Number of Clusters in a Dataset: A Regularized K-means Approach

• URL: http://arxiv.org/abs/2505.22991v1
• Date: Thu, 29 May 2025 01:58:44 GMT
• Title: Number of Clusters in a Dataset: A Regularized K-means Approach
• Authors: Behzad Kamgar-Parsi, Behrooz Kamgar-Parsi,
• Abstract summary: Regularized k-means algorithm is used to find the correct number of distinct clusters in datasets.<n>In this paper, we derive rigorous bounds for $lambda$ assuming clusters are em ideal.<n> Experiments show that the k-means algorithm with additive regularizer often yields multiple solutions.
• Score: 0.6445605125467572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\lambda k$, where $k$ is the number of clusters and $\lambda$ a positive coefficient. Currently, there are no principled guidelines for setting a value for the critical hyperparameter $\lambda$. In this paper, we derive rigorous bounds for $\lambda$ 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.

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