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This paper critiques the reliance on the periodicity assumption in tensorial multi-view clustering (TMC) frameworks that utilize t-SVD and FFT for low-rank constraints, revealing that performance degrades significantly when sample ordering is randomized. The authors introduce a graph-spectral low-rank tensor learning framework that employs the Graph Fourier Transform (GFT) to eliminate dependency on sample arrangement, thereby capturing intrinsic manifold structures. Extensive experiments show that their approach not only addresses the identified flaws but also achieves competitive or superior performance against existing TMC methods across various benchmarks.
Randomly permuting samples reveals that existing TMC methods may be misleadingly reliant on privileged sample arrangements, leading to severe performance drops.
Tensorial multi-view clustering (TMC) has achieved strong performance due to its ability to capture high-order correlations across multiple views. Most existing t-SVD-based TMC frameworks apply the Fast Fourier Transform (FFT) along the sample mode to impose frequency-domain low-rank constraints. However, we reveal that this widely adopted design critically relies on an implicit ``periodicity assumption''induced by the sample arrangement. When samples are ordered by class, neighboring indices tend to be semantically similar, creating artificial local continuity along the sample mode and a favorable spectral structure for FFT-based low-rank regularization. Once this ordering is removed by random permutation, existing t-SVD-based TMC methods suffer severe performance degradation. This strong sensitivity to class ordering conflicts with the permutation-invariant nature of clustering and indicates that part of the reported performance may be attributed to a privileged sample arrangement rather than genuine high-order structure modeling. In this paper, we systematically investigate this phenomenon and its underlying algebraic and spectral mechanisms. To address this fundamental flaw, we further propose a graph-spectral low-rank tensor learning framework based on the Graph Fourier Transform (GFT), which replaces the fixed Fourier basis along the sample mode with a data-driven graph spectral basis, thereby capturing the intrinsic manifold structure without relying on a particular sample ordering. Moreover, we develop an anchor-based variant to address large-scale datasets efficiently. Extensive experiments on various benchmarks validate our findings and demonstrate the competitive or superior performance of the proposed methods compared with state-of-the-art TMC approaches.
