arXiv:2607.25295cs.LG2026-07

提出新方法打破样本顺序依赖,让多视图聚类更稳定可靠。

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

论文配图:Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning
图 1 · 摘自论文原文
  • 用图谱基替代FFT,数据驱动捕捉内在结构,不再依赖样本排序。
  • 在随机排列样本后仍保持高性能,验证了方法的鲁棒性。
  • 适合对聚类结果稳定性要求高的实际应用,如医疗或金融数据。

张量多视图聚类(TMC)因能捕捉多视图间的高阶相关性而表现优异。现有基于t-SVD的TMC框架通常在样本模式上使用快速傅里叶变换(FFT)施加频域低秩约束,但本文揭示该设计隐含依赖于样本按类别排列的周期性假设。当样本顺序被随机打乱时,原有方法性能显著下降。这种对样本顺序的敏感性违背聚类任务的置换不变性,表明部分性能提升可能源于人为排列而非真实结构建模。为此,本文系统分析该现象的代数与谱机制,并提出基于图傅里叶变换(GFT)的图谱低秩张量学习框架,以数据驱动的图谱基替代固定傅里叶基,从而无需依赖特定样本顺序即可捕获内在流形结构。此外,还设计了锚点变体以高效处理大规模数据。在多个基准上的实验验证了结论,并证明所提方法优于现有先进TMC方法。

原文摘要 · Abstract (English)

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.

多视图聚类张量学习图神经网络鲁棒性

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