On Lempel–Ziv complexity for multidimensional data analysis |
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| Institution: | 1. Laboratoire des Images et des Signaux, LIS-ENSIEG CNRS UPRESA 5083, Rue de la Houille Blanche, B.P. 46, 38420 Saint Martin d''Hères Cedex, France;2. Laboratoire d''Électronique, Signaux, Images, 12 rue de Blois, B.P. 6744, 45067, Orléans Cedex 2, France;3. Laboratoire Activité Motrice et Conception Ergonomique, Rue de Vendôme, B.P. 6237, 45062 Orléans Cedex 2, France;1. School of Information Science and Engineering, Yanshan University, Qinhuangdao, China;2. Department of Neurology, The Rocket Force General Hospital of PLA, Beijing, China;1. State Key Laboratory of Industrial Control Technology, Zhejiang University, 310027 Hangzhou, China;2. Department of Chemical Engineering, Chung-Yuan Christian University, Chung-Li 320, Taiwan, ROC;3. ABB Corporate Research Center Germany, 68526 Ladenburg, Germany;1. School of Information Engineering, China University of Geosciences, Beijing, China;2. School of Humanities and Economic Management, China University of Geosciences, Beijing, China;1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, IL 60607, USA;2. Department of Biological Sciences, Chicago State University, IL 60628, USA;3. Department of Mathematical Sciences, Tsinghua University, Haidian District, Beijing 100084, PR China;1. Department of Anesthesiology and Center for Consciousness Science, University of Michigan, Ann Arbor, MI, United States;2. Department of Anesthesiology, Medical College of Wisconsin, Milwaukee, WI, United States;3. Department of Psychiatry, University of Wisconsin-Madison, Madison, WI, United States;4. Department of Neurology, University of Wisconsin-Madison, Madison, WI, United States |
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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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