一种带离群点的层次聚类算法的统计分析
Statistical analysis of a hierarchical clustering algorithm with outliers
摘要：
众所周知，经典的单连接算法通常无法识别存在离群值的聚类。在本文中，我们提出了一个新的版本，这种算法，我们研究了它的数学性能。特别是，我们建立了一个预言型不等式，确保我们的程序允许恢复集群的离群值的分布在最小的假设下，具有很大的概率。我们推导出这个不等式的一致性和我们的算法在各种情况下的收敛速度。我们的方法的性能也通过模拟研究和模拟数据与经典的聚类算法的比较进行了评估。
英文摘要：
It is well known that the classical single linkage algorithm usually fails to identify clusters in the presence of outliers. In this paper, we propose a new version of this algorithm, and we study its mathematical performances. In particular, we establish an oracle type inequality which ensures that our procedure allows to recover the clusters with large probability under minimal assumptions on the distribution of the outliers. We deduce from this inequality the consistency and some rates of convergence of our algorithm for various situations. Performances of our approach is also assessed through simulation studies and a comparison with classical clustering algorithms on simulated data is also presented.
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