A Fuzzy Bayesian Classifier with Learned Mahalanobis Distance

Abstract

Recent developments show that naive Bayesian classifier (NBC) performs significantly better in applications, although it is based on the assumption that all attributes are independent of each other. However, in the NBC each variable has a finite number of values, which means that in large data sets NBC may not be so effective in classifications. For example, variables may take continuous values. To overcome this issue, many researchers used fuzzy naive Bayesian classification for partitioning the continuous values. On the other hand, the choice of the distance function is an important subject that should be taken into consideration in fuzzy partitioning or clustering. In this study, a new fuzzy Bayes classifier is proposed for numerical attributes without the independency assumption. To get high accuracy in classification, membership functions are constructed by using the fuzzy C-means clustering (FCM). The main objective of using FCM is to obtain membership functions directly from the data set instead of consulting to an expert. The proposed method is demonstrated on the basis of two well-known data sets from the literature, which consist of numerical attributes only. The results show that the proposed the fuzzy Bayes classification is at least comparable to other methods.