无需设定聚类数k，自动确定最优聚类数的新型聚类算法。
K*-Means: A Parameter-free Clustering Algorithm
- 基于最小描述长度原则动态调整聚类数，边分边合优化目标。
- 实验显示在未知k时性能显著优于传统方法，且能准确估计k。
- 收敛性有理论保证，运行效率与现有方法相当，可扩展性强。
聚类是广泛使用的机器学习技术，但其效果常受限于需预先设定聚类数k，或依赖隐含决定k的阈值。本文提出k*-means，一种无需设置k或其他参数的新聚类算法。该算法利用最小描述长度原则，通过不断分裂与合并聚类来自动确定最优聚类数k*，同时优化标准k-means目标。我们证明了k*-means保证收敛，并实验表明其在k未知场景下显著优于现有方法。此外，它能准确估计k，实测运行时间与现有方法相当，且随数据集规模良好扩展。
原文摘要 · Abstract (English)
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a novel clustering algorithm that eliminates the need to set k or any other parameters. Instead, it uses the minimum description length principle to automatically determine the optimal number of clusters, k*, by splitting and merging clusters while also optimising the standard k-means objective. We prove that k*-means is guaranteed to converge and demonstrate experimentally that it significantly outperforms existing methods in scenarios where k is unknown. We also show that it is accurate in estimating k, and that empirically its runtime is competitive with existing methods, and scales well with dataset size.
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