Semisupervised Adaptive Symmetric Non-Negative Matrix Factorization.

As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose. However, the similarity matrix in the traditional SymNMF methods is usually predefined, resulting in limited clustering performance. Considering that the quality of the similarity graph is crucial to the final clustering performance, we propose a new semisupervised model, which is able to simultaneously learn the similarity matrix with supervisory information and generate the clustering results, such that the mutual enhancement effect of the two tasks can produce better clustering performance. Our model fully utilizes the supervisory information in the form of pairwise constraints to propagate it for obtaining an informative similarity matrix. The proposed model is finally formulated as a non-negativity-constrained optimization problem. Also, we propose an iterative method to solve it with the convergence theoretically proven. Extensive experiments validate the superiority of the proposed model when compared with nine state-of-the-art NMF models.