Kernel based non-negative matrix factorization method with general kernel functions

Abstract

Kernel based Non-Negative Matrix Factorizations (KNMFs) are one of the most important methods for non-negative nonlinear feature extractions and have achieved good performance in pattern classifications. However, most existing KNMF algorithms are merely valid for one special kernel function. Also, they model the pre-images inaccurately. In this paper, we utilize kernel matrix learning strategy to develop a Universal KNMF (UKNMF) algorithm, which is able to use all Mercer kernel functions. The proposed method avoids the pre-image learning simultaneously. We first establish three objective functions and then derive three update formula to determine three matrices, namely one feature matrix and two kernel matrices. The iterative rules are theoretically proven to be convergence by means of auxiliary function technique. Our UKNMF approaches with polynomial kernel and RBF kernel (UKNMF-Poly and UKNMF-RBF) are applied to face recognition respectively. The face databases, including ORL and Yale face databases, are selected for evaluations. Compared with some state of the art kernel based algorithms, experimental results show the effectiveness and superior performance of the proposed methods.