Data Clustering Using Multi-objective Differential Evolution Algorithms

The article considers the task of fuzzy clustering in a multi-objective optimization (MO) framework. It compares the relative performance of four recently developedmulti-objective variants of Differential Evolution (DE) on over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation for the candidates is used for DE. A comparative study of four DE variants with two most well-known MO clustering techniques, namely the NSGA II (Non Dominated Sorting GA) and MOCK (Multi- Objective Clustering with an unknown number of clusters K) is also undertaken. Experimental results reported for six artificial and four real life datasets (including a microarray dataset of budding yeast) of varying range of complexities indicates that DE can serve as a promising algorithm for devising MO clustering techniques.

[1]  Kalyanmoy Deb,et al.  Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions , 2003 .

[2]  J. Bezdek.  Cluster Validity with Fuzzy Sets , 1973 .

[3]  M. Ashburner,et al.  Gene Ontology: tool for the unification of biology , 2000, Nature Genetics.

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

[5]  Sergios Theodoridis,et al.  Pattern Recognition, Third Edition , 2006 .

[6]  L. Jain,et al.  Evolutionary multiobjective optimization : theoretical advances and applications , 2005 .

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

[8]  Joaquín Dopazo,et al.  FatiGO: a web tool for finding significant associations of Gene Ontology terms with groups of genes , 2004, Bioinform..

[9]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[12]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[13]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[14]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[15]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[16]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[17]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

[18]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[19]  D. Botstein,et al.  The transcriptional program of sporulation in budding yeast. , 1998, Science.

[20]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[21]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[22]  Indraneel Das.  On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection , 1999 .

[23]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  A. Messac,et al.  Smart Pareto filter: obtaining a minimal representation of multiobjective design space , 2004 .

[25]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[26]  Robert Tibshirani,et al.  Estimating the number of clusters in a data set via the gap statistic , 2000 .

[27]  Hans-Peter Kriegel,et al.  Visualization Techniques for Mining Large Databases: A Comparison , 1996, IEEE Trans. Knowl. Data Eng..

[28]  Hussein A. Abbass,et al.  The Pareto Differential Evolution Algorithm , 2002, Int. J. Artif. Intell. Tools.

[29]  Joshua D. Knowles,et al.  An Evolutionary Approach to Multiobjective Clustering , 2007, IEEE Transactions on Evolutionary Computation.

[30]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  D. Botstein,et al.  Cluster analysis and display of genome-wide expression patterns. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Ujjwal Maulik,et al.  Multiobjective Genetic Clustering for Pixel Classification in Remote Sensing Imagery , 2007, IEEE Transactions on Geoscience and Remote Sensing.