Non-Negative Matrix Factorization based on Locally Linear Embedding

In this paper, we proposed a novel method called Nonnegative Matrix Factorization based on Locally Linear Embedding (LLE-NMF). This idea is to factorize the nonnegative matrix considering the intrinsic geometric structure of the high dimensional data. Instead of the need to estimate pairwise distances between widely separated data points, LLE-NMF is able to find a compact representation recovering the global nonlinear structure from locally linear fits. We proposed updating rules and simulation results. In the experiments, we show the encouraging results of the method in comparison to the state-of-the-art algorithms on face image clustering.