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

2024-12-24

AI Summary

Multi-view clustering suffers from severe noise and redundant partitions, alongside inadequate modeling of high-order cross-view correlations. Method: This paper proposes a theoretical error-bound framework based on the principal eigenvalue ratio and designs a low-pass graph filtering strategy to enhance the robustness and discriminability of late fusion. It integrates local Rademacher complexity analysis, multilinear k-means, multiple kernel learning, and spectral graph theory. Contribution/Results: We establish, for the first time, an $O(1/n)$ convergence rate for the generalization error of multi-kernel k-means—improving upon the prior $O(sqrt{k/n})$ bound—and introduce the principal eigenvalue ratio as an optimizable metric for fusion quality. Evaluated on standard benchmarks, our method achieves an average 3.2% improvement in clustering accuracy and demonstrates significantly enhanced robustness against both feature-level noise and view-level missingness.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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 .

Problem

• Multi-view Clustering
• Redundancy Handling
• Deep Correlation Capturing

Innovation

• Multi-view Clustering
• K-means Optimization
• Noise Reduction