Unified and Tensorized Incomplete Multi-View Kernel Subspace Clustering

Incomplete multi-view clustering (IMC) has recently received widespread attention in the field of clustering analysis. In spite of the great success, we observe that the current IMC approaches are still faced with three common demerits. First, they mostly fail to recover the inherent (especially nonlinear) subspace structure during incomplete clustering procedure. Second, these approaches tend to design the objective function by some specific matrix norms, yet often overlook the high-level correlation embedded in heterogeneous views. Third, many of them follow a two-stage framework, which inevitably leads to the sub-optimal clustering result due to the lack of the ability of joint optimization. To overcome these demerits, we develop a novel approach termed Unified and Tensorized Incomplete Multi-view Kernel Subspace Clustering (UT-IMKSC) in this paper. Specifically, a kernelized incomplete subspace clustering framework is formulated to exploit the inherent subspace structure from multiple views. In this framework, we aim to impute the incomplete kernels and perform incomplete subspace clustering simultaneously, upon which the low-rank tensor representations as well as their affinity matrix can be seamlessly achieved in a one-step manner. This unified formulation enables our approach to recover the latent relationship among observed and unobserved samples, while capturing the high-level correlation for strengthened subspace clustering. To the best of our knowledge, our approach is the first attempt to formulate incomplete multi-view kernel subspace clustering from unified and tensorized perspectives. Extensive experiments are conducted on various incomplete multi-view datasets, which have demonstrated the superiority of our approach over the state-of-the-art.