Multi-objective clustering: a kernel based approach using Differential Evolution

ABSTRACT A multi-objective algorithm is always favoured over a single objective algorithm as it considers different aspects of a dataset in the form of various objectives. In this article, a multi-objective clustering algorithm has been proposed based on Differential Evolution. Here, three objectives have been considered to handle different complex datasets. In addition to this, a kernel function is hybridised with the objectives to evaluate the data on a hyperspace for reducing the impact of nonlinearity on cluster formation. Moreover, to get the best compromised solution from the Pareto front an effective fuzzy concept has been followed. Five metaheuristic approaches have been taken into consideration for performance comparison. These methodologies have been applied to twelve datasets and the result reveals the efficacy of the proposed model in data clustering.

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

[2]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[3]  Yuchou Chang,et al.  Unsupervised feature selection using clustering ensembles and population based incremental learning algorithm , 2008, Pattern Recognit..

[4]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

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

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

[7]  Wilfrido Gómez-Flores,et al.  Automatic clustering using nature-inspired metaheuristics: A survey , 2016, Appl. Soft Comput..

[8]  S. Bandyopadhyay,et al.  Nonparametric genetic clustering: comparison of validity indices , 2001, IEEE Trans. Syst. Man Cybern. Syst..

[9]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[10]  King-Sun Fu,et al.  A Sentence-to-Sentence Clustering Procedure for Pattern Analysis , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  M.-C. Su,et al.  A new cluster validity measure and its application to image compression , 2004, Pattern Analysis and Applications.

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

[13]  Amit Konar,et al.  Automatic kernel clustering with a Multi-Elitist Particle Swarm Optimization Algorithm , 2008, Pattern Recognit. Lett..

[14]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[15]  Satchidananda Dehuri,et al.  Genetic Algorithms for Multi-Criterion Classification and Clustering in Data Mining , 2006 .

[16]  Sanghamitra Bandyopadhyay,et al.  Multiobjective Simulated Annealing for Fuzzy Clustering With Stability and Validity , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[17]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[18]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[19]  Wolfgang Rosenstiel,et al.  Automatic Cluster Detection in Kohonen's SOM , 2008, IEEE Transactions on Neural Networks.

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

[21]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[22]  Shokri Z. Selim,et al.  K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[24]  James C. Bezdek,et al.  Fuzzy mathematics in pattern classification , 1973 .

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

[26]  Sanghamitra Bandyopadhyay,et al.  A Point Symmetry-Based Clustering Technique for Automatic Evolution of Clusters , 2008, IEEE Transactions on Knowledge and Data Engineering.

[27]  Yee Leung,et al.  Clustering by Scale-Space Filtering , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Sanghamitra Bandyopadhyay,et al.  A symmetry based multiobjective clustering technique for automatic evolution of clusters , 2010, Pattern Recognit..

[29]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

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

[31]  Ujjwal Maulik,et al.  Validity index for crisp and fuzzy clusters , 2004, Pattern Recognit..

[32]  Xianda Zhang,et al.  A genetic algorithm with gene rearrangement for K-means clustering , 2009, Pattern Recognit..

[33]  Ujjwal Maulik,et al.  Genetic clustering for automatic evolution of clusters and application to image classification , 2002, Pattern Recognit..

[34]  Siripen Wikaisuksakul,et al.  A multi-objective genetic algorithm with fuzzy c-means for automatic data clustering , 2014, Appl. Soft Comput..

[35]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[36]  José-GarcíaAdán,et al.  Automatic clustering using nature-inspired metaheuristics , 2016 .

[37]  Hichem Frigui,et al.  A Robust Competitive Clustering Algorithm With Applications in Computer Vision , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  Donald W. Bouldin,et al.  A Cluster Separation Measure , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Arlindo L. Oliveira,et al.  Biclustering algorithms for biological data analysis: a survey , 2004, IEEE/ACM Transactions on Computational Biology and Bioinformatics.