Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Performance Evaluation of Some Clustering Algorithms and Validity Indices
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy cluster validation index based on inter-cluster proximity
Pattern Recognition Letters
A new cluster validity measure and its application to image compression
Pattern Analysis & Applications
A cluster validation index for GK cluster analysis based on relative degree of sharing
Information Sciences—Informatics and Computer Science: An International Journal
Combining Multiple Clusterings by Soft Correspondence
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
New indices for cluster validity assessment
Pattern Recognition Letters
Classification and Learning Using Genetic Algorithms: Applications in Bioinformatics and Web Intelligence (Natural Computing Series)
Best of both: a hybridized centroid-medoid clustering heuristic
Proceedings of the 24th international conference on Machine learning
Hierarchical clustering of mixed data based on distance hierarchy
Information Sciences: an International Journal
GAPS: A clustering method using a new point symmetry-based distance measure
Pattern Recognition
A clustering method to identify representative financial ratios
Information Sciences: an International Journal
A tabu search approach for the minimum sum-of-squares clustering problem
Information Sciences: an International Journal
Clustering algorithm for intuitionistic fuzzy sets
Information Sciences: an International Journal
GAKREM: A novel hybrid clustering algorithm
Information Sciences: an International Journal
Clustering high dimensional data: A graph-based relaxed optimization approach
Information Sciences: an International Journal
On the efficiency of evolutionary fuzzy clustering
Journal of Heuristics
On comparing two sequences of numbers and its applications to clustering analysis
Information Sciences: an International Journal
SPARCL: Efficient and Effective Shape-Based Clustering
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Immune K-means and negative selection algorithms for data analysis
Information Sciences: an International Journal
Cluster Analysis
Information Sciences: an International Journal
IEEE Transactions on Pattern Analysis and Machine Intelligence
A weighted sum validity function for clustering with a hybrid niching genetic algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A New Convergence Proof of Fuzzy c-Means
IEEE Transactions on Fuzzy Systems
A new separation measure for improving the effectiveness of validity indices
Information Sciences: an International Journal
Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm
Information Sciences: an International Journal
Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization
Information Sciences: an International Journal
A robust dynamic niching genetic clustering approach for image segmentation
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Information Sciences: an International Journal
A genetic clustering algorithm using a message-based similarity measure
Expert Systems with Applications: An International Journal
Segmentation of multiple sclerosis lesions in brain MRI: A review of automated approaches
Information Sciences: an International Journal
A two-stage genetic algorithm for automatic clustering
Neurocomputing
Gene expression data clustering using a multiobjective symmetry based clustering technique
Computers in Biology and Medicine
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In this paper a fuzzy point symmetry based genetic clustering technique (Fuzzy-VGAPS) is proposed which can automatically determine the number of clusters present in a data set as well as a good fuzzy partitioning of the data. The clusters can be of any size, shape or convexity as long as they possess the property of symmetry. Here the membership values of points to different clusters are computed using the newly proposed point symmetry based distance. A variable number of cluster centers are encoded in the chromosomes. A new fuzzy symmetry based cluster validity index, FSym-index is first proposed here and thereafter it is utilized to measure the fitness of the chromosomes. The proposed index can detect non-convex, as well as convex-non-hyperspherical partitioning with variable number of clusters. It is mathematically justified via its relationship to a well-defined hard cluster validity function: the Dunn's index, for which the condition of uniqueness has already been established. The results of the Fuzzy-VGAPS are compared with those obtained by seven other algorithms including both fuzzy and crisp methods on four artificial and four real-life data sets. Some real-life applications of Fuzzy-VGAPS to automatically cluster the gene expression data as well as segmenting the magnetic resonance brain image with multiple sclerosis lesions are also demonstrated.