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

Guido Nolte, Andreas Ziehe, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Pages (from-to)10
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
Publication statusPublished - 2001

ASJC Scopus subject areas

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


Dive into the research topics of 'Noise robust estimates of correlation dimension and [Formula Presented] entropy'. Together they form a unique fingerprint.

Cite this