Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning

2026-07-28

AI Summary

This work addresses a critical yet overlooked limitation in existing tensor-based multi-view clustering methods that rely on the t-SVD framework: they implicitly assume a periodic structure in sample ordering, which violates the permutation invariance inherent to clustering tasks and leads to significant performance degradation on real-world unordered data. The study is the first to systematically identify and analyze this flaw, and proposes the first graph spectral low-rank tensor clustering approach that is independent of sample ordering. By replacing the fixed Fourier basis with a data-driven graph Fourier basis, the method effectively captures the intrinsic manifold structure of the data, while an anchor-point strategy enhances scalability for large-scale datasets. Extensive experiments demonstrate that the proposed method maintains stable performance under random sample permutations and consistently outperforms existing t-SVD-based approaches, achieving state-of-the-art results in multi-view clustering.

Abstract

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.

Problem

• tensorial multi-view clustering
• periodicity assumption
• sample ordering
• permutation invariance
• low-rank learning

Innovation

• graph Fourier transform
• tensorial multi-view clustering
• low-rank learning
• periodicity assumption
• anchor-based approximation