Robust Nonnegative Matrix Factorization with Ordered Structure Constraints.

Abstract

Nonnegative matrix factorization (NMF) as a popular technique to find parts- based representations of nonnegative data has been widely used in real-world applications. Often the data which these applications process, such as motion sequences and video clips, are with ordered structure, i.e., consecutive neighbouring data samples are very likely share similar features unless a sudden change occurs. Therefore, traditional NMF assumes the data samples and features to be independently distributed, making it not proper for the analysis of such data. In this paper, we propose an ordered robust NMF (ORNMF) by capturing the embedded ordered structure to improve the accuracy of data representation. With a novel neighbour penalty term, ORNMF enforces the similarity of neighbouring data. ORNMF also adopts the $L_{2,1}$-norm based loss function to improve its robustness against noises and outliers. A new iterative updating optimization algorithm is derived to solve ORNMF's objective function. The proofs of the convergence and correctness of the scheme are also presented. Experiments on both synthetic and real-world datasets have demonstrated the effectiveness of ORNMF.