Online discriminant projective non-negative matrix factorization

Abstract

Projective non-negative matrix factorization (PNMF) learns a subspace spanned by several non-negative bases by minimizing the distance between samples and their reconstructions in the subspace. Due to its effective representation ability, PNMF has attracted a lot of attention in the computer vision community. However, PNMF suffers from the following limitations: 1) it requires entire dataset to reside in computer's memory, and as a consequence it cannot handle large-scale or streaming data, and 2) it completely ignores discriminative information of available labeled data, and thus has poor performance in classification tasks. Here, we propose an online discriminant PNMF (ODPNMF) method to overcome these deficiencies. Specifically, ODPNMF receives one or a few samples per step and updates the basis via a multiplicative update rule (MUR), which guarantees the non-negativity constraint over basis. To best utilize discriminative information, ODPNMF maintains and adaptively updates both within-class and between-class scatter matrices, during each round of updating the basis. Experimental results on three popular face image datasets verify the effectiveness of ODPNMF compared to representative algorithms.