A kernel based non-negative matrix factorization

In this paper, we extend the original projective non-negative matrix factorization (P-NMF) to kernel P-NMF (KP-NMF). The advantages of KP-NMF over P-NMF are:1) it could extract more useful features hidden in the original data through some kernel-induced nonlinear mappings; 2) it can deal with non-linear data well; 3) it can process data with negative values by using some specific kernel functions. Thus, KP-NMF is more general than P-NMF. Experimental on ORL datasets and the UMIST face database results show that KP-NMF derives bases which are somewhat better suitable for localized representation than KP-NMF.