COKE: Core Kernel for More Efficient Approximation of Kernel Weights in Multiple Kernel Clustering

Weixuan Liang, Xinwang Liu, Ke Liang, Jiyuan Liu, En Zhu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:37257-37280, 2025.

Abstract

Inspired by the well-known coreset in clustering algorithms, we introduce the definition of the core kernel for multiple kernel clustering (MKC) algorithms. The core kernel refers to running MKC algorithms on smaller-scale base kernel matrices to obtain kernel weights similar to those obtained from the original full-scale kernel matrices. Specifically, the core kernel refers to a set of kernel matrices of size $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ that perform MKC algorithms on them can achieve a $(1+\varepsilon)$-approximation for the kernel weights. Subsequently, we can leverage approximated kernel weights to obtain a theoretically guaranteed large-scale extension of MKC algorithms. In this paper, we propose a core kernel construction method based on singular value decomposition and prove that it satisfies the definition of the core kernel for three mainstream MKC algorithms. Finally, we conduct experiments on several benchmark datasets to verify the correctness of theoretical results and the efficiency of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liang25j, title = {{COKE}: Core Kernel for More Efficient Approximation of Kernel Weights in Multiple Kernel Clustering}, author = {Liang, Weixuan and Liu, Xinwang and Liang, Ke and Liu, Jiyuan and Zhu, En}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {37257--37280}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/liang25j/liang25j.pdf}, url = {https://proceedings.mlr.press/v267/liang25j.html}, abstract = {Inspired by the well-known coreset in clustering algorithms, we introduce the definition of the core kernel for multiple kernel clustering (MKC) algorithms. The core kernel refers to running MKC algorithms on smaller-scale base kernel matrices to obtain kernel weights similar to those obtained from the original full-scale kernel matrices. Specifically, the core kernel refers to a set of kernel matrices of size $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ that perform MKC algorithms on them can achieve a $(1+\varepsilon)$-approximation for the kernel weights. Subsequently, we can leverage approximated kernel weights to obtain a theoretically guaranteed large-scale extension of MKC algorithms. In this paper, we propose a core kernel construction method based on singular value decomposition and prove that it satisfies the definition of the core kernel for three mainstream MKC algorithms. Finally, we conduct experiments on several benchmark datasets to verify the correctness of theoretical results and the efficiency of the proposed method.} }
Endnote
%0 Conference Paper %T COKE: Core Kernel for More Efficient Approximation of Kernel Weights in Multiple Kernel Clustering %A Weixuan Liang %A Xinwang Liu %A Ke Liang %A Jiyuan Liu %A En Zhu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-liang25j %I PMLR %P 37257--37280 %U https://proceedings.mlr.press/v267/liang25j.html %V 267 %X Inspired by the well-known coreset in clustering algorithms, we introduce the definition of the core kernel for multiple kernel clustering (MKC) algorithms. The core kernel refers to running MKC algorithms on smaller-scale base kernel matrices to obtain kernel weights similar to those obtained from the original full-scale kernel matrices. Specifically, the core kernel refers to a set of kernel matrices of size $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ that perform MKC algorithms on them can achieve a $(1+\varepsilon)$-approximation for the kernel weights. Subsequently, we can leverage approximated kernel weights to obtain a theoretically guaranteed large-scale extension of MKC algorithms. In this paper, we propose a core kernel construction method based on singular value decomposition and prove that it satisfies the definition of the core kernel for three mainstream MKC algorithms. Finally, we conduct experiments on several benchmark datasets to verify the correctness of theoretical results and the efficiency of the proposed method.
APA
Liang, W., Liu, X., Liang, K., Liu, J. & Zhu, E.. (2025). COKE: Core Kernel for More Efficient Approximation of Kernel Weights in Multiple Kernel Clustering. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:37257-37280 Available from https://proceedings.mlr.press/v267/liang25j.html.

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