Tensorized scaled simplex representation for multi-view clustering

Tensor-based multi-view clustering, which incorporates high-order correlations among views, has emerged as a promising research direction. These methods aim to capture intrinsic structure through a tensor-based constraint and then construct an affinity matrix. However, when constructing the affinity matrix, the negative entries in the coefficient matrices are forced to be positive via absolute operation, which can inadvertently destroy the inherent relationships within the data. Furthermore, existing methods may lack the flexibility to effectively handle and fuse multiple views. To address these issues, we propose a novel approach called Tensorized Scaled Simplex Representation (TSSR) for multi-view clustering. TSSR leverages a low-rank tensor constraint to capture the consensus and complementary information among the views. Besides, it introduces the scaled simplex representation, ensuring non-negative coefficient matrices, thus preserving inherent relationships and enhancing flexibility. Thirdly, TSSR extends the scaling range of the affine constraint to capture authentic structural information. Finally, an auto-weighted strategy assigns ideal weights to diverse views, enabling them to contribute appropriately. We integrate these techniques into a unified framework solved by an iterative algorithm. Experimental results demonstrate that TSSR outperforms state-of-the-art methods in terms of performance and efficiency. The codes and datasets are available at https://github.com/bingly/TSSR.