Dual Tensor Low-Rank Representation for Subspace Clustering

Benefiting from the powerful tensor techniques, the tensor low-rank representation has been proposed to construct sophisticated subspace clustering models. Existing tensor low-rank representation methods predominantly rely on a single low-rank prior to reconstruct the row space, which is instrumental in determining the subspace membership of samples by the row space information. However, this strategy neglects the column space and would lead to a subspace information loss. To address this issue, we propose a Dual Tensor Low-Rank Representation method (DTLRR), the first subspace clustering framework to theoretically recover both row and column subspaces simultaneously. Particularly, not simply formulating a dual self-representation model, we instead prove the recovery of both row and column spaces via a unified theoretical framework. Then, we impose low-rank constraints on the two corresponding affinity tensors to effectively capture high-order correlations. Meanwhile, we theoretically demonstrate the existence of compact dictionary tensors within the dual self-representation framework, which effectively eliminates the null spaces of the affinity tensors and significantly reduces computational complexity. Furthermore, an efficient Alternating Direction Method of Multipliers (ADMM) algorithm is designed to solve the proposed DTLRR model with guaranteed convergence. Extensive experiments validate the superior performance of the proposed DTLRR in data clustering, hyperspectral image denoising, and hyperspectral anomaly detection.