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Spectral clustering via half-quadratic optimization

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Abstract

Spectral clustering has been demonstrated to often outperform K-means clustering in real applications because it improves the similarity measurement of K-means clustering. However, previous spectral clustering method still suffers from the following issues: 1) easily being affected by outliers; 2) constructing the affinity matrix from original data which often contains redundant features and outliers; and 3) unable to automatically specify the cluster number. This paper focuses on address these issues by proposing a new clustering algorithm along with the technique of half-quadratic optimization. Specifically, the proposed method learns the affinity matrix from low-dimensional space of original data, which is obtained by using a robust estimator to remove the influence of outliers as well as a sparsity regularization to remove redundant features. Moreover, the proposed method employs the ℓ2,1-norm regularization to automatically learn the cluster number according to the data distribution. Experimental results on both synthetic and real data sets demonstrated that the proposed method outperforms the state-of-the-art methods in terms of clustering performance.

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Acknowledgments

This work is partially supported by the China Key Research Program (Grant No: 2016YFB1000905), the Natural Science Foundation of China (Grants No: 61836016, 61876046, 61573270, and 61672177), the Project of Guangxi Science and Technology (GuiKeAD17195062), the Guangxi Collaborative Innovation Center of Multi-Source Information Integration and Intelligent Processing, the Guangxi High Institutions Program of Introducing 100 High-Level Overseas Talents, the Strategic Research Excellence Fund at Massey University, the Marsden Fund of New Zealand (Grant No: MAU1721), and the Research Fund of Guangxi Key Lab of Multisource Information Mining and Security (18-A-01-01).

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, 611731, China

    Xiaofeng Zhu

  2. SNCS of Massey University Auckland Campus, Auckland, 0745, New Zealand

    Xiaofeng Zhu & Jiangzhang Gan

  3. Guangxi Key Lab of MIMS, Guangxi Normal University, Guilin, 541004, China

    Guangquan Lu & Jiaye Li

  4. Central South University, Changsha, 410083, China

    Shichao Zhang

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  1. Xiaofeng Zhu
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  2. Jiangzhang Gan
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  3. Guangquan Lu
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Correspondence to Shichao Zhang.

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This article belongs to the Topical Collection: Computational Social Science as the Ultimate Web Intelligence

Guest Editors: Xiaohui Tao, Juan D. Velasquez, Jiming Liu, and Ning Zhong

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Zhu, X., Gan, J., Lu, G. et al. Spectral clustering via half-quadratic optimization. World Wide Web 23, 1969–1988 (2020). https://doi.org/10.1007/s11280-019-00731-8

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