A Novel Nonnegative Matrix Factorization Algorithm for Multi-manifold Learning

Nonnegative matrix factorization (NMF) is a promising approach to extract the sparse features of facial images. It is known that the facial images usually reside on multi-manifold due to the variations of illumination, pose and facial expression. However, NMF lacks the ability of modeling the structure of data manifold. To improve the performance of NMF for multi-manifold learning, we propose a novel Manifold based NMF (Mani-NMF) algorithm which incorporates the multi-manifold structure. The proposed algorithm simultaneously minimizes the local scatter in the same manifold and maximizes the non-local scatter between different manifolds. It theoretically proves the convergence of the algorithm. Finally, experiments on the face databases demonstrate the superiority of our method over some state of the art algorithms.