Graph-theoretic procedures for dimension identification

JOURNAL OF MULTIVARIATE ANALYSIS

卷:81

Article

Brito, MR ; Quiroz, AJ ; Yukich, JE

关键词: proximity data;    multidimensional scaling;    k-nearest-neighbors graph;    dimensionality reduction;   

DOI  :  10.1006/jmva.2001.1992

来源: Elsevier

【 摘 要 】

We consider the problem of identifying the dimension in which a sample of data points lives, when only their interpoint distances are known. We study as a random variable the average reach of vertices in the k-nearest-neighbors graph associated to the interpoint distance matrix, and we show how this variable can be used to accurately (from a probabilistic viewpoint) identify the unknown dimension at low computational cost. We discuss results that serve as the theoretical foundation for the methodology proposed. We illustrate how our method can help in dimension reduction procedures. (C) 2001 Elsevier Science (USA).

【 授权许可】

Free