Semi-Supervised Non-Negative Matrix Factorization With Dissimilarity and Similarity Regularization

In this article, we propose a semi-supervised non-negative matrix factorization (NMF) model by means of elegantly modeling the label information. The proposed model is capable of generating discriminable low-dimensional representations to improve clustering performance. Specifically, a pair of complementary regularizers, i.e., similarity and dissimilarity regularizers, is incorporated into the conventional NMF to guide the factorization. And, they impose restrictions on both the similarity and dissimilarity of the low-dimensional representations of data samples with labels as well as a small number of unlabeled ones. The proposed model is formulated as a well-posed constrained optimization problem and further solved with an efficient alternating iterative algorithm. Moreover, we theoretically prove that the proposed algorithm can converge to a limiting point that meets the Karush-Kuhn-Tucker conditions. Extensive experiments as well as comprehensive analysis demonstrate that the proposed model outperforms the state-of-the-art NMF methods to a large extent over five benchmark data sets, i.e., the clustering accuracy increases to 82.2% from 57.0%.