Multiple Graph Adaptive Regularized Semi-Supervised Nonnegative Matrix Factorization with Sparse Constraint for Data Representation

Multiple graph and semi-supervision techniques have been successfully introduced into the nonnegative matrix factorization (NMF) model for taking full advantage of the manifold structure and priori information of data to capture excellent low-dimensional data representation. However, the existing methods do not consider the sparse constraint, which can enhance the local learning ability and improve the performance in practical applications. To overcome this limitation, a novel NMF-based data representation method, namely, the multiple graph adaptive regularized semi-supervised nonnegative matrix factorization with sparse constraint (MSNMFSC) is developed in this paper for obtaining the sparse and discriminative data representation and increasing the quality of decomposition of NMF. Particularly, based on the standard NMF, the proposed MSNMFSC method combines the multiple graph adaptive regularization, the limited supervised information and the sparse constraint together to learn the more discriminative parts-based data representation. Moreover, the convergence analysis of MSNMFSC is studied. Experiments are conducted on several practical image datasets in clustering tasks, and the clustering results have shown that MSNMFSC achieves better performance than several most related NMF-based methods.