Abstract
‘Complexity’ has several definitions in diverse fields. These measures are indicators of some aspects of the nature of the signal. Such measures are used to analyse and classify signals and as a signal diagnostics tool to distinguish between periodic, quasiperiodic, chaotic and random signals. Lempel–Ziv (LZ) complexity and approximate entropy (ApEn) are such popular complexity measures that are widely used for characterizing biological signals also. In this paper, we compare the utility of ApEn, LZ complexities and Shannon’s entropy in characterizing data from a nonlinear chaotic map (logistic map). In this work, we show that LZ and ApEn complexity measures can characterize the data complexities correctly for data sequences as short as 20 in length while Shannon’s entropy fails for length less than 50. In the case of noisy sequences with 10% uniform noise, Shannon’s entropy works only for lengths greater than 200 while LZ and ApEn are successful with sequences of lengths greater than 30 and 20, respectively.
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References
C E Shannon, Bell System Tech. J. 27, 379 (1948)
Nithin Nagaraj, Karthi Balasubramanian and Sutirth Dey, Eur. Phys. J. Spec. Top. 222(3–4), 847 (2013)
Abraham Lempel and Jacob Ziv, Inform. Theory, IEEE Trans. 22(1), 75 (1976)
Steve Pincus, Chaos 5(1), 110 (1995)
Fei Nan and Donald Adjeroh, Proceedings of the Computational Systems Bioinformatics Conference (CSB 2004) pp. 522–526
Dario Benedetto, Emanuele Caglioti and Vittorio Loreto, Phys. Rev. Lett. 88(4), 048702 (2002)
Ari L Goldberger, News Physiol. Sci. 6, 87 (1991)
H M Teager and S M Teager, Speech production and speech modelling (Springer, 1990) pp. 241–261
Mehran Talebinejad, Georgios Tsoulfas and Sam Musallam, in: Proceedings of Canadian Med. and Biological Engg. (2011)
Steven M Pincus, Proc. Natl Acad. Sci. 88(6), 2297 (1991)
Acknowledgements
The authors gratefully acknowledge the help rendered by Sutirth Dey (IISER, Pune), Sriram Devanathan (Amrita Vishwa Vidyapeetham) and Gayathri R Prabhu (Indian Institute of Space Science and Technology) towards the successful completion of this work. The authors are thankful to Sutirth and Sriram for their help in the statistical analysis of these results and to Gayathri for her help in writing test scripts, formatting and proofreading the document.
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BALASUBRAMANIAN, K., NAIR, S.S. & NAGARAJ, N. Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures. Pramana - J Phys 84, 365–372 (2015). https://doi.org/10.1007/s12043-015-0938-3
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DOI: https://doi.org/10.1007/s12043-015-0938-3