Noise robust estimates of correlation dimension and [Formula Presented] entropy

Guido Nolte, Andreas Ziehe, Klaus Muller

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and (Formula presented) entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume64
Issue number1
DOIs
Publication statusPublished - 2001 Jan 1
Externally publishedYes

Fingerprint

Robust Estimate
Correlation Dimension
Entropy
entropy
Chaotic Time Series
Functional Dependency
Gaussian Kernel
Colored Noise
Gaussian White Noise
Scale Parameter
estimates
Estimate
embedding
Adjacent
random noise
Simulation
simulation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Noise robust estimates of correlation dimension and [Formula Presented] entropy. / Nolte, Guido; Ziehe, Andreas; Muller, Klaus.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 64, No. 1, 01.01.2001.

Research output: Contribution to journalArticle

@article{4548169114d24e0dbd26fda6ae42b7c5,
title = "Noise robust estimates of correlation dimension and [Formula Presented] entropy",
abstract = "Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and (Formula presented) entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.",
author = "Guido Nolte and Andreas Ziehe and Klaus Muller",
year = "2001",
month = "1",
day = "1",
doi = "10.1103/PhysRevE.64.016112",
language = "English",
volume = "64",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Noise robust estimates of correlation dimension and [Formula Presented] entropy

AU - Nolte, Guido

AU - Ziehe, Andreas

AU - Muller, Klaus

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and (Formula presented) entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.

AB - Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and (Formula presented) entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.

UR - http://www.scopus.com/inward/record.url?scp=85035251088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035251088&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.64.016112

DO - 10.1103/PhysRevE.64.016112

M3 - Article

VL - 64

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

ER -