A simple and fast method to determine the parameters for fuzzy c-means cluster analysis.

Motivation: Fuzzy c-means clustering is widely used to identify cluster structures in high-dimensional datasets, such as those obtained in DNA microarray and quantitative proteomics experiments. One of its main limitations is the lack of a computationally fast method to set optimal values of algorithm parameters. Wrong parameter values may either lead to the inclusion of purely random fluctuations in the results or ignore potentially important data. The optimal solution has parameter values for which the clustering does not yield any results for a purely random dataset but which detects cluster formation with maximum resolution on the edge of randomness.
Results: Estimation of the optimal parameter values is achieved by evaluation of the results of the clustering procedure applied to randomized datasets. In this case, the optimal value of the fuzzifier follows common rules that depend only on the main properties of the dataset. Taking the dimension of the set and the number of objects as input values instead of evaluating the entire dataset allows us to propose a functional relationship determining the fuzzifier directly. This result speaks strongly against using a predefined fuzzifier as typically done in many previous studies. Validation indices are generally used for the estimation of the optimal number of clusters. A comparison shows that the minimum distance between the centroids provides results that are at least equivalent or better than those obtained by other computationally more expensive indices.