Intrinsic dimension estimation of manifolds by incising balls

被引：39

作者：

Fan, Mingyu ^{[2
]}

Qiao, Hong ^{[3
]}

Zhang, Bo ^{[1
]}

机构：

[1] Chinese Acad Sci, AMSS, Inst Appl Math, LSEC, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, AMSS, Inst Appl Math, Grad Sch, Beijing 100190, Peoples R China

[3] Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China

来源：

PATTERN RECOGNITION | 2009年 / 42卷 / 05期

关键词：

Nonlinear dimensionality reduction; Manifold learning; Intrinsic dimension estimation; Data mining; REDUCTION; EIGENMAPS;

D O I：

10.1016/j.patcog.2008.09.016

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Dimensionality reduction is a very important tool in data mining. Intrinsic dimension of data sets is a key parameter for dimensionality reduction. However, finding the correct intrinsic dimension is a challenging task. In this paper, a new intrinsic dimension estimation method is presented. The estimator is derived by finding the exponential relationship between the radius of an incising ball and the number of samples included in the ball. The method is compared with the previous dimension estimation methods. Experiments have been conducted on synthetic and high dimensional image data sets and on data sets of the Santa Fe time series competition, and the results show that the new method is accurate and robust. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：780 / 787

页数：8

共 24 条

[1] [Anonymous], 2018, TIME SERIES PREDICTI
[2] [Anonymous], 2001, MULTIDIMENSIONAL SCA
[3] Laplacian eigenmaps for dimensionality reduction and data representation
Belkin, M
Niyogi, P
[J]. NEURAL COMPUTATION, 2003, 15 (06) : 1373 - 1396
[4] Intrinsic dimensionality estimation with optimally topology preserving maps
Bruske, J
Sommer, G
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1998, 20 (05) : 572 - 575
[5] Estimating the intrinsic dimension of data with a fractal-based method
Camastra, F
Vinciarelli, A
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2002, 24 (10) : 1404 - 1407
[6] Data dimensionality estimation methods: a survey
Camastra, F
[J]. PATTERN RECOGNITION, 2003, 36 (12) : 2945 - 2954
[7] Intrinsic dimension estimation of data: An approach based on Grassberger-Procaccia's algorithm
Camastra, F
Vinciarelli, A
[J]. NEURAL PROCESSING LETTERS, 2001, 14 (01) : 27 - 34
[8] Geodesic entropic graphs for dimension and entropy estimation in manifold learning
Costa, JA
Hero, AO
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2004, 52 (08) : 2210 - 2221
[9] COSTA JA, 2005, IEEE WORKSH STAT SIG, P417
[10] Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
Donoho, DL
Grimes, C
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2003, 100 (10) : 5591 - 5596

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