Max-margin Non-negative Matrix Factorization

In this paper we introduce a supervised, maximum margin framework for linear and non-linear Non-negative Matrix Factorization. By contrast to existing methods in which the matrix factorization phase (i.e. the feature extraction phase) and the classification phase are separated, we incorporate the maximum margin classification constraints within the NMF formulation. This results to a non-convex constrained optimization problem with respect to the bases and the separating hyperplane, which we solve following a block coordinate descent iterative optimization procedure. At each iteration a set of convex (constrained quadratic or Support Vector Machine-type) sub-problems are solved with respect to subsets of the unknown variables. By doing so, we obtain a bases matrix that maximizes the margin of the classifier in the low dimensional space (in the linear case) or in the high dimensional feature space (in the nonlinear case). The proposed algorithms are evaluated on several computer vision problems such as pedestrian detection, image retrieval, facial expression recognition and action recognition where they are shown to consistently outperform schemes that extract features using bases that are learned using semi-NMF and classify them using an SVM classifier.