Group Sparse Non-negative Matrix Factorization for Multi-Manifold Learning

Many observable data sets such as images, videos and speech can be modeled by a mixture of manifolds which are the result of multiple factors (latent variables). In this paper, we propose a novel algorithm to learn multiple linear manifolds for face recognition, called Group Sparse Non-negative Matrix Factorization (GSNMF). Via the group sparsity constraint imposed on the column vectors of the coefficient matrix, we obtain multiple linear manifolds each of them belongs to a particular class. For a test image, we represent it as a linear combination of the learned multiple linear manifolds, and then the representation is naturally group sparse: only the coefficients corresponding to the same class are nonzero. We conduct extensive experiments to verify the proposed algorithm using the ORL database, the Yale database and the Extended Yale B database. Our evaluation shows that GSNMF achieves accurate recognition on face images with varying illuminations and expressions.