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On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

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  • Tamara Skoric
  • Olivera Sarenac
  • Branislav Milovanovic
  • Nina Japundzic-Zigon
  • Dragana Bajic

Abstract

Cross-approximate entropy (XApEn) quantifies the mutual orderliness of simultaneously recorded time series. Despite being derived from the firmly established solitary entropies, it has never reached their reputation and deployment. The aim of this study is to identify the problems that preclude wider XApEn implementation and to develop a set of solutions. Exact expressions for XApEn and its constitutive parts are derived and compared to values estimated from artificial data. This comparison revealed vast regions within the parameter space that do not guarantee reliable probability estimation, making XApEn estimates inconsistent. A simple correction to one of the XApEn procedural steps is proposed. Three sets of formulae for joint parameter selection are derived. The first one is intended to maximize threshold profile. The remaining ones minimize XApEn instability according to the strong and weak criteria. The derived expressions are verified using cardiovascular signals recorded from rats (long signals) and healthy volunteers (short clinical signals), proposing a change of traditional parameter guidelines.

Suggested Citation

  • Tamara Skoric & Olivera Sarenac & Branislav Milovanovic & Nina Japundzic-Zigon & Dragana Bajic, 2017. "On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments," Complexity, Hindawi, vol. 2017, pages 1-15, September.
    • Handle: RePEc:hin:complx:8365685
    DOI: 10.1155/2017/8365685
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    References listed on IDEAS

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    1. Ning, Xinbao & Xu, Yinlin & Wang, Jun & Ma, Xiaofei, 2005. "Approximate entropy analysis of short-term HFECG based on wave mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 475-483.
    2. Zurek, Sebastian & Guzik, Przemyslaw & Pawlak, Sebastian & Kosmider, Marcin & Piskorski, Jaroslaw, 2012. "On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6601-6610.
    3. Restrepo, Juan F. & Schlotthauer, Gastón & Torres, María E., 2014. "Maximum approximate entropy and r threshold: A new approach for regularity changes detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 97-109.
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