Local High-Order Graph Learning for Multi-View Clustering

As the accumulation of multi-view data continues to grow, multi-view clustering has become increasingly important in research fields like data mining. However, current methods have been criticized for their unsatisfactory performance, such as insufficient exploration of intra-view high-order relationships and poor characterization of inter-view diverse features. To overcome these challenges, we propose a novel approach called Local High-order Graph Learning for Multi-View Clustering (LHGL_MVC). Our method aims to explore high-order relationships within a view while also considering diverse information between views. In LHGL_MVC, we learn the initial graphs of each view through self-representation, which are decomposed into consistent and diverse parts to better capture the diversity of different views. Based on consistent parts, we propose a novel local high-order graph learning approach to more effectively explore high-order relationships between samples within each view. At the same time, we leverage high-order relationships between views using the rotated tensor nuclear norm. Finally, we obtain a unified graph for clustering by fusing all consistent affinity graphs and their high-order graphs with adaptive weights. All procedures are integrated into an overall objective function, which mutually promotes during the optimization process. The comprehensive experiments conducted on eleven real-world datasets demonstrate that LHGL_MVC significantly outperforms existing algorithms in various measurements, highlighting the superiority of the proposed method.