A method of identifying influential data in fuzzy clustering

In multivariate statistical methods, it is important to identify influential observations for a reasonable interpretation of the data structure. In this paper, we propose a method for identifying influential data in the fuzzy C-means (FCM) algorithm. To investigate such data, we consider a perturbation of the data points and evaluate the effect of a perturbation. As a perturbation, we consider two cases: one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified. By computing the change in the clustering result of FCM when given data points are slightly perturbed, we can look for data points that greatly affect the result. Also, we confirm an efficacy of the proposed method by numerical examples.