LOCAL FALSE NEAREST NEIGHBORS AND DYNAMIC DIMENSIONS FROM OBSERVED CHAOTIC DATA

被引：188

作者：

ABARBANEL, HDI ^{[1
]}

KENNEL, MB ^{[1
]}

机构：

[1] UNIV CALIF SAN DIEGO,SCRIPPS INST OCEANOG,MARINE PHYS LAB,LA JOLLA,CA 92093

来源：

PHYSICAL REVIEW E | 1993年 / 47卷 / 05期

关键词：

D O I：

10.1103/PhysRevE.47.3057

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The time delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. The minimum necessary global embedding dimension d(E) may still be larger than the actual dimension of the underlying dynamics d(L). The embedding theorem only guarantees that the attractor of the system is fully unfolded using d(E) greater than 2d(A), with d(A) the fractal attractor dimension. Using the idea of local false nearest neighbors, we discuss methods for determining the integer-valued d(L).

引用

页码：3057 / 3068

页数：12

共 49 条

[1] Estimating good discrete partitions from observed data: Symbolic false nearest neighbors
Kennel, MB
Buhl, M
[J]. PHYSICAL REVIEW LETTERS, 2003, 91 (08)
[2] k*-Nearest Neighbors: From Global to Local
Anava, Oren
Levy, Kfir Y.
[J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 29 (NIPS 2016), 2016, 29
[3] A distributed memory architecture implementation of the False Nearest Neighbors method based on distribution of dimensions
Marin Carrion, I.
Arias Antunez, E.
Artigao Castillo, M. M.
Miralles Canals, J. J.
[J]. JOURNAL OF SUPERCOMPUTING, 2012, 59 (03): : 1596 - 1618
[4] A distributed memory architecture implementation of the False Nearest Neighbors method based on distribution of dimensions
I. Marín Carrión
E. Arias Antúnez
M. M. Artigao Castillo
J. J. Miralles Canals
[J]. The Journal of Supercomputing, 2012, 59 : 1596 - 1618
[5] Kinetic and Dynamic Data Structures for Closest Pair and All Nearest Neighbors
Agarwal, Pankaj K.
Kaplan, Haim
Sharir, Micha
[J]. ACM TRANSACTIONS ON ALGORITHMS, 2008, 5 (01)
[6] k-Nearest neighbors local linear regression for functional and missing data at random
Rachdi, Mustapha
Laksaci, Ali
Kaid, Zoulikha
Benchiha, Abbassia
Al-Awadhi, Fahimah A.
[J]. STATISTICA NEERLANDICA, 2021, 75 (01) : 42 - 65
[7] Learning k-nearest neighbors classifier from distributed data
Khedr, Ahmed M.
[J]. COMPUTING AND INFORMATICS, 2008, 27 (03) : 355 - 376
[8] The k nearest neighbors local linear estimator of functional conditional density when there are missing data
Almanjahie, Ibrahim M.
Alahmari, Wafaa Mesfer
Laksaci, Ali
[J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (03): : 914 - 931
[9] Fast geometrical extraction of nearest neighbors from multi-dimensional data
Aziz, Yasir
Memon, Kashif Hussain
[J]. PATTERN RECOGNITION, 2023, 136
[10] EXTRACTION OF DYNAMIC EQUATIONS FROM CHAOTIC DATA
ROWLANDS, G
SPROTT, JC
[J]. PHYSICA D, 1992, 58 (1-4): : 251 - 259

← 1 2 3 4 5 →