Box-constrained Discriminant Projective Non-negative Matrix Factorization through Augmented Lagrangian Multiplier Method

Abstract

Projective non-negative matrix factorization (PNMF) learns a non-negative projection matrix to project highdimensional examples onto a lower-dimensional space spanned by the transpose of the learned projection matrix. Since PNMF can learn parts-based representation, it has attracted ample attention from computer vision community. However, existing PNMF methods either completely ignore labels of the dataset or endure the slow convergent optimization algorithm. In this paper, we propose a box-constrained discriminant PNMF (BDPNMF) method to address these issues. Specifically, BDPNMF jointly exploits the Fisher’s criterion and the augmented Lagrangian multiplier (ALM) method into PNMF to boost discriminative capacity of the learned subspace and its efficiency. Experimental results on four popular face image datasets confirm the efficacy of BDPNMF compared to previous PNMF methods in quantity.