Multi-Objective Differential Evolution for Automatic Clustering with Application to Micro-Array Data Analysis

This paper applies the Differential Evolution (DE) algorithm to the task of automatic fuzzy clustering in a Multi-objective Optimization (MO) framework. It compares the performances of two multi-objective variants of DE 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 of the search variables, accommodating variable number of cluster centers, is used for DE. The performances of the multi-objective DE-variants have also been contrasted to that of two most well-known schemes of MO clustering, namely the Non Dominated Sorting Genetic Algorithm (NSGA II) and Multi-Objective Clustering with an unknown number of Clusters K (MOCK). Experimental results using six artificial and four real life datasets of varying range of complexities indicate that DE holds immense promise as a candidate algorithm for devising MO clustering schemes.

[1]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[2]  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.

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

[4]  Joshua D. Knowles,et al.  Multiobjective clustering around medoids , 2005, 2005 IEEE Congress on Evolutionary Computation.

[5]  Andries Petrus Engelbrecht,et al.  Differential evolution methods for unsupervised image classification , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[7]  Ujjwal Maulik,et al.  Fuzzy partitioning using a real-coded variable-length genetic algorithm for pixel classification , 2003, IEEE Trans. Geosci. Remote. Sens..

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

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

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

[11]  H. S. Wolff,et al.  iRun: Horizontal and Vertical Shape of a Region-Based Graph Compression , 2022, Sensors.

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

[13]  Joshua D. Knowles,et al.  Evolutionary Multiobjective Clustering , 2004, PPSN.

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

[15]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[16]  Sandra Paterlini,et al.  Differential evolution and particle swarm optimisation in partitional clustering , 2006, Comput. Stat. Data Anal..

[17]  D. J. Newman,et al.  UCI Repository of Machine Learning Database , 1998 .

[18]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[19]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

[21]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[22]  Joshua D. Knowles,et al.  Exploiting the Trade-off - The Benefits of Multiple Objectives in Data Clustering , 2005, EMO.

[23]  Joshua D. Knowles,et al.  Improvements to the scalability of multiobjective clustering , 2005, 2005 IEEE Congress on Evolutionary Computation.

[24]  椹木 義一,et al.  Theory of multiobjective optimization , 1985 .

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

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

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

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

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

[30]  René Thomsen,et al.  Multimodal optimization using crowding-based differential evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[31]  Swagatam Das,et al.  Automatic Clustering Using an Improved Differential Evolution Algorithm , 2007 .

[32]  Ujjwal Maulik,et al.  An improved algorithm for clustering gene expression data , 2007, Bioinform..

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

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

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

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

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

[38]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

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