Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion

TL;DR

This paper introduces a new theoretical framework for late fusion multi-view clustering that improves error bounds and proposes a graph filtering method to enhance clustering accuracy and robustness.

Contribution

It provides a novel analysis of generalization error bounds using eigenvalue proportions and local Rademacher complexity, and introduces a graph filtering strategy to improve clustering in noisy multi-view data.

Findings

Outperforms state-of-the-art methods in clustering accuracy

Achieves a convergence rate of O(1/n), better than previous O(√k/n)

Enhances robustness against noise and redundancy in multi-view clustering

Abstract

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 .