Robust kernel principal component analysis and classification

Abstract

Kernel principal component analysis (KPCA) extends linear PCA from a real vector space to any high dimensional kernel feature space. The sensitivity of linear PCA to outliers is well-known and various robust alternatives have been proposed in the literature. For KPCA such robust versions received considerably less attention. In this article we present kernel versions of three robust PCA algorithms: spherical PCA, projection pursuit and ROBPCA. These robust KPCA algorithms are analyzed in a classification context applying discriminant analysis on the KPCA scores. The performances of the different robust KPCA algorithms are studied in a simulation study comparing misclassification percentages, both on clean and contaminated data. An outlier map is constructed to visualize outliers in such classification problems. A real life example from protein classification illustrates the usefulness of robust KPCA and its corresponding outlier map.