Self-paced and soft-weighted nonnegative matrix factorization for data representation

Abstract

Nonnegative matrix factorization (NMF) has received intensive attention due to producing a parts-based representation of the data. However, because of the non-convexity of NMF models, these methods easily obtain a bad local solution. To alleviate this deficiency, this paper presents a novel NMF method by gradually including data points into NMF from easy to complex, namely self-paced learning (SPL), which is shown to be beneficial in avoiding a bad local solution. Furthermore, instead of using the conventional hard weighting scheme, we adopt the soft weighting strategy of SPL to further improve the performance of our model. An iterative updating algorithm is proposed to solve the optimization problem of our method. The convergence of the updating rules is also theoretically guaranteed. Experiments on both toy data and real-world benchmark datasets demonstrate the effectiveness of the proposed method.