Nonnegative matrix factorization with manifold structure for face recognition

Abstract

Nonnegative matrix factorization (NMF) is a promising method to represent facial images using nonnegative features under a low-rank nonnegative basis-image matrix. The facial images usually reside on a low-dimensional manifold due to the variations of illumination, pose and facial expression. However, NMF has no ability to uncover the manifold structure of data embedded in a high-dimensional Euclidean space, while the manifold structure contains both local and nonlocal intrinsic features. These two kinds of features are of benefit to class discrimination. To enhance the discriminative power of NMF, this paper proposes a novel NMF algorithm with manifold structure (Mani-NMF). Two quantities related to adjacent graph and non-adjacent graph are incorporated into the objective function, which will be minimized by solving two convex suboptimization problems. Based on the gradient descent method and auxiliary function technique, we acquire the update rules of Mani-NMF and theoretically prove the convergence of the proposed Mani-NMF algorithm. Three publicly available face databases, Yale, pain expression and CMU databases, are selected for evaluations. Experiments results show that our algorithm achieves a better performance than some state-of-the-art algorithms.