Enhanced non-negative matrix factorization via adaptive weighted bipartite graph learning for clustering problems - Huang, Yulei; Liu, Libo (Neurocomputing (Amsterdam), 2025)
Non-negative matrix factorization (NMF)-based clustering models, widely employed in modern applications, typically consist of two principal stages: obtaining low-dimensional representation through NMF and applying clustering algorithms such as k-means to the representation. However, traditional NMF methods consider these stages as independent processes, which fail to fully exploit the cluster centroids to guide the basis vectors. This may limit the optimization of basis vectors and result in low-dimensional representations that are unsuitable for clustering tasks. To address this issue, we propose an enhanced NMF method via adaptive weighted bipartite graph learning (AWBG-NMF). First, the NMF objective function is reformulated using a bipartite graph framework, where a flexible bipartite graph and an original bipartite graph are constructed to model the relationship between basis vectors and cluster centroids. Second, a novel adaptive weighted bipartite graph learning strategy is introduced to exploit high-quality cluster centroids: (a) a weight matrix is incorporated to adaptively assign feature weights, which alleviates the impact of noise; (b) a more precise flexible bipartite graph is learned as pseudo-label information to guide the optimization of basis vectors. Additionally, a centroid correlation strategy is implemented to enhance the low-dimensional representation in NMF by exploiting latent correlations among basis vectors. Finally, an efficient optimization algorithm is developed, and its convergence is theoretically proven. Extensive experiments on eight real-world datasets demonstrate that AWBG-NMF significantly outperforms state-of-the-art methods in clustering performance.