A new entropy measure based on the Renyi entropy rate using Gaussian kernels

D. Woodcock, Ian T. Nabney

Research output: Working paperTechnical report

Abstract

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.
Original languageEnglish
Place of PublicationBirmingham
PublisherAston University
Number of pages15
ISBN (Print)NCRG/2006/008
Publication statusPublished - 24 Feb 2006

Fingerprint

entropy
regularity
retaining
dynamical systems
costs
formulations

Keywords

  • approximate entropy
  • ApEn
  • entropy rate
  • dynamical systems theory
  • sample entropy
  • SampEn

Cite this

Woodcock, D., & Nabney, I. T. (2006). A new entropy measure based on the Renyi entropy rate using Gaussian kernels. Birmingham: Aston University.
Woodcock, D. ; Nabney, Ian T. / A new entropy measure based on the Renyi entropy rate using Gaussian kernels. Birmingham : Aston University, 2006.
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Woodcock, D & Nabney, IT 2006 'A new entropy measure based on the Renyi entropy rate using Gaussian kernels' Aston University, Birmingham.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels. / Woodcock, D.; Nabney, Ian T.

Birmingham : Aston University, 2006.

Research output: Working paperTechnical report

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AU - Nabney, Ian T.

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N2 - The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

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Woodcock D, Nabney IT. A new entropy measure based on the Renyi entropy rate using Gaussian kernels. Birmingham: Aston University. 2006 Feb 24.