Differential Evolution Based Fuzzy Clustering

In this work, two new fuzzy clustering (FC) algorithms based on Differential Evolution (DE) are proposed. Five well-known data sets viz. Iris, Wine, Glass, E. Coli and Olive Oil are used to demonstrate the effectiveness of DEFC-1 and DEFC-2. They are compared with Fuzzy C-Means (FCM) algorithm and Threshold Accepting Based Fuzzy Clustering algorithms proposed by Ravi et al., [1]. Xie-Beni index is used to arrive at the ‘optimal’ number of clusters. Based on the numerical experiments, we infer that, in terms of least objective function value, these variants can be used as viable alternatives to FCM algorithm.

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

[2]  James C. Bezdek,et al.  Clustering with a genetically optimized approach , 1999, IEEE Trans. Evol. Comput..

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

[4]  Joni-Kristian Kämäräinen,et al.  Differential Evolution Training Algorithm for Feed-Forward Neural Networks , 2003, Neural Processing Letters.

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

[6]  A. Hamler,et al.  Analysis of iron loss in interior permanent magnet synchronous motor over a wide-speed range of constant output power operation , 2000 .

[7]  Amit Konar,et al.  Automatic image pixel clustering with an improved differential evolution , 2009, Appl. Soft Comput..

[8]  Feng-Sheng Wang,et al.  Multiobjective parameter estimation problems of fermentation processes using a high ethanol tolerance yeast , 2000 .

[9]  Vadlamani Ravi,et al.  An improved differential evolution method for efficient parameter estimation in biofilter modeling , 2006 .

[10]  W. Land,et al.  A new training algorithm for the general regression neural network , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[11]  Khaled S. Al-Sultan,et al.  A tabu search-based algorithm for the fuzzy clustering problem , 1997, Pattern Recognit..

[12]  Manfred M. Fischer,et al.  A Gobal Search Procedure forParameter Estimation inNeural Spatial Interaction Modelling , 1998 .

[13]  Ivan Zelinka,et al.  Mechanical engineering design optimization by differential evolution , 1999 .

[14]  Steven Doyle,et al.  Automated mirror design using an evolution strategy , 1999 .

[15]  Jin-Cherng Lin,et al.  Fuzzy Clustering by Differential Evolution , 2008, 2008 Eighth International Conference on Intelligent Systems Design and Applications.

[16]  Xiaohua Liu,et al.  Differential Evolution Fuzzy Clustering Algorithm Based on Kernel Methods , 2006, RSKT.

[17]  Ujjwal Maulik,et al.  Automatic Fuzzy Clustering Using Modified Differential Evolution for Image Classification , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[18]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

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

[20]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[21]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[22]  Chris Aldrich,et al.  Combinatorial evolution of regression nodes in feedforward neural networks , 1999, Neural Networks.

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

[24]  Rainer Fuchs,et al.  Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters , 2001, Bioinform..

[25]  Kay Hameyer,et al.  Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm , 2000 .

[26]  Klaus Danzer,et al.  Fuzzy cluster analysis by simulated annealing , 1996 .

[27]  Pierre Hansen,et al.  Fuzzy J-Means: a new heuristic for fuzzy clustering , 2001, Pattern Recognit..

[28]  Vadlamani Ravi,et al.  Threshold Accepting Based Fuzzy Clustering Algorithms , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..