Triplet of FCM classifiers

This paper proposes an additional version of the fuzzy c-means based classifier (FCMC). The classifier FCMC-R treats relational data instead of object data. FCMCs use covariance structures to represent flexible shapes of clusters. Despite its effectiveness, the intense computation of covariance matrices is an impediment for classifying a set of high-dimensional feature data. In order to tackle with this problem, we proposed a way of directly handling high-dimensional data, i.e., FCMC-H. The third type of the FCM classifier is the relational classifier FCMC-R, which is derived from FCMC-H. The relational data represented by a relational matrix are based on dissimilarities or distances between object data. The triplets, i.e., FCMC, FCMC-H, and FCMC-R are equivalent when the dimensionality of feature vectors is not very high and the dissimilarity is represented by Euclidean distances. The randomized test set performance of FCMC on the sets of object data from UCI repository is comparable to that of the support vector machine (SVM) classifier. The performances of the triplet in terms of 100 times three way data splits (3-WDS) procedure are compared. The triplet surpasses the k-nearest neighbor (k-NN) classifier, which is a well established and very popular relational classifier.