A New Credibilistic Clustering Method with Mahalanobis Distance

Abstract

The fuzzy c-means (FCM) is the best known clustering and use the degree of membership fuzzy to data clustering. But the membership is not always for all data correctly. That is, at scattered dataset belonging is less and noisy dataset belonging is more assigned and local optimization problem occurs. Possibility c-means (PCM) was introduced to correspond weaknesses FCM approach. In PCM was not self-duality property. In other words, a sample membership for all clusters be assigned more than one and basic condition FCM were violated. One of the new method is Credibilistic clustering and based on credibility theory proposed that is used to study the behavior of fuzzy phenomenon. The aim is to provide new Credibilistic clustering approach with replacing credibility measure instead of the fuzzy membership and Mahalanobis distance use in FCM objective function. Credibility measure has self-duality property and solves coincident clustering problem. Mahalanobis distance used instead of Euclidian distance to separate cluster centers from each other and dens samples of each cluster. The result of proposed method is evaluated with three numeric dataset and Iris dataset. The most important challenge will be how to choose the initial cluster centers in the noisy dataset. In the future, we can be used FCM combined with particle swarm optimization.