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Clustering via multiple kernel k-means coupled graph and enhanced tensor learning

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Abstract

Kernel k-means based and spectral clustering (SC) based multi-kernel clustering (MKC) has been widely used in recent years due to the efficiency in grouping nonlinear data. However, (1) the methods based on the above two categories only focus on clustering indicator matrix learning or graph learning, few of them have noticed the connection between the two; and (2) it is hard for existing methods to consider the high-order similarities of all pre-defined base kernels, which leads to the waste of inter-kernel information. To solve these problems, we propose kernel k-means coupled graph and enhanced tensor learning (KKG-ETL). Concretely, a new graph learning paradigm, kernel k-means coupled graph (KKG), is proposed to establish the theoretical relation between clustering indicator matrix and affinity graph. Therefore, a better candidate affinity graph can be obtained for each base kernel. Then, enhanced tensor learning (ETL) is proposed to capture the high-order similarities of all candidate graphs via an auto-weighted Schatten p-norm. In this framework, we integrate the indication properties of kernel k-means and the manifold excavation capability of SC, while exploring the high-order similarities among all kernels. Comprehensive experiments on 8 widely used datasets verify the validity and feasibility of our proposed KKG-ETL.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 62106209), the Sichuan Science and Technology Program (Grant no. 2021YJ0083), and the State Key Lab. Foundation for Novel Software Technology of Nanjing University (Grant no. KFKT2021B23), and the Open Research Fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (Grant no. GML-KF-22-04).This work was supported by the National Natural Science Foundation of China (Grant nos. 62106209), the Sichuan Science and Technology Program (Grant no. 2021YJ0083), and the State Key Lab. Foundation for Novel Software Technology of Nanjing University (Grant no. KFKT2021B23), and the Open Research Fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (Grant no. GML-KF-22-04).

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Authors and Affiliations

  1. School of Information Engineering and School of National Defense Science and Technology, Southwest University of Science and Technology, Mianyang, 621010, China

    Jiali You, Chiyu Han, Zhenwen Ren, Haoran Li & Xiaojian You

  2. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210008, China

    Zhenwen Ren

  3. Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, 518060, China

    Zhenwen Ren

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  1. Jiali You
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  2. Chiyu Han
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  5. Xiaojian You
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Correspondence to Zhenwen Ren or Xiaojian You.

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You, J., Han, C., Ren, Z. et al. Clustering via multiple kernel k-means coupled graph and enhanced tensor learning. Appl Intell 53, 2564–2575 (2023). https://doi.org/10.1007/s10489-022-03679-x

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