2016/05/20 by Jisu Kim, Kim, Jisu, Yen‐Chi Chen +7
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1605.06416
openalex publication_date 2016/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by assessing the statistical significance of topological features of an empirical cluster tree. We first study a variety of metrics that can be used to compare different trees, analyze their properties and assess their suitability for inference. We then propose methods to construct and summarize confidence sets for the unknown true cluster tree. We introduce a partial ordering on cluster trees which we use to prune some of the statistically insignificant features of the empirical tree, yielding interpretable and parsimonious cluster trees. Finally, we illustrate the proposed methods on a variety of synthetic examples and furthermore demonstrate their utility in the analysis of a Graft-versus-Host Disease (GvHD) data set.