Tensor multi-subspace learning for robust tensor-based multi-view clustering

Tensor-based multi-view clustering (TMVC) has garnered considerable attention for its efficacy in managing data that originate from multiple perspectives. However, the presence of noise in empirical datasets often undermines the reliability and robustness of the affinity matrices generated through these methods. To address this challenge, we introduce an innovative approach termed tensor multi-subspace learning (TMSL). Our methodology commences with the employment of a typical TMVC method to produce self-representation matrices for each view. Nevertheless, the affinity matrix derived from these self-representation matrices frequently falls short of the desired levels of dependability and robustness. To uncover the intrinsic architecture of the data within the tensor subspace, we harness the concept of tensor low-rank representation. This enables us to extract a higher-dimensional representation of multi-view data, thereby yielding a multi-subspace representation tensor that is both reliable and robust. These two stages are then seamlessly integrated into a unified framework and are resolved by employing the augmented Lagrangian algorithm. Notably, the TMSL method also serves as an effective post-processing strategy capable of being applied to various TMVC methods to augment their performance. Empirical evidence has established that TMSL outperforms other contemporary methods, and the post-processing strategy has proven to be an effective unified approach that can be extended to other TMVC methods.