Multiview Clustering via Enhanced Multiorder Bipartite Graph Learning

Although existing bipartite graph-based multiview clustering (MVC) methods effectively exploit the structural relationships within multiview data, they exhibit three major limitations: 1) they primarily focus on direct similarities between data points and anchors, neglecting underlying neighborhood structures; 2) most existing methods fail to capture high-order correlations across bipartite graphs from different views; and 3) they overlook the relationships among anchor points, limiting the discriminative power of the learned graph. To address these challenges, we propose a unified framework, termed enhanced multiorder bipartite graph learning (EMOBGL) for MVC. The proposed EMOBGL method first constructs a second-order bipartite graph (SOBG) to capture both local and neighboring structural relationships between data points and anchors through first-order similarity (FOS) and second-order similarity (SOS). Then, the tensor Schatten- $p$ regularizer is incorporated to construct a multiorder bipartite graph (MOBG) to capture third-order similarity (TOS) across views. Meanwhile, the anchor structure regularization (ASR) is introduced to model anchor-anchor interactions, further enhancing the structural expressiveness and discriminability of the bipartite graph. The resulting EMOBGL model effectively integrates multiorder and multiview relationships within a unified framework, achieving robust and discriminative clustering performance. An efficient alternating direction method of multipliers (ADMMs) is developed to optimize the model, and we theoretically prove that the solution converges to a Karush-Kuhn-Tucker (KKT) stationary point. Extensive comparative experiments on 13 benchmark datasets demonstrate that the proposed EMOBGL consistently outperforms 13 state-of-the-art methods in both clustering accuracy and robustness. The source code is available at https://github.com/DongHuangTaiYi871/EMOBGL.