Exploring Spatio-temporal Dynamics of Cellular Automata for Pattern Recognition in Networks

Network science is an interdisciplinary field which provides an integrative approach for the study of complex systems. In recent years, network modeling has been used for the study of emergent phenomena in many real-world applications. Pattern recognition in networks has been drawing attention to the importance of network characterization, which may lead to understanding the topological properties that are related to the network model. In this paper, the Life-Like Network Automata (LLNA) method is introduced, which was designed for pattern recognition in networks. LLNA uses the network topology as a tessellation of Cellular Automata (CA), whose dynamics produces a spatio-temporal pattern used to extract the feature vector for network characterization. The method was evaluated using synthetic and real-world networks. In the latter, three pattern recognition applications were used: (i) identifying organisms from distinct domains of life through their metabolic networks, (ii) identifying online social networks and (iii) classifying stomata distribution patterns varying according to different lighting conditions. LLNA was compared to structural measurements and surpasses them in real-world applications, achieving improvement in the classification rate as high as 23%, 4% and 7% respectively. Therefore, the proposed method is a good choice for pattern recognition applications using networks and demonstrates potential for general applicability.

[1]  C. Marr,et al.  Outer-totalistic cellular automata on graphs , 2008, 0812.2408.

[2]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[3]  A. Goldberger,et al.  Emergence of complex dynamics in a simple model of signaling networks. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[4]  D. Watts,et al.  An Experimental Study of Search in Global Social Networks , 2003, Science.

[5]  Potsdam,et al.  Complex networks in climate dynamics. Comparing linear and nonlinear network construction methods , 2009, 0907.4359.

[6]  André Ricardo Backes,et al.  Texture analysis and classification: A complex network-based approach , 2013, Inf. Sci..

[7]  Marc-Thorsten Hütt,et al.  Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics , 2012, Entropy.

[8]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[9]  R. Solé,et al.  The large-scale organization of chemical reaction networks in astrophysics , 2004, cond-mat/0406137.

[10]  F. Rao,et al.  The protein folding network. , 2004, Journal of molecular biology.

[11]  Xin-Jian Xu,et al.  Excitable Greenberg-Hastings cellular automaton model on scale-free networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Odemir Martinez Bruno,et al.  Chaotic encryption method based on life-like cellular automata , 2011, Expert Syst. Appl..

[13]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[14]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[15]  Marco Tomassini,et al.  Evolution and Dynamics of Small-World Cellular Automata , 2005, Complex Syst..

[16]  Master Gardener,et al.  Mathematical games: the fantastic combinations of john conway's new solitaire game "life , 1970 .

[17]  Odemir Martinez Bruno,et al.  Analysis of Stomata Distribution Patterns for Quantification of the Foliar Plasticity of Tradescantia Zebrina , 2015 .

[18]  Yadira Espinal Viktor Mayer-Schonberger and Kenneth Cukier, Big Data: A Revolution That Will Transform How We Live, Work and Think , 2013 .

[19]  A. Tsonis,et al.  Topology and predictability of El Niño and La Niña networks. , 2008, Physical review letters.

[20]  Konstantin Mischaikow,et al.  Topological data analysis of contagion maps for examining spreading processes on networks , 2015, Nature communications.

[21]  Shuangcai Li,et al.  Quantification of 3-D soil macropore networks in different soil types and land uses using computed tomography , 2010 .

[22]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[23]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[24]  Dalibor Fiala,et al.  Network-based statistical comparison of citation topology of bibliographic databases , 2014, Scientific Reports.

[25]  S. Abe,et al.  Dynamical evolution of clustering in complex network of earthquakes , 2007 .

[26]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[27]  Andrew Wuensche,et al.  The X-Rule: Universal Computation in a Non-Isotropic Life-Like Cellular Automaton , 2015, J. Cell. Autom..

[28]  Gordon Broderick,et al.  A life-like virtual cell membrane using discrete automata , 2004, Silico Biol..

[29]  Tolga Tasdizen,et al.  Network modeling of Arctic melt ponds , 2016 .

[30]  Karel De Loof,et al.  Influence of the topology of a cellular automaton on its dynamical properties , 2013, Commun. Nonlinear Sci. Numer. Simul..

[31]  Guido Caldarelli,et al.  Evolution of Controllability in Interbank Networks , 2013, Scientific Reports.

[32]  Reinhard Lipowsky,et al.  Dynamic pattern evolution on scale-free networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Norikazu Suzuki,et al.  Complex-network description of seismicity , 2006 .

[34]  Marco Tomassini,et al.  Performance and Robustness of Cellular Automata Computation on Irregular Networks , 2007, Adv. Complex Syst..

[35]  Odemir Martinez Bruno,et al.  Complex network classification using partially self-avoiding deterministic walks , 2011, Chaos.

[36]  André Ricardo Backes,et al.  A complex network-based approach for boundary shape analysis , 2009, Pattern Recognit..

[37]  L. Fichter,et al.  Complex Systems Theory , 2010 .

[38]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[39]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[40]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[41]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[42]  Bernard De Baets,et al.  Cellular automata on irregular tessellations , 2012 .

[43]  Ying-Cheng Lai,et al.  Signatures of small-world and scale-free properties in large computer programs , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos with Student Solutions Manual , 2016 .

[45]  Florian Greil,et al.  Critical Boolean networks with scale-free in-degree distribution. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[47]  Natalia Maltsev,et al.  WIT: integrated system for high-throughput genome sequence analysis and metabolic reconstruction , 2000, Nucleic Acids Res..

[48]  A. Arenas,et al.  Community analysis in social networks , 2004 .

[49]  Odemir Martinez Bruno,et al.  A complex network approach for dynamic texture recognition , 2015, Neurocomputing.

[50]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[51]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Christopher S. Poultney,et al.  A physical sciences network characterization of non-tumorigenic and metastatic cells , 2013, Scientific Reports.

[53]  Filipi Nascimento Silva,et al.  A pattern recognition approach to complex networks , 2010 .

[54]  Marti A. Hearst Trends & Controversies: Support Vector Machines , 1998, IEEE Intell. Syst..

[55]  Jure Leskovec,et al.  Learning to Discover Social Circles in Ego Networks , 2012, NIPS.

[56]  Shlomo Havlin,et al.  Energy-landscape network approach to the glass transition , 2008, 0808.2203.

[57]  R. Ferrer i Cancho,et al.  Scale-free networks from optimal design , 2002, cond-mat/0204344.

[58]  J. Wojcik,et al.  The protein–protein interaction map of Helicobacter pylori , 2001, Nature.

[59]  Cosma Rohilla Shalizi,et al.  Methods and Techniques of Complex Systems Science: An Overview , 2003, nlin/0307015.

[60]  J. Doye,et al.  Characterizing the network topology of the energy landscapes of atomic clusters. , 2004, The Journal of chemical physics.

[61]  H T Siegelmann,et al.  The global landscape of cognition: hierarchical aggregation as an organizational principle of human cortical networks and functions , 2015, Scientific Reports.

[62]  Miguel Verdú,et al.  Ecological interactions are evolutionarily conserved across the entire tree of life , 2010, Nature.

[63]  Wei Cai,et al.  Using the k-core decomposition to analyze the static structure of large-scale software systems , 2010, The Journal of Supercomputing.

[64]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[65]  Konstantin Mischaikow,et al.  Topological data analysis of contagion maps for examining spreading processes on networks , 2014, Nature Communications.

[66]  André Ricardo Backes,et al.  Contour polygonal approximation using shortest path in networks , 2013, ArXiv.