Intrinsic Dimensionality Estimation of High-Dimension, Low Sample Size Data with D-Asymptotics

被引：15

作者：

Yata, Kazuyoshi ^{[2
]}

Aoshima, Makoto ^{[1
]}

机构：

[1] Univ Tsukuba, Inst Math, Ibaraki 3058571, Japan

[2] Univ Tsukuba, Grad Sch Pure & Appl Sci, Ibaraki 3058571, Japan

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2010年 / 39卷 / 8-9期

基金：

日本学术振兴会;

关键词：

Dual covariance matrix; Effective dimension; HDLSS; Large p small n; Maximum eigenvalue; GEOMETRIC REPRESENTATION; LARGEST EIGENVALUE;

D O I：

10.1080/03610920903121999

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

High-dimension, low sample size (HDLSS) data are becoming common in various fields such as genetic microarrays, medical imaging, text recognition, finance, chemometrics, and so on. Such data have surprising and often counterintuitive geometric structures because of the high-dimensional noise that dominates and corrupts the local neighborhoods. In this article, we estimate the intrinsic dimension (ID) that allows one to distinguish between deterministic chaos and random noise of HDLSS data. A new ID estimating methodology is given and its properties are studied by using a d-asymptotic approach.

引用

页码：1511 / 1521

页数：11

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