Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 199, Issue -, Pages -Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2023.105251
Keywords
Clustering behavior; High-dimension low-sample-size; Multiclass; Ward's linkage function
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This study investigates the asymptotic properties of hierarchical clustering in different settings, including high-dimensional, low-sample-size scenarios. The results show that hierarchical clustering exhibits good asymptotic properties under practical settings for high-dimensional data. The study also extends the analysis to consider scenarios where both the dimension and sample size approach infinity, and generalizes the concept of populations in multiclass HDLSS settings.
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.
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