Split Multiplicative Multi-View Subspace Clustering

Various subspace clustering methods have been successively developed to process multi-view datasets. Most of the existing methods try to obtain a consensus structure coefficient matrix based on view-specific subspace recoveries. However, since view-specific structures contain individualized components that are intrinsically different from the consensus structure, directly adopting view-specific subspace structures might not be a reasonable choice. In this paper, with this concern in mind, our goal is to seek novel strategies to extract valuable components from view-specific structures that are consistent with the consensus subspace structure. To this end, we propose a novel multi-view subspace clustering method named split multiplicative multi-view subspace clustering (SM²SC) with the joint strength of a multiplicative decomposition scheme and a variable splitting scheme. Specifically, the multiplicative decomposition scheme effectively guarantees the structural consistency of the extracted components. Then, the variable splitting scheme takes a step further via extracting the structural consistent components from view-specific structures. Furthermore, an alternating optimization algorithm is proposed to optimize the resulting optimization problem, which is non-convex and constrained. We prove that this algorithm could converge to a critical point. Finally, we provide empirical studies on real-world datasets that speak to the practical efficacy of our proposed method. The source code is released on GitHub https://github.com/joshuaas/SM2SC.