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.
Bibliographical noteThis work was supported in part by the Natural Science Foundation of China under Grant 61871342, Grant 61772344, and Grant 61672443, and in part by the Hong Kong RGC General Research Funds under Grant 9042820 (CityU 11219019), Grant 9042489 (CityU 11206317), Grant 9042322 (CityU 11200116), Grant 9042816 (CityU 11209819), and Grant 9048123 (CityU 21211518).
- Graph learning
- non-negative matrix factorization (NMF)
- symmetric NMF (SymNMF)