TCS Journal 2026 Journal Article
A new study on clustering of adaptive asymmetric graph regularized semi-nonnegative matrix factorization under orthogonal subspace with auxiliary variable
- Wen Li
- Junjian Zhao
- Yasong Chen
Clustering plays a fundamental role in network analysis, yet clustering for directed networks remains underexplored. To address this gap, we propose a novel clustering algorithm named Adaptive Asymmetric Graph Regularized semi-Nonnegative Matrix Factorization under Orthogonal Subspace with Auxiliary Variable (semi-AAGNMFOSV), which is applicable to both directed and conventional datasets. Our model first constructs an adaptive neighborhood graph that captures the local manifold structure by dynamically learning neighborhood relationships based on data features, instead of relying on static graphs. This adaptively learned similarity matrix is then used not only as a graph regularizer in the objective function but also directly as the target matrix in asymmetric matrix factorization, thereby better preserving intrinsic geometric information. To enhance interpretability and solution sparsity, we incorporate orthogonal subspace constraints along with auxiliary variables. Moreover, we relax the nonnegativity constraint to the coefficient matrix only, increasing the model’s flexibility in approximating clustering relations. We also provide a rigorous convergence proof for the proposed optimization algorithm by introducing auxiliary variables, establishing its theoretical soundness and stability. Extensive experiments on benchmark datasets demonstrate that our method consistently outperforms state-of-the-art clustering algorithms.