Modified fuzzy c-means for ordinal valued attributes with particle swarm for optimization
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. (C) 2009 Elsevier B.V. All rights reserved.
fuzzy c-means fuzzy clustering ordinal features particle swarm optimization pattern classification