Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 124, Issue -, Pages 465-479Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2013.11.010
Keywords
Hierarchical clustering; Linkage function; Clustering behavior
Categories
Funding
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007543, 1016441] Funding Source: National Science Foundation
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Modern day science presents many challenges to data analysts. Advances in data collection provide very large (number of observations and number of dimensions) data sets. In many areas of data analysis an informative task is to find natural separations of data into homogeneous groups, i.e. clusters. In this paper we study the asymptotic behavior of hierarchical clustering in situations where both sample size and dimension grow to infinity. We derive explicit signal vs noise boundaries between different types of clustering behaviors. We also show that the clustering behavior within the boundaries is the same across a wide spectrum of asymptotic settings. (C) 2013 Elsevier Inc. All rights reserved.
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