Recurrence matrices and the preservation of dynamical properties

Gary McGuire; Nabeel B. Azar; Mark Shelhamer

doi:10.1016/S0375-9601(97)00697-X

Recurrence matrices and the preservation of dynamical properties

Gary McGuire, Nabeel B. Azar, Mark Shelhamer

School of Medicine

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

We prove that the construction of a recurrence matrix (a matrix of inter-vector distances) preserves the dynamical properties of an observed attractor. Because of this fact, a recurrence matrix is a useful transform for studying high-dimensional systems, "compressing" high-dimensional vector sets into a two-dimensional format without losing relevant information. Practical issues are discussed in an example.

Original language	English (US)
Pages (from-to)	43-47
Number of pages	5
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	237
Issue number	1-2
DOIs	https://doi.org/10.1016/S0375-9601(97)00697-X
State	Published - Dec 29 1997

Keywords

Embedding
Mutual distances
Reconstruction
State space

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/S0375-9601(97)00697-X

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title = "Recurrence matrices and the preservation of dynamical properties",

abstract = "We prove that the construction of a recurrence matrix (a matrix of inter-vector distances) preserves the dynamical properties of an observed attractor. Because of this fact, a recurrence matrix is a useful transform for studying high-dimensional systems, {"}compressing{"} high-dimensional vector sets into a two-dimensional format without losing relevant information. Practical issues are discussed in an example.",

keywords = "Embedding, Mutual distances, Reconstruction, State space",

author = "Gary McGuire and Azar, {Nabeel B.} and Mark Shelhamer",

note = "Funding Information: We would like to thank Edward R. Scheinerman for his helpful discussions and insight. This work was supported by grants from the Whitaker Foundation (M.S., N.A.) and the National Science Foundation (M.S.).",

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T1 - Recurrence matrices and the preservation of dynamical properties

AU - McGuire, Gary

AU - Azar, Nabeel B.

AU - Shelhamer, Mark

N1 - Funding Information: We would like to thank Edward R. Scheinerman for his helpful discussions and insight. This work was supported by grants from the Whitaker Foundation (M.S., N.A.) and the National Science Foundation (M.S.).

PY - 1997/12/29

Y1 - 1997/12/29

N2 - We prove that the construction of a recurrence matrix (a matrix of inter-vector distances) preserves the dynamical properties of an observed attractor. Because of this fact, a recurrence matrix is a useful transform for studying high-dimensional systems, "compressing" high-dimensional vector sets into a two-dimensional format without losing relevant information. Practical issues are discussed in an example.

AB - We prove that the construction of a recurrence matrix (a matrix of inter-vector distances) preserves the dynamical properties of an observed attractor. Because of this fact, a recurrence matrix is a useful transform for studying high-dimensional systems, "compressing" high-dimensional vector sets into a two-dimensional format without losing relevant information. Practical issues are discussed in an example.

KW - Embedding

KW - Mutual distances

KW - Reconstruction

KW - State space

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -

Recurrence matrices and the preservation of dynamical properties

Abstract

Keywords

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