Correntropy-based dual graph regularized nonnegative matrix factorization with Lp smoothness for data representation

Nonnegative matrix factorization methods have been widely used in many applications in recent years. However, the clustering performances of such methods may deteriorate dramatically in the presence of non-Gaussian noise or outliers. To overcome this problem, in this paper, we propose correntropy-based dual graph regularized NMF with L-P smoothness (CDNMFS) for data representation. Specifically, we employ correntropy instead of the Euclidean norm to measure the incurred reconstruction error. Furthermore, we explore the geometric structures of both the input data and the feature space and impose an L-p norm constraint to obtain an accurate solution. In addition, we introduce an efficient optimization scheme for the proposed model and present its convergence analysis. Experimental results on several image datasets demonstrate the superiority of the proposed CDNMFS method.