### Abstract

Original language | English |
---|---|

Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 15 |

ISBN (Print) | NCRG/2006/008 |

Publication status | Published - 24 Feb 2006 |

### Fingerprint

### Keywords

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

### Cite this

*A new entropy measure based on the Renyi entropy rate using Gaussian kernels*. Birmingham: Aston University.

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

Research output: Working paper › Technical report

TY - UNPB

T1 - A new entropy measure based on the Renyi entropy rate using Gaussian kernels

AU - Woodcock, D.

AU - Nabney, Ian T.

PY - 2006/2/24

Y1 - 2006/2/24

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.

AB - 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.

KW - approximate entropy

KW - ApEn

KW - entropy rate

KW - dynamical systems theory

KW - sample entropy

KW - SampEn

M3 - Technical report

SN - NCRG/2006/008

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

PB - Aston University

CY - Birmingham

ER -