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On Lempel–Ziv complexity for multidimensional data analysis

Listed author(s):
  • Zozor, S.
  • Ravier, P.
  • Buttelli, O.
Registered author(s):

    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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    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
    DOI: 10.1016/j.physa.2004.07.025
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    1. Damien Challet & Matteo Marsili & Gabriele Ottino, 2004. "Shedding light on El Farol," Game Theory and Information 0406002, EconWPA.
    2. 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.
    3. 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.
    4. Rajković, Milan, 2000. "Extracting meaningful information from financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 383-395.
    5. 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.
    6. 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.
    7. 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.
    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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