Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion
This work addresses limitations in multi-view clustering for data integration, offering incremental improvements in error bounds and practical performance.
The paper tackles the problem of noisy and redundant partitions in Late Fusion Multi-View Clustering by developing a theoretical framework that improves generalization error bounds, achieving a convergence rate of O(1/n) compared to the previous O(sqrt(k/n)), and proposes a low-pass graph filtering method that enhances clustering accuracy and robustness on benchmark datasets.
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 .