Asymptotic properties of hierarchical clustering in high-dimensional settings

Abstract

In this study, three asymptotic behaviors of hierarchical clustering are defined and studied with strict conditions under several asymptotic settings, from large samples to high dimensionality, when having two independent populations. We proceed with the current comprehension of the asymptotic properties of hierarchical clustering in high-dimensional, low-sample-size (HDLSS) settings. For high-dimensional data, the asymptotic properties of hierarchical clustering are demonstrated under mild and practical settings, and we present simulation studies and hierarchical clustering performance discussions. Furthermore, hierarchical clustering was theoretically investigated when both the dimension and sample size approach infinity, and we generalized a latent number of populations considering hierarchical clustering in multiclass HDLSS settings.