  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.
