Multiple graph regularized semi-supervised nonnegative matrix factorization with adaptive weights for clustering

Traditional multiple graph regularized nonnegative matrix factorization (NMF) techniques have shown good performance in image clustering applications. However, existing multiple graph regularized NMF methods are unsupervised learning methods which fail to take full advantage of priori information. To solve this issue, this paper develops a novel multiple graph regularized NMF method, namely the multiple graph regularized semi-supervised NMF with adaptive weights (MSNMF), to capture the discriminative data representation. Specifically, the MSNMF method combines the limited supervised information in the form of pairwise constraints, into multiple graph regularization, and propagates the pairwise constraints from the constrained data samples to the unconstrained data samples. Moreover, convergence, connection with the gradient descent method, and computational cost of the proposed method are studied. The relationships between MSNMF and some typical NMF methods are also discussed. Experimental results on eight practical image datasets have shown that the MSNMF method can obtain better clustering results than several related NMF methods.