Double Discrete Cosine Transform-Oriented Multi-view Subspace Clustering

Low-rank tensor representation with the tensor nuclear norm has been rising in popularity in multi-view subspace clustering (MVSC), in which the tensor nuclear norm is commonly implemented using discrete Fourier transform (DFT). Unfortunately, existing DFT-oriented MVSC methods may provide unsatisfactory results since (1) DFT exploits complex arithmetic in the Fourier domain, usually resulting in high tubal tensor rank, and (2) local structural information is rarely considered. To solve these problems, in this paper, we propose a novel double discrete cosine transform (DCT)-oriented multi-view subspace clustering (D2CTMSC) method, in which the first DCT aims to derive the tensor nuclear norm without complex arithmetic while the second DCT aims to explore the local structure of the self-representation tensor, such that the essential low-rankness and sparsity embedding in multi-view features can be thoroughly exploited. Moreover, we design an effective alternating iteration strategy to solve the proposed model. Experimental results on four types of multi-view datasets (News stories, Face images, Scene images, and Generic objects) demonstrate the superiority of the D2CTMSC method compared with DFT-based methods and other state-of-the-art clustering methods.