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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2505.22991 |
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| _version_ | 1866916765448011776 |
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| author | Kamgar-Parsi, Behzad Kamgar-Parsi, Behrooz |
| author_facet | Kamgar-Parsi, Behzad Kamgar-Parsi, Behrooz |
| contents | Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most common formulation of the regularization function is the additive linear term $λk$, where $k$ is the number of clusters and $λ$ a positive coefficient. Currently, there are no principled guidelines for setting a value for the critical hyperparameter $λ$. In this paper, we derive rigorous bounds for $λ$ assuming clusters are {\em ideal}. Ideal clusters (defined as $d$-dimensional spheres with identical radii) are close proxies for k-means clusters ($d$-dimensional spherically symmetric distributions with identical standard deviations). Experiments show that the k-means algorithm with additive regularizer often yields multiple solutions. Thus, we also analyze k-means algorithm with multiplicative regularizer. The consensus among k-means solutions with additive and multiplicative regularizations reduces the ambiguity of multiple solutions in certain cases. We also present selected experiments that demonstrate performance of the regularized k-means algorithms as clusters deviate from the ideal assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi, Behzad Kamgar-Parsi, Behrooz Machine Learning Computer Vision and Pattern Recognition 68 I.5.3 Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most common formulation of the regularization function is the additive linear term $λk$, where $k$ is the number of clusters and $λ$ a positive coefficient. Currently, there are no principled guidelines for setting a value for the critical hyperparameter $λ$. In this paper, we derive rigorous bounds for $λ$ assuming clusters are {\em ideal}. Ideal clusters (defined as $d$-dimensional spheres with identical radii) are close proxies for k-means clusters ($d$-dimensional spherically symmetric distributions with identical standard deviations). Experiments show that the k-means algorithm with additive regularizer often yields multiple solutions. Thus, we also analyze k-means algorithm with multiplicative regularizer. The consensus among k-means solutions with additive and multiplicative regularizations reduces the ambiguity of multiple solutions in certain cases. We also present selected experiments that demonstrate performance of the regularized k-means algorithms as clusters deviate from the ideal assumption. |
| title | Number of Clusters in a Dataset: A Regularized K-means Approach |
| topic | Machine Learning Computer Vision and Pattern Recognition 68 I.5.3 |
| url | https://arxiv.org/abs/2505.22991 |