Kernel Methods for Nonlinear Discriminative Data Analysis

Optimal Component Analysis (OCA) is a linear subspace technique for dimensionality reduction designed to optimize object classification and recognition performance. The linear nature of OCA often limits recognition performance, if the underlying data structure is nonlinear or cluster structures are complex. To address these problems, we investigate a kernel analogue of OCA, which consists of applying OCA techniques to the data after it has been mapped nonlinearly into a new feature space, typically a high (possibly infinite) dimensional Hilbert space. In this paper, we study both the theoretical and algorithmic aspects of the problem and report results obtained in several object recognition experiments.