Robust clustering of imprecise data

Robust fuzzy clustering models for fuzzy data are proposed. In particular, using a “Partitioning Around Medoids” (PAM) approach, first a timid robustification of fuzzy clustering for a general class of fuzzy data is proposed. Successively, we propose three robust fuzzy clustering models based on, respectively, the so-called metric, noise and trimmed approaches. The metric approach achieves its robustness with respect to outliers by taking into account a “robust” distance measure, the noise approach by introducing a noise cluster represented by a noise prototype, and the trimmed approach by trimming away a certain fraction of data units. A comparative simulation study and measures of misclassification and of robustness with respect to prototype detection in the presence of outliers have been developed. Several applications to chemometrical and benchmark data are also presented.