Fuzzy mathematical techniques with applications
Fuzzy mathematical techniques with applications
A multi-start global minimization algorithm with dynamic search trajectories
Journal of Optimization Theory and Applications
Algorithms for clustering data
Algorithms for clustering data
Selecting typical instances in instance-based learning
ML92 Proceedings of the ninth international workshop on Machine learning
A conceptual version of the K-means algorithm
Pattern Recognition Letters
Machine Learning - Special issue on applications of machine learning and the knowledge discovery process
CACTUS—clustering categorical data using summaries
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
J: the natural language for analytic computing
J: the natural language for analytic computing
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
COOLCAT: an entropy-based algorithm for categorical clustering
Proceedings of the eleventh international conference on Information and knowledge management
Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values
Data Mining and Knowledge Discovery
Journal of Global Optimization
Learning Feature Weights for Similarity Measures using Genetic Algorithms
INTSYS '98 Proceedings of the IEEE International Joint Symposia on Intelligence and Systems
A Dynamic Clustering Algorithm Based on PSO and Its Application in Fuzzy Identification
IIH-MSP '06 Proceedings of the 2006 International Conference on Intelligent Information Hiding and Multimedia
A method for fuzzy clustering with ordinal attributes: Research Articles
International Journal of Intelligent Systems
Clustering with a genetically optimized approach
IEEE Transactions on Evolutionary Computation
A fuzzy k-modes algorithm for clustering categorical data
IEEE Transactions on Fuzzy Systems
Genetic Algorithms and Very Fast Simulated Reannealing: A comparison
Mathematical and Computer Modelling: An International Journal
Simulated annealing: Practice versus theory
Mathematical and Computer Modelling: An International Journal
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There are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale. Not so well established are methods to be applied when the feature values are ordinal or nominal. In that case there is no satisfactory method it seems. This paper discusses a modified fuzzy c-means clustering method where an ordinal to numeric mapping for the ordinal features is obtained as part of the clustering process. Part of minimizing the objective function for the clustering is to find this ordinal to numeric mapping. Having this mapping allows standard methods of fuzzy c-means clustering to be used since then if there are no categorical features all the features are numeric. The mapping is not of interest in itself and to obtain it is only a subsidiary objective of the clustering process. The mapping allows for the degrees of freedom that is characteristic of the data. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion may be used in combination with a multi-start strategy for the PSO. Other clustering methods generally find local optimum of their objective function. Through simulations and experiments with real and artificial data the method proposed here is shown to be quite effective.