An algorithm of nonnegative matrix factorization under structure constraints for image clustering

Nonnegative matrix factorization (NMF) is a crucial method for image clustering. However, NMF may obtain low accurate clustering results because the factorization results contain no data structure information. In this paper, we propose an algorithm of nonnegative matrix factorization under structure constraints (SNMF). The factorization results of SNMF could maintain data global and local structure information simultaneously. In SNMF, the global structure information is captured by the cosine measure under the l(2) norm constraints. Meanwhile, l(2) norm constraints are utilized to get more discriminant data representations. A graph regularization term is employed to maintain the local structure. Effective updating rules are given in this paper. Moreover, the effects of different normalizations on similarities are investigated through experiments. On real datasets, the numerical results confirm the effectiveness of the SNMF.