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December 2009 An outlier map for Support Vector Machine classification
Michiel Debruyne
Ann. Appl. Stat. 3(4): 1566-1580 (December 2009). DOI: 10.1214/09-AOAS256

Abstract

Support Vector Machines are a widely used classification technique. They are computationally efficient and provide excellent predictions even for high-dimensional data. Moreover, Support Vector Machines are very flexible due to the incorporation of kernel functions. The latter allow to model nonlinearity, but also to deal with nonnumerical data such as protein strings. However, Support Vector Machines can suffer a lot from unclean data containing, for example, outliers or mislabeled observations. Although several outlier detection schemes have been proposed in the literature, the selection of outliers versus nonoutliers is often rather ad hoc and does not provide much insight in the data. In robust multivariate statistics outlier maps are quite popular tools to assess the quality of data under consideration. They provide a visual representation of the data depicting several types of outliers. This paper proposes an outlier map designed for Support Vector Machine classification. The Stahel–Donoho outlyingness measure from multivariate statistics is extended to an arbitrary kernel space. A trimmed version of Support Vector Machines is defined trimming part of the samples with largest outlyingness. Based on this classifier, an outlier map is constructed visualizing data in any type of high-dimensional kernel space. The outlier map is illustrated on 4 biological examples showing its use in exploratory data analysis.

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Michiel Debruyne. "An outlier map for Support Vector Machine classification." Ann. Appl. Stat. 3 (4) 1566 - 1580, December 2009. https://doi.org/10.1214/09-AOAS256

Information

Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1185.62112
MathSciNet: MR2752147
Digital Object Identifier: 10.1214/09-AOAS256

Keywords: data visualization , high-dimensional data analysis , robust statistics , Support Vector Machine

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 4 • December 2009
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