Probability Preserving Discriminative Nonnegative Matrix Factorization

Abstract

Non-negative matrix factorization (NMF) has received increasing attention since it is a practical decomposition approach in computer vision and pattern recognition. NMF allows only additive combinations which leads to parts-based representation. Further, NMF and its variants often ignore the underlying local structure information. In this paper, we propose a novel objective which provides enough probabilistic semantics of intrinsic local topology via the probability preserving regularizer, together with the joint multiplicative update routine. Additionally, through the class indictor matrix coupled with the loss function, the generative and discriminative components with the property of local probability preservation can be simultaneously acquired which is rather optimal for the classification. The experimental results of both clustering and classification tasks demonstrate that performance of the proposed approach is clearly competitive with several other state-of-the-art algorithms.