Problems in Fuzzy c-means and Its Possible Solutions

Abstract

Clustering is one of the well-known unsupervised learning methods, in which a data set is grouped into some number of homogeneous clusters. There are numerous clustering algorithms available and they have been used in various applications. Fuzzy c-means (FCM), the most well-known partitional clustering algorithm, was established in 1970's and still in use. However, there are some unsolved problems in FCM and variants of FCM are still under development. In this paper, the problems in FCM are first explained and the available solutions are investigated, which is aimed to give researchers some possible ways of future research. Most of the FCM variants try to solve the problems using domain knowledge specific to a given problem. However, in this paper, we try to give general solutions without using any domain knowledge. Although there are more things left than discovered, this paper may be a good starting point for researchers newly entered into a clustering area.

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“…The input of FCM is a data set of pending clustering, and each element has p features. The output is a matrix with c lines and n columns named U , where c is the amount of clusters, n is the number of elements of the data set; we can use this matrix to represent the result of the classification [31]. A column in the matrix represents the degree to which this element belongs to each class, and which the value is the largest represents which class this element belongs to equation ( 4) is FCM's value function.…”