DSNMF: Deep symmetric non-negative matrix factorization representation algorithm for clustering

Clustering is a significant and complex endeavor in machine learning. Symmetric non-negative matrix factorization (SNMF) has attracted considerable interest for its capacity to inherently capture the clustering structure prevalent in graph representation. However, existing SNMF algorithms suffer from issues such as the absence of learning rate and nonlinear learning strategies. To address these issues, this paper proposes a deep symmetric non-negative matrix factorization (DSNMF) representation algorithm for clustering. This algorithm organically integrates the nonlinear strategies of deep learning with the optimization method of SNMF. Specifically, the algorithm focuses on matrix elements and constructs a DSNMF deep network based on non-negative nonlinear constraints and neural network principle. Based on this network, the objective function is minimized. Finally, we evaluated the method on twelve publicly available datasets, including facial recognition images, object images, news text, and biological data. DSNMF achieved favorable clustering performance across these datasets.