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Mean (plain) and standard deviation (dotted around the mean) of the Median squared error in test of all models for four distance definitions, over 10 runs. Blue: LLNKWW, Green: KKNN, Red: RBFNOrr, Cyan: LSSVM, Pink: SVM
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One the earliest challenges a practitioner is faced with when using distance-based tools lies in the choice of the distance,
for which there often is very few information to rely on. This chapter proposes to find a compromise between an a priori unoptimized
choice (e.g. the Euclidean distance) and a fully-optimized, but computationally expensive, c...
Context in source publication
Context 1
... Manhattan distance, Euclidean distance and Chebyshev distance. The boxes represent the inter-quartile range, the horizontal line inside the box is the median, and the tails represent the fifth and 95th percentile respectively. The plusses represent single outliers. Table 1 provides with the mean and standard deviation of those distributions. For Friedman and Hardware, the visual inspection of the plots seems to favor the Euclidean distance, at least in terms of median results, although the difference, might not be statistically significant. As far as dataset Tecator is concerned, the Chebyshev metric seems to be the favorite choice. The same conclusion can be seen for Delve, although this is much less obvious. For both Housingburst and Tecatorburst, the 1/2-norm seems to be preferable. The same conclusion can be drawn about Concrete while it is not as clear as for the latter. The results for Housing seem to point out the Manhattan norm as most relevant; it nevertheless does not outperform the 1/2-norm and the Euclidean norm significantly, while for the Forest dataset, all distances seem to perform equally. For those datasets, defaulting to the Euclidean distance seems also reasonable. The results of 10 runs of the random splitting are shown in Figure 2. Most of the time, the results of the different models are comparable. No model outperforms all other over all datasets. Sometimes, however, one model performs worse than the others. It is the case for instance with the RBFNOrr model on Tecator and Hardware. For Friedman and Concrete, the KKNN performs really badly with the 1/2-norm while for Delve, the SVM performs worse with the Euclidean norm than any other model on those data. Note that some models deliver poor performances (around 0.6 and above) with specific distances measures ; in those cases, the choice of the correct distance measure is ...
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Citations
... It is a well-established principle in machine-learning that understanding the manifold structure of cases in dataspace can help guide appropriate selection of a classification model and/or geometric features that enable more accurate classification [39,40]. Data-space inter-sample distance measures are fundamental to many machinelearning algorithms such as k-Nearest-Neighbors [41] (k-NN), and in the case of k-NN, the choice of distance measure can be a key determinant of the accuracy of the classifier [42]. ...
Background
We previously reported on CERENKOV, an approach for identifying regulatory single nucleotide polymorphisms (rSNPs) that is based on 246 annotation features. CERENKOV uses the xgboost classifier and is designed to be used to find causal noncoding SNPs in loci identified by genome-wide association studies (GWAS). We reported that CERENKOV has state-of-the-art performance (by two traditional measures and a novel GWAS-oriented measure, AVGRANK) in a comparison to nine other tools for identifying functional noncoding SNPs, using a comprehensive reference SNP set (OSU17, 15,331 SNPs). Given that SNPs are grouped within loci in the reference SNP set and given the importance of the data-space manifold geometry for machine-learning model selection, we hypothesized that within-locus inter-SNP distances would have class-based distributional biases that could be exploited to improve rSNP recognition accuracy. We thus defined an intralocus SNP “radius” as the average data-space distance from a SNP to the other intralocus neighbors, and explored radius likelihoods for five distance measures.
Results
We expanded the set of reference SNPs to 39,083 (the OSU18 set) and extracted CERENKOV SNP feature data. We computed radius empirical likelihoods and likelihood densities for rSNPs and control SNPs, and found significant likelihood differences between rSNPs and control SNPs. We fit parametric models of likelihood distributions for five different distance measures to obtain ten log-likelihood features that we combined with the 248-dimensional CERENKOV feature matrix. On the OSU18 SNP set, we measured the classification accuracy of CERENKOV with and without the new distance-based features, and found that the addition of distance-based features significantly improves rSNP recognition performance as measured by AUPVR, AUROC, and AVGRANK. Along with feature data for the OSU18 set, the software code for extracting the base feature matrix, estimating ten distance-based likelihood ratio features, and scoring candidate causal SNPs, are released as open-source software CERENKOV2.
Conclusions
Accounting for the locus-specific geometry of SNPs in data-space significantly improved the accuracy with which noncoding rSNPs can be computationally identified.
Electronic supplementary material
The online version of this article (10.1186/s12859-019-2637-4) contains supplementary material, which is available to authorized users.
... , y n ) with p ? (0, 1). In practical applications experimental determination of the exact value for p can be recommended (Fran?ois et al., 2011). As an alternative to sophisticated dissimilarity measures algorithms reducing the number of features are often being employed. ...
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Full version: http://authors.elsevier.com/a/1T1pc5c6cKexuw
... Experiments [15] also show that choosing the right fractional norm, as opposed to the Euclidean norm, could significantly improve the effectiveness of standard k– nearest neighbor (kNN) classification in high-dimensional spaces. This observation was more closely investigated by François et al. [18] who follow a supervised approach to infer the optimum ℓ p norm using labeled training data. More precisely, the authors use a simple regression model to choose an optimal norm which is then evaluated on more elaborate regression models. ...
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The book focuses on different variants of decision tree induction but also describes the meta-learning approach in general which is applicable to other types of machine learning algorithms. The book discusses different variants of decision tree induction and represents a useful source of information to readers wishing to review some of the techniques used in decision tree learning, as well as different ensemble methods that involve decision trees. It is shown that the knowledge of different components used within decision tree learning needs to be systematized to enable the system to generate and evaluate different variants of machine learning algorithms with the aim of identifying the top-most performers or potentially the best one. A unified view of decision tree learning enables to emulate different decision tree algorithms simply by setting certain parameters. As meta-learning requires running many different processes with the aim of obtaining performance results, a detailed description of the experimental methodology and evaluation framework is provided. Meta-learning is discussed in great detail in the second half of the book. The exposition starts by presenting a comprehensive review of many meta-learning approaches explored in the past described in literature, including for instance approaches that provide a ranking of algorithms. The approach described can be related to other work that exploits planning whose aim is to construct data mining workflows. The book stimulates interchange of ideas between different, albeit related, approaches.
The problems of learning and meta-learning have been introduced formally in Sect. 1.1. Many learning algorithms have been proposed by the CI community to solve miscellaneous problems like classification, approximation, clustering , time series prediction and others.
