Enhancing Kernel Power K-means: Scalable and Robust Clustering with Random Fourier Features and Possibilistic Method
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912707077210112 |
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| author | Chen, Yixi Liang, Weixuan Liu, Tianrui Huang, Jun-Jie Li, Ao Zhu, Xueling Liu, Xinwang |
| author_facet | Chen, Yixi Liang, Weixuan Liu, Tianrui Huang, Jun-Jie Li, Ao Zhu, Xueling Liu, Xinwang |
| contents | Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive data, and (2) the lack of authentic centroid-sample assignment learning reduces its noise robustness. To overcome these challenges, we propose RFF-KPKM, introducing the first approximation theory for applying random Fourier features (RFF) to KPKM. RFF-KPKM employs RFF to generate efficient, low-dimensional feature maps, bypassing the need for the whole kernel matrix. Crucially, we are the first to establish strong theoretical guarantees for this combination: (1) an excess risk bound of $\mathcal{O}(\sqrt{k^3/n})$, (2) strong consistency with membership values, and (3) a $(1+\varepsilon)$ relative error bound achievable using the RFF of dimension $\mathrm{poly}(\varepsilon^{-1}\log k)$. Furthermore, to improve robustness and the ability to learn multiple kernels, we propose IP-RFF-MKPKM, an improved possibilistic RFF-based multiple kernel power $k$-means. IP-RFF-MKPKM ensures the scalability of MKPKM via RFF and refines cluster assignments by combining the merits of the possibilistic membership and fuzzy membership. Experiments on large-scale datasets demonstrate the superior efficiency and clustering accuracy of the proposed methods compared to the state-of-the-art alternatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhancing Kernel Power K-means: Scalable and Robust Clustering with Random Fourier Features and Possibilistic Method Chen, Yixi Liang, Weixuan Liu, Tianrui Huang, Jun-Jie Li, Ao Zhu, Xueling Liu, Xinwang Machine Learning Artificial Intelligence Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive data, and (2) the lack of authentic centroid-sample assignment learning reduces its noise robustness. To overcome these challenges, we propose RFF-KPKM, introducing the first approximation theory for applying random Fourier features (RFF) to KPKM. RFF-KPKM employs RFF to generate efficient, low-dimensional feature maps, bypassing the need for the whole kernel matrix. Crucially, we are the first to establish strong theoretical guarantees for this combination: (1) an excess risk bound of $\mathcal{O}(\sqrt{k^3/n})$, (2) strong consistency with membership values, and (3) a $(1+\varepsilon)$ relative error bound achievable using the RFF of dimension $\mathrm{poly}(\varepsilon^{-1}\log k)$. Furthermore, to improve robustness and the ability to learn multiple kernels, we propose IP-RFF-MKPKM, an improved possibilistic RFF-based multiple kernel power $k$-means. IP-RFF-MKPKM ensures the scalability of MKPKM via RFF and refines cluster assignments by combining the merits of the possibilistic membership and fuzzy membership. Experiments on large-scale datasets demonstrate the superior efficiency and clustering accuracy of the proposed methods compared to the state-of-the-art alternatives. |
| title | Enhancing Kernel Power K-means: Scalable and Robust Clustering with Random Fourier Features and Possibilistic Method |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2511.10392 |