提出新理论框架，提升多视图聚类的准确性和抗噪能力。
Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion
- 基于特征值比例分析误差边界，改进收敛速度
- 引入低通图滤波减少冗余与噪声，提升聚类精度
- 适合需要高鲁棒性聚类的多源数据研究者
多视图聚类（MVC）旨在融合多视角的互补信息以提升聚类性能。晚期融合多视图聚类（LFMVC）通过整合不同视图的聚类结果生成统一共识，已展现出良好效果。然而，现有方法在处理噪声和冗余划分时表现不佳，且难以捕捉跨视图的高阶相关性。为此，本文提出一种新的理论框架，分析多核k-means的泛化误差边界，结合局部Rademacher复杂度与主特征值比例，建立$\/mathcal{O}(1/n)$的收敛速率，显著优于现有$\/mathcal{O}(\sqrt{k/n})$的量级。基于此，我们在多线性k-means框架中设计低通图滤波策略，降低噪声与冗余，进一步优化主特征值比例，提升聚类准确率。在基准数据集上的实验表明，该方法在聚类性能与鲁棒性方面均优于当前最优方法。代码开源地址：https://github.com/csliangdu/GMLKM。
原文摘要 · Abstract (English)
Multi-view clustering (MVC) aims to integrate complementary information from multiple views to enhance clustering performance. Late Fusion Multi-View Clustering (LFMVC) has shown promise by synthesizing diverse clustering results into a unified consensus. However, current LFMVC methods struggle with noisy and redundant partitions and often fail to capture high-order correlations across views. To address these limitations, we present a novel theoretical framework for analyzing the generalization error bounds of multiple kernel $k$-means, leveraging local Rademacher complexity and principal eigenvalue proportions. Our analysis establishes a convergence rate of $\mathcal{O}(1/n)$, significantly improving upon the existing rate in the order of $\mathcal{O}(\sqrt{k/n})$. Building on this insight, we propose a low-pass graph filtering strategy within a multiple linear $k$-means framework to mitigate noise and redundancy, further refining the principal eigenvalue proportion and enhancing clustering accuracy. Experimental results on benchmark datasets confirm that our approach outperforms state-of-the-art methods in clustering performance and robustness. The related codes is available at https://github.com/csliangdu/GMLKM .
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