Complex Network Clustering by Multiobjective Discrete Particle Swarm Optimization Based on Decomposition

The field of complex network clustering has been very active in the past several years. In this paper, a discrete framework of the particle swarm optimization algorithm is proposed. Based on the proposed discrete framework, a multiobjective discrete particle swarm optimization algorithm is proposed to solve the network clustering problem. The decomposition mechanism is adopted. A problem-specific population initialization method based on label propagation and a turbulence operator are introduced. In the proposed method, two evaluation objectives termed as kernel k-means and ratio cut are to be minimized. However, the two objectives can only be used to handle unsigned networks. In order to deal with signed networks, they have been extended to the signed version. The clustering performances of the proposed algorithm have been validated on signed networks and unsigned networks. Extensive experimental studies compared with ten state-of-the-art approaches prove that the proposed algorithm is effective and promising.

[1]  Vittorio Zaccaria,et al.  Discrete Particle Swarm Optimization for Multi-objective Design Space Exploration , 2008, 2008 11th EUROMICRO Conference on Digital System Design Architectures, Methods and Tools.

[2]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[3]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[4]  Carlos A. Coello Coello,et al.  A fast particle swarm algorithm for solving smooth and non-smooth economic dispatch problems , 2011 .

[5]  Pin Luarn,et al.  A discrete version of particle swarm optimization for flowshop scheduling problems , 2007, Comput. Oper. Res..

[6]  John A. W. McCall,et al.  D 2 MOPSO: Multi-Objective Particle Swarm Optimizer Based on Decomposition and Dominance , 2012, EvoCOP.

[7]  Ponnuthurai N. Suganthan,et al.  Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization , 2011, Inf. Sci..

[8]  Alex Arenas,et al.  Analysis of the structure of complex networks at different resolution levels , 2007, physics/0703218.

[9]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[11]  Ying Wang,et al.  Quantitative Function for Community Detection , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  W. Renhart,et al.  Pareto optimality and particle swarm optimization , 2004, IEEE Transactions on Magnetics.

[13]  Carlos A. Coello Coello,et al.  A proposal to use stripes to maintain diversity in a multi-objective particle swarm optimizer , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[14]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[15]  Bin Wu,et al.  Multi-objective community detection in complex networks , 2012, Appl. Soft Comput..

[16]  Chunguang Zhou,et al.  Fuzzy discrete particle swarm optimization for solving traveling salesman problem , 2004, The Fourth International Conference onComputer and Information Technology, 2004. CIT '04..

[17]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

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

[19]  Xiaodong Li,et al.  Cooperatively Coevolving Particle Swarms for Large Scale Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[20]  Clara Pizzuti,et al.  A Multiobjective Genetic Algorithm to Find Communities in Complex Networks , 2012, IEEE Transactions on Evolutionary Computation.

[21]  Xiaohua Liu,et al.  Solving multi objective optimization problems using particle swarm optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[22]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Dipti Srinivasan,et al.  Particle Swarm Inspired Evolutionary Algorithm (PS-EA) for Multi-Criteria Optimization Problems , 2003, Evolutionary Multiobjective Optimization.

[24]  Maoguo Gong,et al.  Memetic algorithm for community detection in networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Fang Wu,et al.  Finding communities in linear time: a physics approach , 2003, ArXiv.

[26]  Yangyang Li,et al.  An improved memetic algorithm for community detection in complex networks , 2012, 2012 IEEE Congress on Evolutionary Computation.

[27]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Lamia Benameur,et al.  A New Hybrid Particle Swarm Optimization Algorithm for Handling Multiobjective Problem Using Fuzzy Clustering Technique , 2009, 2009 International Conference on Computational Intelligence, Modelling and Simulation.

[30]  M. Mitrovic,et al.  Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[32]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[33]  Gary G. Yen,et al.  Cultural-Based Multiobjective Particle Swarm Optimization , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[34]  Andrej Mrvar,et al.  An Analysis of the Slovene Parliamentary Parties Network , 2003 .

[35]  Ujjwal Maulik,et al.  A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA , 2008, IEEE Transactions on Evolutionary Computation.

[36]  J. Reichardt,et al.  Statistical mechanics of community detection. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[38]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[39]  Jun Zhang,et al.  A Novel Set-Based Particle Swarm Optimization Method for Discrete Optimization Problems , 2010, IEEE Transactions on Evolutionary Computation.

[40]  S Boccaletti,et al.  Identification of network modules by optimization of ratio association. , 2006, Chaos.

[41]  Russell C. Eberhart,et al.  Particle swarm with extended memory for multiobjective optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[42]  Jiming Liu,et al.  Community Mining from Signed Social Networks , 2007, IEEE Transactions on Knowledge and Data Engineering.

[43]  Zhiyong Li,et al.  A Novel Diversity Guided Particle Swarm Multi-objective Optimization Algorithm , 2011 .

[44]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  P. Doreian,et al.  A partitioning approach to structural balance , 1996 .

[46]  M. N. Vrahatis,et al.  Particle swarm optimization method in multiobjective problems , 2002, SAC '02.

[47]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[48]  Pascal Pons,et al.  Post-processing hierarchical community structures: Quality improvements and multi-scale view , 2006, Theor. Comput. Sci..

[49]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[50]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[51]  Pablo Jensen,et al.  Analysis of community structure in networks of correlated data. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  D. Y. Sha,et al.  A hybrid particle swarm optimization for job shop scheduling problem , 2006, Comput. Ind. Eng..

[53]  Qingfu Zhang,et al.  Community detection in networks by using multiobjective evolutionary algorithm with decomposition , 2012 .

[54]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[55]  Jun Zhang,et al.  Optimizing the Vehicle Routing Problem With Time Windows: A Discrete Particle Swarm Optimization Approach , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[56]  Clara Pizzuti,et al.  GA-Net: A Genetic Algorithm for Community Detection in Social Networks , 2008, PPSN.

[57]  K. E. Read,et al.  Cultures of the Central Highlands, New Guinea , 1954, Southwestern Journal of Anthropology.

[58]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[59]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[60]  Zhen Ji,et al.  DNA Sequence Compression Using Adaptive Particle Swarm Optimization-Based Memetic Algorithm , 2011, IEEE Transactions on Evolutionary Computation.

[61]  Mario Köppen,et al.  Multi-objective particle swarm optimization by fuzzy-pareto-dominance meta-heuristic , 2006, Int. J. Hybrid Intell. Syst..

[62]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[63]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[64]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[65]  Jürgen Teich,et al.  Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO) , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[66]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[67]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[68]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[69]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

[70]  Imtiaz Ahmad,et al.  Particle swarm optimization for task assignment problem , 2002, Microprocess. Microsystems.

[71]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.