Constrained Clustering With Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) and symmetric NMF (SymNMF) have been shown to be effective for clustering linearly separable data and nonlinearly separable data, respectively. Nevertheless, many practical applications demand constrained algorithms in which a small number of constraints in the form of must link and cannot link are available. In this paper, we propose an NMF based constrained clustering framework in which the similarity between two points on a must link is enforced to approximate 1 and the similarity between two points on a cannot link is enforced to approximate 0. We then formulate the framework using NMF and SymNMF to deal with clustering of linearly separable data and nonlinearly separable data, respectively. Furthermore, we present multiplicative update rules to solve them and show the correctness and convergence. Experimental results on various text data sets, University of California, Irvine (UCI) data sets, and gene expression data sets demonstrate the superiority of our algorithms over existing constrained clustering algorithms.
IEEE Transactions on Neural Networks and Learning Systems