Hierarchical Representation for Multi-view Clustering: From Intra-sample to Intra-view to Inter-view

Multi-view clustering (MVC) aims at exploiting the consistent features within different views to divide samples into different clusters. Existing subspace-based MVC algorithms usually assume linear subspace structures and two-stage similarity matrix construction strategies, thereby posing challenges in imprecise low-dimensional subspace representation and inadequacy of exploring consistency. This paper presents a novel hierarchical representation for MVC method via the integration of intra-sample, intra-view, and inter-view representation learning models. In particular, we first adopt the deep autoencoder to adaptively map the original high-dimensional data into the latent low-dimensional representation of each sample. Second, we use the self-expression of the latent representation to explore the global similarity between samples of each view and obtain the subspace representation coefficients. Third, we construct the third-order tensor by arranging multiple subspace representation matrices and impose the tensor low-rank constraint to sufficiently explore the consistency among views. Being incorporated into a unified framework, these three models boost each other to achieve a satisfactory clustering result. Moreover, an alternating direction method of multipliers algorithm is developed to solve the challenging optimization problem. Extensive experiments on both simulated and real-world multi-view datasets show the superiority of the proposed method over eight state-of-the-art baselines.