Nonnegative Matrix Factorization with Joint Regularization of Manifold Learning and Pairwise Constraints

Abstract

In order to handle semi-supervised clustering scenarios where only part of the pairwise constraint information is available in the target dataset, on the basis of nonnegative matrix factorization (NMF) architecture, this paper proposes a nonnegative matrix factorization-based clustering algorithm using joint regularization of manifold learning and pairwise constraints (NMF-JRMLPC) by learning given pairwise constraint knowledge and using manifold regularization theory. On the one hand, graph Laplacian is introduced to depict the manifold structure information contained in a large number of unlabeled samples, and on the other hand, the must-link or cannot-link pair-constraint rules among known samples are integrated into the target optimization design, which greatly improves the clustering performance of the algorithm. In addition, the [l2,1] norm based loss function design also helps to optimize the robustness of NMF-JRMLPC. Experimental results on eight real datasets confirm the validity of the proposed method.