Simulated annealing: theory and applications
Simulated annealing: theory and applications
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Statistical Pattern Recognition: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Optimal Expected-Time Algorithms for Closest Point Problems
ACM Transactions on Mathematical Software (TOMS)
A Modified Version of the K-Means Algorithm with a Distance Based on Cluster Symmetry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Performance Evaluation of Some Clustering Algorithms and Validity Indices
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art
Evolutionary Computation
Classification and Learning Using Genetic Algorithms: Applications in Bioinformatics and Web Intelligence (Natural Computing Series)
Statistical Comparisons of Classifiers over Multiple Data Sets
The Journal of Machine Learning Research
GAPS: A clustering method using a new point symmetry-based distance measure
Pattern Recognition
A genetic algorithm for cluster analysis
Intelligent Data Analysis
A Point Symmetry-Based Clustering Technique for Automatic Evolution of Clusters
IEEE Transactions on Knowledge and Data Engineering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonparametric genetic clustering: comparison of validity indices
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
An Evolutionary Approach to Multiobjective Clustering
IEEE Transactions on Evolutionary Computation
A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA
IEEE Transactions on Evolutionary Computation
A weighted sum validity function for clustering with a hybrid niching genetic algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
Validity index for clusters of different sizes and densities
Pattern Recognition Letters
A two-stage genetic algorithm for automatic clustering
Neurocomputing
Engineering Applications of Artificial Intelligence
Engineering Applications of Artificial Intelligence
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In this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization (MOO) problem, optimizing a set of cluster validity indices simultaneously. The proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy. Here variable number of cluster centers is encoded in the string. The number of clusters present in different strings varies over a range. The points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing Euclidean distance. Two cluster validity indices, one based on the Euclidean distance, XB-index, and another recently developed point symmetry distance based cluster validity index, Sym-index, are optimized simultaneously in order to determine the appropriate number of clusters present in a data set. Thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters. A new semi-supervised method is also proposed in the present paper to select a single solution from the final Pareto optimal front of the proposed multiobjective clustering technique. The efficacy of the proposed algorithm is shown for seven artificial data sets and six real-life data sets of varying complexities. Results are also compared with those obtained by another multiobjective clustering technique, MOCK, two single objective genetic algorithm based automatic clustering techniques, VGAPS clustering and GCUK clustering.