Non-negative low-rank and group-sparse matrix factorization

Abstract

Non-negative matrix factorization (NMF) has been a popular data analysis tool and has been widely applied in computer vision. However, conventional NMF methods cannot adaptively learn grouping structure froma dataset.This paper proposes a non-negative low-rank and group-sparse matrix factorization (NLRGS) method to overcome this deficiency. Particularly, NLRGS captures the relationships among examples by constraining rank of the coefficients meanwhile identifies the grouping structure via group sparsity regularization. By both constraints, NLRGS boosts NMF in both classification and clustering. However, NLRGS is difficult to be optimized because it needs to deal with the low-rank constraint. To relax such hard constraint, we approximate the low-rank constraint with the nuclear norm and then develop an optimization algorithm for NLRGS in the frame of augmented Lagrangian method(ALM). Experimental results of both face recognition and clustering on four popular face datasets demonstrate the effectiveness of NLRGS in quantities.