Estimating the intrinsic dimension of data with a fractal-based method

被引：141

作者：

Camastra, F

Vinciarelli, A

机构：

[1] Univ Genoa, INFM DISI, I-16146 Genoa, Italy

[2] Inst Dalle Molle Intelligence Artificielle Percep, CH-1920 Martigny, Switzerland

来源：

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE | 2002年 / 24卷 / 10期

关键词：

Bayesian information criterion; correlation integral; Grassberger-Procaccia's algorithm; intrinsic dimension; nonlinear principal component analysis; box-counting dimension; fractal dimension; Kolmogorov capacity;

D O I：

10.1109/TPAMI.2002.1039212

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, the problem of estimating the intrinsic dimension of a data set is investigated A fractal-based approach using the Grassberger-Procaccia algorithm is proposed. Since the Grassberger-Procaccia algorithm performs badly on sets of high dimensionality, an empirical procedure that improves the original algorithm has been developed The procedure has been tested on data sets of known dimensionality and on time series of Santa Fe competition.

引用

页码：1404 / 1407

页数：4

共 32 条

[1] [Anonymous], 1993, NETWORKS CHAOS STAT
[2] [Anonymous], 1982, Classification, Pattern Recognition and Reduction of Dimensionality, Handbook of Statistics
[3] [Anonymous], 1988, GRUNDLEHREN MATH WIS
[4] [Anonymous], 1993, CHAOS DYNAMICAL SYST
[5] Bishop C. M., 1995, NEURAL NETWORKS PATT
[6] A new approach to dimensionality reduction: theory and algorithms
Broomhead, DS
Kirby, M
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 60 (06) : 2114 - 2142
[7] 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
[8] ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS
ECKMANN, JP
RUELLE, D
[J]. REVIEWS OF MODERN PHYSICS, 1985, 57 (03) : 617 - 656
[9] FUNDAMENTAL LIMITATIONS FOR ESTIMATING DIMENSIONS AND LYAPUNOV EXPONENTS IN DYNAMIC-SYSTEMS
ECKMANN, JP
RUELLE, D
[J]. PHYSICA D, 1992, 56 (2-3): : 185 - 187
[10] Nonlinear principal components analysis of neuronal spike train data
Fotheringhame, D
Baddeley, R
[J]. BIOLOGICAL CYBERNETICS, 1997, 77 (04) : 283 - 288

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