发表机构
Griffith University; The Hong Kong University of Science and Technology; Beijing Jiaotong University（格里菲斯大学; 香港科技大学; 北京交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究张量多视图聚类中基于t-SVD方法依赖样本排列“周期性假设”的问题，提出基于图傅里叶变换的图谱低秩张量学习框架及锚点变体，不依赖特定排序捕捉内在结构，实验证明该方法性能优于现有方法。
AI 中文摘要
张量多视图聚类（TMC）因其能捕捉多视图高阶相关性而表现出色。多数基于t-SVD的TMC框架沿样本模式应用快速傅里叶变换（FFT）施加频域低秩约束。但本文揭示该设计严重依赖样本排列诱导的隐含“周期性假设”。一旦随机排列去除这种排序，现有基于t-SVD的TMC方法性能严重下降。本文系统研究此现象及其代数和谱机制，提出基于图傅里叶变换（GFT）的图谱低秩张量学习框架，用数据驱动的图谱基取代沿样本模式的固定傅里叶基，不依赖特定样本排序捕捉内在流形结构，还开发基于锚点的变体处理大规模数据集。大量实验验证了结果，表明所提方法性能优于现有TMC方法。
英文摘要
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.
