Permutation Sensitivity in t-SVD-based Multi-view Clustering

Tensor Singular Value Decomposition (t-SVD) has achieved strong empirical performance in multi-view clustering (MVC) and its incomplete setting (IMVC). However, the success of this framework heavily relies on the implicit dependency of its Fourier transform on the sample sequence, which raises serious concerns regarding sample-permutation sensitivity. To address this issue, we first formulate the permutation sensitivity in multi-view clustering by providing rigorous definitions of invariance at both the outcome level and the representation level. Secondly, by revealing the potential structural risks associated with the fixed Fourier basis, we propose two plug-and-play strategies: (1) an Order-Restoration strategy (K-OR), designed to reconstruct a locally smooth signal favored by the Fourier transform; and (2) an equivariant t-SVD framework (Cor-SVD), which fundamentally resolves the sensitivity of the Fourier transform by replacing fixed bases with data-dependent, equivariant transforms. Finally, we design a controlled permutation evaluation protocol to verify the robustness of tensorial clustering models. Extensive experiments demonstrate the significant performance variability of existing t-SVD-based methods under sample permutations, whereas our approaches substantially improve their permutation robustness while maintaining competitive clustering performance. These findings reveal critical vulnerabilities in current tensorial clustering benchmarks and underscore the necessity of the proposed method for achieving robust performance and reliable evaluation.