Fuzzy C-Means Clustering and Facility Location Problems

K.R. ┼Żalik (Slovenia)

Keywords

clustering, k-means, fuzzy c-means, facility location

Abstract

Clustering is an optimization problem described by the objective function, which minimize distances between data points of one cluster and maximize distances between points belonging to two or more clusters. In this paper, the focus is on objective functions more commonly referred to as facility location problem, which is transformed into the problem to determine a set of k points from the given set of n data points in d-dimensional space, called centers, so as to minimize the mean squared distance from each data point to its nearest center. This is called k-means clustering. We used also fuzzy c-means clustering method that is similar to k-means clustering, but it allows data belonging to two or more clusters. In facility location problems, fuzzy c-means algorithm gives better results than hard-k-means algorithm. Another important feature of fuzzy c-means algorithm is membership function and an object can belong to several clusteres at the same time but with different degrees. This is a useful feature for a facility location problem.

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