Nonlinearity and optimal component analysis

Optimal component analysis (OCA) is a linear subspace technique for dimensionality reduction designed to optimize object classification and recognition performance in specific applications. The inherently linear nature of OCA often limits recognition performance, if the underlying data structure is nonlinear or cluster structures are complex. To address these problems, following a modern trend, we investigate kernel OCA (KOCA), which consists of applying OCA techniques to the data after it has been mapped nonlinearly into a new feature space, referred to in the literature as a reproducing kernel Hilbert space. In this paper, we study theoretical and algorithmic aspects of KOCA and report results obtained in several face recognition experiments using the ORL database.