Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering
Abstract
Fuzzy C-Means is a distance-based clustering process which applied by fuzzy logic concept. Clustering process worked in linear to the iteration process to minimizing the objective function. The objective function is an addition of the multiplication between the coordinates distance towards their closest cluster centroid and their membership degree. The more the iteration process, the objective function should get lower and lower. The objective of this research is to observe whether the distances which usually applied are able to fulfill the aforementioned hypothesis for determining the most suitable distance for Fuzzy C-Means clustering application. Few distance function was applied in the same dataset. 5 standard datasets and 2 random datasets were used to test the fuzzy c-means clustering performance with the 7 different distance function. Accuracy, purity, and Rand Index also applied to measure the quality of the resulted cluster. The observation result depicted that the distance function which resulted in the best quality of clusters are Euclidean, Average, Manhattan, Minkowski, Minkowski-Chebisev, and Canberra distance. These 6 distances were able to fulfill the basic hypothesis of the objective function behavior on Fuzzy C-Means Clustering method. The only distance who were not able to fulfill the basic hypothesis is Chebisev distance.
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DOI: http://dx.doi.org/10.26555/jiteki.v7i1.20516
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