In multivariate statistical methods, it is important to identify influ
ential observations for a reasonable interpretation of the data struct
ure, In this paper, we propose a method for identifying influential da
ta 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 c
ase in which the direction of a perturbation is specified and the othe
r is the case in which the direction of a perturbation is not specifie
d, By computing the change in the clustering result of FCM when given
data points are slightly perturbed, we can look for data points that g
reatly affect the result, Also, we confirm an efficacy of the proposed
method by numerical examples.