Unified K-Means Clustering with Label-Guided Manifold Learning

Qianqian Wang, Mengping Jiang, Zhengming Ding, Quanxue Gao
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:63186-63199, 2025.

Abstract

K-Means clustering is a classical and effective unsupervised learning method attributed to its simplicity and efficiency. However, it faces notable challenges, including sensitivity to random initial centroid selection, a limited ability to discover the intrinsic manifold structures within nonlinear datasets, and difficulty in achieving balanced clustering in practical scenarios. To overcome these weaknesses, we introduce a novel framework for K-Means that leverages manifold learning. This approach eliminates the need for centroid calculation and utilizes a cluster indicator matrix to align the manifold structures, thereby enhancing clustering accuracy. Beyond the traditional Euclidean distance, our model incorporates Gaussian kernel distance, K-nearest neighbor distance, and low-pass filtering distance to effectively manage data that is not linearly separable. Furthermore, we introduce a balanced regularizer to achieve balanced clustering results. The detailed experimental results demonstrate the efficacy of our proposed methodology.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25ao, title = {Unified K-Means Clustering with Label-Guided Manifold Learning}, author = {Wang, Qianqian and Jiang, Mengping and Ding, Zhengming and Gao, Quanxue}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {63186--63199}, 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/wang25ao/wang25ao.pdf}, url = {https://proceedings.mlr.press/v267/wang25ao.html}, abstract = {K-Means clustering is a classical and effective unsupervised learning method attributed to its simplicity and efficiency. However, it faces notable challenges, including sensitivity to random initial centroid selection, a limited ability to discover the intrinsic manifold structures within nonlinear datasets, and difficulty in achieving balanced clustering in practical scenarios. To overcome these weaknesses, we introduce a novel framework for K-Means that leverages manifold learning. This approach eliminates the need for centroid calculation and utilizes a cluster indicator matrix to align the manifold structures, thereby enhancing clustering accuracy. Beyond the traditional Euclidean distance, our model incorporates Gaussian kernel distance, K-nearest neighbor distance, and low-pass filtering distance to effectively manage data that is not linearly separable. Furthermore, we introduce a balanced regularizer to achieve balanced clustering results. The detailed experimental results demonstrate the efficacy of our proposed methodology.} }
Endnote
%0 Conference Paper %T Unified K-Means Clustering with Label-Guided Manifold Learning %A Qianqian Wang %A Mengping Jiang %A Zhengming Ding %A Quanxue Gao %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-wang25ao %I PMLR %P 63186--63199 %U https://proceedings.mlr.press/v267/wang25ao.html %V 267 %X K-Means clustering is a classical and effective unsupervised learning method attributed to its simplicity and efficiency. However, it faces notable challenges, including sensitivity to random initial centroid selection, a limited ability to discover the intrinsic manifold structures within nonlinear datasets, and difficulty in achieving balanced clustering in practical scenarios. To overcome these weaknesses, we introduce a novel framework for K-Means that leverages manifold learning. This approach eliminates the need for centroid calculation and utilizes a cluster indicator matrix to align the manifold structures, thereby enhancing clustering accuracy. Beyond the traditional Euclidean distance, our model incorporates Gaussian kernel distance, K-nearest neighbor distance, and low-pass filtering distance to effectively manage data that is not linearly separable. Furthermore, we introduce a balanced regularizer to achieve balanced clustering results. The detailed experimental results demonstrate the efficacy of our proposed methodology.
APA
Wang, Q., Jiang, M., Ding, Z. & Gao, Q.. (2025). Unified K-Means Clustering with Label-Guided Manifold Learning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:63186-63199 Available from https://proceedings.mlr.press/v267/wang25ao.html.

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