一种用于K-medians选择聚类数量的惩罚准则
A penalized criterion for selecting the number of clusters for K-medians
AI总结：
本文针对受污染数据聚类中K-medians的聚类数量选择问题，提出一种基于惩罚风险最小化的准则，推导出合适的惩罚形式及oracle型不等式，并通过模拟研究验证其性能。
摘要：
聚类是一种常见的无监督机器学习技术，用于根据相似特征将数据点分组。本文关注受污染数据的无监督聚类，即由于K-medians具有稳健性而应优先于K-means的情形。更具体地说，我们聚焦于聚类中的一个常见问题：如何选择聚类数量？本文提出的答案是，将最优聚类数量的选择视为通过惩罚实现风险函数最小化。在本文中，我们为所提准则得到了合适的惩罚形式，并推导出相应的oracle型不等式。最后，在模拟研究中将该方法与不同类型的K-medians算法以及其他流行技术的性能进行了比较。所有研究的算法均可在CRAN上的R包Kmedians中获取。
英文摘要：
Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be preferred to K-means because of its robustness. More precisely, we concentrate on a common question in clustering: how to chose the number of clusters? The answer proposed here is to consider the choice of the optimal number of clusters as the minimization of a risk function via penalization. In this paper, we obtain a suitable penalty shape for our criterion and derive an associated oracle-type inequality. Finally, the performance of this approach with different types of K-medians algorithms is compared on a simulation study with other popular techniques. All studied algorithms are available in the R package Kmedians on CRAN.
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