Learning sparse Fuzzy Cognitive Maps by Ant Colony Optimization

Fuzzy Cognitive Maps (FCMs) are a causal modelling technique. FCM models contain nodes (representing the concepts to be modelled) and directed weighted edges (representing the causal relations between the concepts). Data-driven FCM learning algorithms are an objective approach with the potential to discover the causal relations that are unknown to human experts. Learning FCM from data can be a difficult problem because the size of the solution space grows quadratically with the number of nodes in the FCM models. A data-driven learning algorithm based on Ant Colony Optimization (ACO) is proposed to develop Fuzzy Cognitive Maps (FCMs). The FCM models can be isomorphically represented as weight vectors. The objective function is to minimize the difference between the estimated response of the FCM model and the target response observed from the to-be-modelled system. An ACO algorithm with heuristic information is proposed to find the best FCM model. The performance of the ACO algorithm was tested on both randomly generated data and DREAM4 project data (publicly available in-silico gene expression data). The experiment results show that the ACO algorithm is able to learn FCMs with at least 40 nodes.

[1]  D. E. Koulouriotis,et al.  A fuzzy cognitive map-based stock market model: synthesis, analysis and experimental results , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[2]  Wei-Po Lee,et al.  Computational methods for discovering gene networks from expression data , 2009, Briefings Bioinform..

[3]  D. Floreano,et al.  Revealing strengths and weaknesses of methods for gene network inference , 2010, Proceedings of the National Academy of Sciences.

[4]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Robert Ivor John,et al.  Computer aided fuzzy medical diagnosis , 2004, Inf. Sci..

[6]  Witold Pedrycz,et al.  Data-driven Nonlinear Hebbian Learning method for Fuzzy Cognitive Maps , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[7]  Chrysostomos D. Stylios,et al.  Fuzzy Cognitive Map Learning Based on Nonlinear Hebbian Rule , 2003, Australian Conference on Artificial Intelligence.

[8]  Witold Pedrycz,et al.  A divide and conquer method for learning large Fuzzy Cognitive Maps , 2010, Fuzzy Sets Syst..

[9]  Christopher A. Penfold,et al.  How to infer gene networks from expression profiles, revisited , 2011, Interface Focus.

[10]  Elpiniki I. Papageorgiou,et al.  A new methodology for Decisions in Medical Informatics using fuzzy cognitive maps based on fuzzy rule-extraction techniques , 2011, Appl. Soft Comput..

[11]  Dimitris E. Koulouriotis,et al.  Comparing simulated annealing and genetic algorithm in learning FCM , 2007, Appl. Math. Comput..

[12]  Lawrence J. Mazlack,et al.  Learning fuzzy cognitive maps from data by ant colony optimization , 2012, GECCO '12.

[13]  Witold Pedrycz,et al.  Genetic learning of fuzzy cognitive maps , 2005, Fuzzy Sets Syst..

[14]  Michael Hecker,et al.  Gene regulatory network inference: Data integration in dynamic models - A review , 2009, Biosyst..

[15]  D. E. Koulouriotis,et al.  FUZZY COGNITIVE MAPS IN STOCK MARKET , 2001 .

[16]  Mostafa Jafari,et al.  Learning FCM by Tabu Search , 2007 .

[17]  Richard Bonneau,et al.  DREAM4: Combining Genetic and Dynamic Information to Identify Biological Networks and Dynamical Models , 2010, PloS one.

[18]  Athanasios K. Tsadiras,et al.  Comparing the inference capabilities of binary, trivalent and sigmoid fuzzy cognitive maps , 2008, Inf. Sci..

[19]  Jishou Ruan,et al.  Novel scales based on hydrophobicity indices for secondary protein structure. , 2007, Journal of theoretical biology.

[20]  Bart Kosko,et al.  Fuzzy Cognitive Maps , 1986, Int. J. Man Mach. Stud..

[21]  Michael N. Vrahatis,et al.  A first study of fuzzy cognitive maps learning using particle swarm optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[22]  Wojciech J Stach,et al.  Learning and aggregation of Fuzzy Cognitive Maps - an evolutionary approach , 2010 .

[23]  D. E. Koulouriotis,et al.  Learning fuzzy cognitive maps using evolution strategies: a novel schema for modeling and simulating high-level behavior , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[24]  Somayeh Alizadeh,et al.  Learning FCM by chaotic simulated annealing , 2009 .

[25]  Chrysostomos D. Stylios,et al.  Active Hebbian learning algorithm to train fuzzy cognitive maps , 2004, Int. J. Approx. Reason..