Fuzzy C-means Clustering Algorithm for Cluster Membership Determination

Abstract

Membership of open star clusters or Galactic open clusters is very important roles to study the formation and evaluation of gravitationally bound system. In the field of an image, the relative x and y coordinate positions of each star with respect to all the other stars are adapted. Therefore, in this paper, a new method for the determination open star cluster membership based on Fuzzy C-means Clustering algorithm is proposed. In the fuzzy clustering algorithm, a data point may belong to several clusters with different degree of memberships. Therefore, the membership values for a data point will represents the degree to which that point belongs to a particular cluster. The proposed method allows to efficiently discriminating the cluster membership from the field stars. The membership probabilities have been calculated and compared to those obtained by the other methods. To validate the method, we applied it on Berkeley 39 and NGC 188 open star clusters, where the membership stars in these clusters are obtained. The membership probability of stars clusters is assigned through the approach provides number of probable members.