Enhanced Residual Tensor Norm Minimization for Multiview Subspace Clustering

The low-rank tensor constraint is widely used in multiview subspace clustering (MSC) and has demonstrated promising clustering performance on many datasets. The key challenges in most existing low-rank tensor constraint-based methods include: 1) the choice of surrogate functions for the tensor rank and 2) the rotation operation applied to the tensor formed by stacking multiple subspace representations along the third mode. The latter plays a critical role in enhancing clustering performance in multiview settings. In this work, we rethink the low-rank tensor constraint and present the enhanced residual tensor norm (ERTN) for multiview subspace clustering, dubbed ERTN-MSC. To be specific, ERTN employs a novel surrogate for the tensor rank, based on the residual learning of singular values, which facilitates better exploitation of the structural information in multiview data. Furthermore, ERTN applies the tensor-singular value decomposition (t-SVD) on three modes of the tensor constructed by multiple subspaces, which generalizes the rotation operation of tensor and enables comprehensive exploration of both intraview information and interview information of multiview data. An augmented Lagrangian multiplier-based algorithm with a convergence guarantee is designed for optimization. Experiments conducted on several real-world multiview datasets demonstrate the effectiveness and competitiveness of our ERTN-MSC.