Nonlinear Nonnegative Component Analysis

Abstract

In this paper general solutions for nonlinear nonnegative component analysis for data representation and recognition are proposed. That is, motivated by a combination of the Nonnegative Matrix Factorization (NMF) algorithm and kernel theory, which has lead to an NMF algorithm in a polynomial feature space, we propose a general framework where one can build a nonlinear nonnegative component analysis using kernels, the so-called projected gradient Kernel Nonnegative Matrix Factorization (PGKNMF). In the proposed approach, arbitrary positive kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem. Moreover, we propose fixed point algorithms for the special case of Radial Basis Function (RBF) kernels. We demonstrate the power of the proposed methods in face and facial expression recognition applications.