Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915078158155776 |
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| author | Du, Liang Jiang, Henghui Li, Xiaodong Guo, Yiqing Chen, Yan Li, Feijiang Zhou, Peng Qian, Yuhua |
| author_facet | Du, Liang Jiang, Henghui Li, Xiaodong Guo, Yiqing Chen, Yan Li, Feijiang Zhou, Peng Qian, Yuhua |
| contents | 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 . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion Du, Liang Jiang, Henghui Li, Xiaodong Guo, Yiqing Chen, Yan Li, Feijiang Zhou, Peng Qian, Yuhua Machine Learning Artificial Intelligence 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 . |
| title | Sharper Error Bounds in Late Fusion Multi-view Clustering Using Eigenvalue Proportion |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2412.18207 |