Anchor Tensor Factorization with Manifold Regularization: A Unified Framework for Multi-view Clustering

With the data explosion, the efficiency of complex multi-view data processing and clustering remains a critical challenge. Non-negative matrix factorization (NMF) has garnered widespread attention in multi-view clustering (MVC) due to its interpretability and efficiency. However, traditional NMF-based MVC approaches process each view separately, which fails to capture cross-view relationships. Considering these issues, this paper presents an innovative MVC method utilizing orthogonal non-negative anchor tensor factorization, termed ATFMC. This model employs a shared-nearest-neighbor density peaks clustering algorithm, which integrates cross-view features to select high-quality anchors. After constructing the anchor tensor by stacking anchor graphs, we apply one-side orthogonal non-negative tensor factorization to it. This approach improves interpretability and eliminates post-processing steps for cluster label extraction. To accurately approximate the tensor rank, the tensor Schatten \(p\) -norm is employed on the rotated clustering indicator tensor. In addition, anchor-driven manifold regularization is leveraged to preserve the local geometric relationships among anchors, ensuring consistent topological connectivity across views. An efficient optimization algorithm is proposed, with proven convergence of its iterative sequence to a Karush-Kuhn-Tucker (KKT) critical point. Numerous experiments on multiple benchmark datasets demonstrate that ATFMC achieves superior clustering performance.