Hierarchical structure-guided high-dimensional multi-view clustering

Multi-view data clustering is pivotal for comprehending the heterogeneous structure of data by integrating information from diverse aspects. Nevertheless, practical challenges arise due to the differences in the granularity from different views, resulting in a hierarchical clustering structure within these distinct data types. In this work, we consider such structure information and propose a novel high-dimensional multi-view clustering approach with a hierarchical structure across views. The proposed non-convex problem is effectively tackled using the Alternating Direction Method of Multipliers algorithm, and we establish the statistical properties of the estimator. Simulation results demonstrate the effectiveness and superiority of our proposed method. In the analysis of the histopathological imaging data and gene expression data related to lung adenocarcinoma, our method unveils a hierarchical clustering structure that significantly diverges from alternative approaches.