Fuzzy C-Means Clustering Using Asymmetric Loss Function

Abstract

In this work, a fuzzy clustering algorithm is proposed based on the asymmetric loss function instead of the usual symmetric dissimilarities. Linear Exponential (LINEX) loss function is a commonly used asymmetric loss function, which is considered in this paper. We prove that the negative likelihood of an extreme value distribution is equal to LINEX loss function and clarify some of its advantages. Using such a loss function, the so-called LINEX Fuzzy C-Means algorithm is introduced. The introduced clustering method is compared with its crisp version and Fuzzy C-Means algorithms through a few real datasets as well as some simulated datasets.