高维环境下层次聚类的渐近性质

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
Kento Egashira , Kazuyoshi Yata , Makoto Aoshima
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引用次数: 0

摘要

本文在两个独立总体的情况下,定义并研究了从大样本到高维数的几种渐近设置下,层次聚类的三种渐近行为。我们继续当前的理解在高维,低样本大小(HDLSS)设置的层次聚类的渐近性质。对于高维数据,在温和和实际的环境下证明了层次聚类的渐近特性,并进行了仿真研究和层次聚类性能的讨论。此外,从理论上研究了维数和样本量都趋近于无穷大时的层次聚类,并在多类HDLSS设置中推广了考虑层次聚类的潜在总体数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic properties of hierarchical clustering in high-dimensional 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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来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
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