Semi-supervised nonnegative matrix factorization with label propagation and constraint propagation

Abstract

Semi-supervised nonnegative matrix factorization (SNMF) improves the clustering effect of nonnegative matrix factorization (NMF) by integrating label information. However, as one of the most commonly used semi-supervised learning methods, label propagation algorithm (LP) has some limitations due to its heavy dependence on the predefined similarity matrix. To address this deficiency and effectively use limited supervisory information, a structural NMF algorithm with label propagation and constraint propagation (PNLP-SCNMF) is proposed in this paper, which simultaneously performs data representation and classification in a joint manner. Both positive label information and negative label information are introduced into the proposed method, and the factor matrix is constrained by label information to construct the tri-decomposition form. Constraint propagation algorithm (CPA) is used to correct the constructed similarity matrix, so that the low-dimensional subspace obtained by matrix decomposition can retain the geometric structure characteristics of the original sample space. In addition, an efficient iterative update optimization scheme is proposed to solve this objective function, and its convergence is proved theoretically. A large number of comparative experiments on nine real datasets show that the proposed method can consistently achieve higher clustering accuracy in image clustering tasks.