Improved self-paced learning framework for nonnegative matrix factorization

Nonnegative matrix factorization (NMF) has been attracting intensive attention due to its wide applications. However due to the non-convexity of the NMF models, most of the existing methods are easily stuck into a bad local minima, especially in presence of noise or outliers. To alleviate this deficiency, in this paper we propose a novel NMF method by incorporating self-paced learning (SPL) methodology with traditional NMF model, to sequentially include matrix elements into NMF training from easy to complex, which draws the merits of SPL that have been demonstrated to be beneficial in avoiding bad local minima. To make the SPL methodology play a more stable and efficient role in NMF, we suggest to base on multicriteria to select training elements. The effectiveness of the proposed multicriteria self-paced NMF (MSPNMF) method is demonstrated by a series of numerical experiments on synthetic and real face image data. We also discuss the effects of different initializations on MSPNMF. Experimental results show that MSPNMF is sensitive to the starting values and different initializations should be adopted for MSPNMF based on different situations.