Tensor schatten-p norm guided incomplete multi-view self-representation clustering

Abstract

Incomplete multi-view clustering (IMC), which aims to handle incomplete data with missing views, has recently received more attention. According to the investigation of the existing IMC methods, they have at least one of the four limitations. First, some methods do not recover the missing view-specific information. Second, some approaches rely on fixed similarity graphs of incomplete views. Third, some methods need a separate spectral clustering step to produce the final cluster indicator. Last, most works utilize tensor nuclear norm to characterize the low-rank property of multi-view representation. These four limitations degrade the clustering performance. Hence, this paper proposes a tensor schatten-p norm guided incomplete multi-view self-representation clustering (TIMSRC) method to handle these four limitations simultaneously. TIMSRC models the missing instances as a data matrix for each view. And it integrates the missing samples inferring and complete self-representation graph learning into a unified framework. TIMSRC adopts a multi-view spectral clustering with adaptive weights to mine the semantic information while considering the contributions of multiple self-representing graphs. TIMSRC exploits the tensor schatten-p norm to enhance the low-rank property of a three-order tensor constructed with multiple self-representation graphs. We present an optimization algorithm to solve the objective function. The experiments demonstrate that TIMSRC outperforms the state-of-the-art IMC approaches.