‎a new approach to define the number of clusters for partitional clustering algorithms

‎data clustering consists of grouping similar objects according to some characteristic‎. ‎in the literature‎, ‎there are several clustering algorithms‎, ‎among which stands out the fuzzy c-means (fcm)‎, ‎one of the most discussed algorithms‎, ‎being used in different applications‎. ‎although it is a simple and easy to manipulate clustering method‎, ‎the fcm requires as its initial parameter the number of clusters‎. ‎usually‎, ‎this information is unknown‎, ‎beforehand and this becomes a relevant problem in the data cluster analysis process‎. ‎in this context‎, ‎this work proposes a new methodology to determine the number of clusters of partitional algorithms‎, ‎using subsets of the original data in order to define the number of clusters‎. ‎this new methodology‎, ‎is intended to reduce the side effects of the cluster definition phase‎, ‎possibly making the processing time faster and decreasing the computational cost‎. ‎to evaluate the proposed methodology‎, ‎different cluster validation indices will be used to evaluate the quality of the clusters obtained by the fcm algorithms and some of its variants‎, ‎when applied to different databases‎. ‎through the empirical analysis‎, ‎we can conclude that the results obtained in this article are promising‎, ‎both from an experimental point of view and from a statistical point of view‎.