Adaptive graph regularized non-negative matrix factorization with self-weighted learning for data clustering

In general, fully exploiting the local structure of the original data space can effectively improve the clustering performance of nonnegative matrix factorization (NMF). Therefore, graph-based NMF algorithms have been widely studied and applied. However, traditional graph-based NMF methods generally employ predefined models to construct similarity graphs, so that the clustering results depend heavily on the quality of the similarity graph. Furthermore, most of these methods follow the ideal assumption that the importance of different features is equal in the process of learning the similarity matrix, which results in irrelevant features being valued. To alleviate the above issues, this paper develops an adaptive graph regularized nonnegative matrix factorization with self-weighted learning (SWAGNMF) method. Firstly, the proposed method learns the similarity matrix flexibly and adaptively to explore the local structure of samples based on the assumption that data points with smaller distances should have a higher probability of adjacency. Furthermore, the self-weight matrix assigns different weights automatically according to the importance of features in the process of constructing similarity graph, i.e., discriminative features are assigned more significant weights than redundant features, which can effectively suppress irrelevant features and enhance the robustness of our model. Finally, considering the duality between samples and features, the proposed method is capable of exploring the local structures of both the data space and the feature space. An effective alternative optimization algorithm is proposed, and convergence is theoretically guaranteed. Extensive experiments on benchmark and synthetic datasets show that the proposed method outperforms compared state-of-the-art clustering methods.