Hybrid differential evolution algorithm for optimal clustering

Graphical abstractDisplay Omitted HighlightsNew hybrid algorithm for optimal clustering is proposed.Algorithm combines differential evolution with k-means.Efficient heuristic for rearrangement of cluster centers is proposed.Hybrid algorithm with center rearrangement is much faster than other variants. The problem of optimal non-hierarchical clustering is addressed. A new algorithm combining differential evolution and k-means is proposed and tested on eight well-known real-world data sets. Two criteria (clustering validity indexes), namely TRW and VCR, were used in the optimization of classification. The classification of objects to be optimized is encoded by the cluster centers in differential evolution (DE) algorithm. It induced the problem of rearrangement of centers in the population to ensure an efficient search via application of evolutionary operators. A new efficient heuristic for this rearrangement was also proposed. The plain DE variants with and without the rearrangement were compared with corresponding hybrid k-means variants. The experimental results showed that hybrid variants with k-means algorithm are essentially more efficient than the non-hybrid ones. Compared to a standard k-means algorithm with restart, the new hybrid algorithm was found more reliable and more efficient, especially in difficult tasks. The results for TRW and VCR criterion were compared. Both criteria provided the same optimal partitions and no significant differences were found in efficiency of the algorithms using these criteria.

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

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

[3]  P. Brucker.  On the Complexity of Clustering Problems , 1978 .

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

[5]  Daniela Zaharie,et al.  Influence of crossover on the behavior of Differential Evolution Algorithms , 2009, Appl. Soft Comput..

[6]  Sandra Paterlini,et al.  Using differential evolution to improve the accuracy of bank rating systems , 2007, Comput. Stat. Data Anal..

[7]  Shu-Mei Guo,et al.  Enhancing Differential Evolution Utilizing Eigenvector-Based Crossover Operator , 2015, IEEE Transactions on Evolutionary Computation.

[8]  Ville Tirronen,et al.  Recent advances in differential evolution: a survey and experimental analysis , 2010, Artificial Intelligence Review.

[9]  Josef Tvrdík.  Adaptation in differential evolution: A numerical comparison , 2009, Appl. Soft Comput..

[10]  André Carlos Ponce de Leon Ferreira de Carvalho,et al.  Efficiency issues of evolutionary k-means , 2011, Appl. Soft Comput..

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

[12]  Alex S. Fukunaga,et al.  Success-history based parameter adaptation for Differential Evolution , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[14]  Wojciech Kwedlo,et al.  A clustering method combining differential evolution with the K-means algorithm , 2011, Pattern Recognit. Lett..

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

[16]  Jason Sheng-Hong Tsai,et al.  Improving Differential Evolution With a Successful-Parent-Selecting Framework , 2015, IEEE Transactions on Evolutionary Computation.

[17]  Dervis Karaboga,et al.  A novel clustering approach: Artificial Bee Colony (ABC) algorithm , 2011, Appl. Soft Comput..

[18]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[19]  Alex S. Fukunaga,et al.  Improving the search performance of SHADE using linear population size reduction , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[20]  Alex Alves Freitas,et al.  A Survey of Evolutionary Algorithms for Clustering , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[21]  Amit Konar,et al.  Metaheuristic Clustering , 2009, Studies in Computational Intelligence.

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

[23]  J. Tvrdík.  Self-adaptive Variants of Differential Evolution with Exponential Crossover , 2009 .

[24]  F. Marriott.  Optimization methods of cluster analysis , 1982 .

[25]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[26]  Sivakumar Ramakrishnan,et al.  A survey: hybrid evolutionary algorithms for cluster analysis , 2011, Artificial Intelligence Review.

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

[28]  Vitaliy Feoktistov.  Differential Evolution: In Search of Solutions , 2006 .

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

[30]  J. Tvrdík,et al.  HYBRID ADAPTIVE DIFFERENTIAL EVOLUTION IN PARTITIONAL CLUSTERING , 2011 .

[31]  H. P. Friedman,et al.  On Some Invariant Criteria for Grouping Data , 1967 .

[32]  Josef Tvrdík,et al.  Differential Evolution with Competing Strategies Applied to Partitional Clustering , 2012, ICAISC.

[33]  Swagatam Das,et al.  Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm , 2010, Inf. Sci..

[34]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[35]  Petr Bujok,et al.  Adaptive Variants of Differential Evolution: Towards Control-Parameter-Free Optimizers , 2013, Handbook of Optimization.

[36]  Greg Hamerly,et al.  Alternatives to the k-means algorithm that find better clusterings , 2002, CIKM '02.

[37]  Vitaliy Feoktistov,et al.  Differential Evolution: In Search of Solutions (Springer Optimization and Its Applications) , 2006 .

[38]  Ajith Abraham,et al.  Swarm Intelligence Algorithms for Data Clustering , 2008, Soft Computing for Knowledge Discovery and Data Mining.

[39]  Jay Prakash,et al.  Partitional Algorithms for Hard Clustering Using Evolutionary and Swarm Intelligence Methods: A Survey , 2012, BIC-TA.

[40]  Josef Tvrdík,et al.  Competitive differential evolution for constrained problems , 2010, IEEE Congress on Evolutionary Computation.

[41]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..