationships
Analysis of two variables
simultaneously. Focus is on
the variables and the
empirical relationships.
Deals with causes or
relationships.
Analysis of two or more variables
simultaneously.
Graphical
Representation
Bar graph, histogram, pie chart,
line graph, box-and-whisker plot,
Stem-and-leaf Plot, Q-Q Plots,
violin plot
Scatter plot
Multivariate Profile, Andrew’s
Fourier Transformation,
Chernoff’s faces, Scatter plot,
Contour Plots
Methods
Single and Sequential Procedure
Inward and Outward Procedure
Univariate Robust measure
-
Masking effect
Swamping effect
Multivariate Robust Measures
Computational
Measures
Measure of Central Tendency
Measures of dispersion
Measures of Skewness
One-way ANOVA
Index Numbers
Simple correlation & Regression
Simple Regression
Simple Correlation
Two-way ANOVA
Association of attributes
Multiple regression & correlation
Multiple discriminant analysis
Multi-ANOVA
Canonical analysis
Factor analysis
Cluster analysis & PCA
Outliers are considered as those points that are distant from their own neighbors in the data set.
Compared to parametric methods, these non-parametric methods are more flexible and autonomous
due to the fact that they require no data distribution knowledge [5][107]. Some of the computational
measures for parametric and nonparametric test are discussed in table 4.
Table 4: Parametric and nonparametric test for outlier
Feature Parametric Nonparametric
Two samples – compare mean value for
some variable of interest t-test for independent samples
Wald-Wolfowitz runs test, Mann-
Whitney U test, Kolmogorov-
Smirnov two sample test
Multiple groups Analysis of variance (ANOVA/
MANOVA)
Kruskal-Wallis analysis of ranks,
Median test
Compare two variables measured in the
same sample t-test for dependent samples Sign test, Wilcoxon’s matched pairs
test
If more than two variables are measured
in same sample Repeated measures ANOVA Friedman’s two way analysis of
variance, Cochran Q
Two variables of interest are categorical Correlation coefficient
Spearman R, Kendall Tau, Coefficient
Gamma, Chi square, Phi coefficient,
Fisher exact test, Kendall coefficient
of concordance

A Five Step Procedure for Outlier Analysis in Data Mining 332
Table 3: Comparison of outlier detection techniques for complex data sets
Outlier Property Outlier Detection Technique
Property Data Sets Property
Reference
Outlier Type Outlier Degree Technique
Based on
No of Outlier
Detected at Once Data Dimension Data Type
Global Local Scalar Outlierness One Multiple Univariate Multivariate
Moderate High
√ √ Subspace √ √ Numeric 3
√ √ Subspace √ √ Numeric 106
√ √ Subspace √ √ Numeric 65
√ √ Distance √ √ Numeric 4
√ √ Distance √ √ Numeric 31
√ √ Distance √ √ Numeric 18
√ √ Graph √ √ Mixed-type 25
√ √ Graph √ √ Mixed-type 58
√ √ Graph √ √ Mixed-type 39
√ √ Clustering √ √ Sequence 15
√ √ Tree √ √ Sequence 73
√ √ Distribution √ √ Spatial 84
√ √ Distribution √ √ Spatial 16
√ √ Distribution √ √ Spatial 54
√ √ Distribution √ √ Spatial 94
√ √ Distribution √ √ Spatial 47
√ √ Model √ √ Streams 102
√ √ Model √ √ Streams 101
√ √ Graph √ √ Streams 82
√ √ Density √ √ Streams 75
√ √ Density √ √ Streams 93
√ √ Clustering&
Distribution
√ √ Spatial-
temporal
19
√ √ Clustering&
Distribution
√ √ Spatial-
temporal
12
iii). Univariate, Bivariate and Multivariate Data sets: The technical description of different
data set properties are described in Table 2, Table 3 and Table 5. Univariate analysis is the simplest
form of quantitative (statistical) analysis. A basic way of presenting univariate data is to create a
frequency distribution of the individual cases, which involves presenting the number of attributes of
the variable studied for each case observed in the sample. This can be done in a table format, with a bar
chart or a similar form of graphical representation.[44]. Bivariate data involves the analysis of two
variables for determining the empirical relationship between them. Common forms of bivariate
analysis involve creating a percentage table, a scatter plot graph, or the computation of a simple
correlation coefficient [42]. Multivariate analysis (MVA) is based on the Analysis of two or more
variables simultaneously [1][35]. Table 6 narrates the classification of outlier detection methods and
their strength and weakness along with related
algorithm[2][6][33][40][46][48][49][55][56][64][67][68][71][72][74] [88][89][90][98][99]. c).Outlier
Representation Stage: Once outlier is detected, it must be represented in understandable form. The
representation can be in the visual form of graphical display [26]. The goal of visualization is the
interpretation of the visualized information. [108] explain the following principle for effective
graphical display: Apprehension, Clarity, Consistency, Efficiency, Necessity and Truthfulness. [109]
has also explained the following principle for graphical excellence: Graphical excellence consists of
complex ideas communicated with clarity, precision and efficiency. Graphical excellence requires
telling the truth about the data. Identified outlier can be represented using the above principles.
d).Profiling and Outlier Description: Examples of outliers abound in social as well as scientific
contexts. Outliers could also be indications of interesting events that have never been known before
and hence; detecting outliers may lead to the discovery of critical information contained in data. In

333 V. Ilango, R. Subramanian and V. Vasudevan
such cases, uncovering underlying cause(s) is necessary. For example, if one happens to find an UFO
(Unidentified Flying Object), throwing it away is obviously not a good idea. Studying its structure to
understand its flying mechanism is certainly much more interesting and beneficial [79]. Once the
outliers have been identified, the analyst should generate profile on each outlier observation and
carefully examine the data for the variables responsible for its being an outlier. In addition to this the
analyst can perform statistical and mathematical methods to identify the difference between outliers
and the other observations. Retention and Deletion: After the outliers have been identified, profiled and
categorized the analyst must decide on the retention or deletion of each one. Either deletion or
accommodation of outlier depends on application domain, types of data sets and researchers. Person
should have strong domain knowledge to decide about deletion and accommodation of detected
outliers. If we want to reduce the weight of the outlier, we can use the following options: firstly if we
have only a few outliers, we may simply delete those values, so they become blank or missing values.
Secondly if there are too many outliers in a variable, or if we do not need that variable, we can delete
the variable. Thirdly we can transform the values or variables. After dealing with the outlier, we re-run
the outlier analysis procedure to determine if the data are outlier free. Sometimes new outliers emerge
because they were masked by the old outliers and the data is now different after removing the old
outlier so existing extreme data points may now qualify as outliers [110]. If new outliers emerge, and
we want to reduce the influence of the outliers, we choose one of the above mentioned options again.
Then, re-run the outlier analysis to determine if any new outliers emerge or if the data are outlier free,
and repeat again [91]. e). Evaluation of the Outlier: Evaluation of detected outlier is an important task
in the data analysis. It has number of measures; some of them are discussed as follow. Detection Rate,
False Alarm Rate and ROC Curves. Intuitively, detection rate gives information about the number of
correctly identified outliers, while the false alarm rate represents the number of outliers misclassified as
normal data records. The most widely used tool to assess detection techniques' accuracy is ROC
(Receiver Operating Characteristic) curve. Computational Complexity. The efficiency of outlier
detection techniques can be evaluated by the computational cost, which is known as time & space
complexity. In addition, the amount of memory occupation required to execute outlier detection
techniques can be viewed as an important performance evaluation metrics. [24][36][60].
Table 6: Outlier Detection Approach
Approach Definition Strength Weakness Application Methods/ Algorithm
Statistical Tests Statistical methods
assume that the
normal data follow
some statistical
model. The data
not following the
model are outliers.
Utilize existing
statistical modeling
techniques to
model various type
of distributions
Most tests are for
single
attribute.With high
dimensions,
difficult to
estimate
distributions.
Parametric
assumptions often
do not hold for real
data sets
Fraud detection,
Intrusion detection,
Medical and health
parametric vs. non-
parametric
Depth-based
Approaches Search for outliers
at the border of the
data space but
independent of
statistical
distributions.
Organize data
objects in convex
hull layers Outliers
are objects on
outer layers
Depth-based
approaches avoid
the problem of
fitting to a data
distribution. No
assumption of
probability
distribution. No
distance function
required.
They are
inefficient for the
large data set with
high
dimensionality,
where the convex
hull will be harder
to discern and is
computationally
more expensive.
Environmental
monitoring,
Localization and
tracking, Logistics
and transportation
ISODEPTH,FDC,
Minimum Volume
Ellipsoid (MVE) and
Convex peeling.

A Five Step Procedure for Outlier Analysis in Data Mining 334
Table 6: Outlier Detection Approach - continued
Distance-based
Approaches The concept of
distance-based
outlier relies on the
notion of the
neighborhood of a
point, typically, the
k-nearest
neighbors.
This method
avoids the
excessive
computation that
can be associated
with fitting the
observed
distribution into
some standard
distribution and in
selecting
discordancy tests.
Distance based
method suffer from
detecting local
Outliers in a data
set with diverse
densities.
Intrusion detection,
Environmental
monitoring,
Medical and
Health care data
Index-based, Nested-
loop based, Grid-
based
Density-based
Approaches The density-based
approach estimates
the density
distribution of the
data and identifies
outliers as those
lying in low-
density regions
Density-based
techniques have
the advantage that
they can detect
outliers that would
be missed by
techniques with a
single, global
criterion
Parameter
selection for upper
bound and lower
bound is difficult.
Intrusion detection,
Environmental
monitoring,
Medical and
Health care,
localization and
tracking
Local outlier factor,
k-distance, k-distance
neighborhood, reach
ability distance
Cluster Based
Approaches
Cluster based
approach finds
groups of strongly
related objects. An
object is an outlier
if it does not
belong to any
cluster, there is a
large distance
between the object
and its closest
cluster , or it
belongs to a small
or sparse cluster
Detect outliers
without requiring
any labeled data
Work for many
types of data.
Clusters can be
regarded as
summaries of the
data. Once the
cluster are
obtained, need
only compare any
object against the
clusters to
determine whether
it is an outlier
(fast)
Effectiveness
depends highly on
the clustering
method used—they
may not be
optimized for
outlier detection.
High
computational
cost:
Fraud detection,
Intrusion detection,
Medical and
health,
Environmental
monitoring,
localization and
tracking
BIRCH, CLARANS,
DBSCAN,
GDBSCAN, OPTICS
and
PROCLUS,CBLOF
3. Conclusions
In this paper we have proposed five step procedure of outlier analysis and tried to provide a broad view
of latest techniques associated with each steps but obviously, we are unable to describe all approaches
in a single paper. The limitation of this study is focused mainly on outlier detection techniques for low-
dimensional simple static data, followed by some of recent advancements in outlier detection for high-
dimensional data. Based on our review, we observe that the notion of outlier is different for different
application domains. Outlier detection is an extremely important problem. It involves exploring unseen
spaces. Some outlier detection techniques are developed in a more generic fashion and can be ported to
various application domains while others directly target a particular application domain. Outlier
detection is an important research problem in data mining that aims to discover useful abnormal and
irregular patterns hidden in large data sets. Most existing outlier detection methods only deal with
static data with relatively low dimensionality. Recently, outlier detection for high-dimensional stream
data, ensemble outlier detection, and subspace outlier mining, addressing the issues of concept drift,
dimension reduction, and detection result visualization became a new emerging research problem.
Minimum number of research has been done using categorical data. Robust methods to be discovered

335 V. Ilango, R. Subramanian and V. Vasudevan
to explore interesting patterns. This necessitates the development of relevant approaches to handle the
issue. These are to point out that outlier detection is a very active field of data mining research and an
extensive study will bring many benefits to various practical applications as mentioned above.
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