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On Lempel–Ziv complexity for multidimensional data analysis

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  • Zozor, S.
  • Ravier, P.
  • Buttelli, O.
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    Abstract

    In this paper, a natural extension of the Lempel–Ziv complexity for several finite-time sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel–Ziv complexity are given, as well as properties in connection with the Lempel–Ziv complexity of the individual sequences. Also, some links with Shannon entropies are exhibited and, by analogy, some derived quantities are proposed. Lastly, the potential use of the extended complexities for data analysis is illustrated on random boolean networks and on a proposed multidimensional extension of the minority game.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 345 (2005)
    Issue (Month): 1 ()
    Pages: 285-302

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    Handle: RePEc:eee:phsmap:v:345:y:2005:i:1:p:285-302

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Complexity measures; Lempel–Ziv complexity; Shannon entropy; Nonlinear deterministic multidimensional systems; Random boolean network; Minority game;

    References

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    1. Ballesteros, Fernando J & Luque, Bartolo, 2002. "Random Boolean networks response to external periodic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 289-300.
    2. Rajković, Milan, 2000. "Extracting meaningful information from financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 383-395.
    3. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    4. Földy, Csaba & Somogyvári, Zoltán & Érdi, Péter, 2003. "Hierarchically organized minority games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 735-742.
    5. Torres, M.E. & Gamero, L.G., 2000. "Relative complexity changes in time series using information measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(3), pages 457-473.
    6. Challet, Damien & Marsili, M & Ottino, Gabriele, 2004. "Shedding light on El Farol," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 469-482.
    7. Luque, Bartolo & Solé, Ricard V., 2000. "Lyapunov exponents in random Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 33-45.
    8. Rajković, Milan & Mihailović, Zoran, 2003. "Quantifying complexity in the minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 40-47.
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