Fuzzy c-Regression Models Based on Optimal Scaling of Categorical Observation with Tolerance

Abstract

Switching regression is a powerful tool for revealing intrinsic non-linear dependencies among exploratory variables and objective variables. In this paper, Fuzzy c-Regression Models (FCRM), which is an FCM-type switching regression model, is modified so that it can handle uncertain categorical observations. In data mining applications, we often deal with databases consisting of mixed measurement levels. The alternating least squares method is a technique for mixed measurement situations, in which categorical observations are quantified such that they suit the current model by optimal scaling, and has been applied to FCM-type fuzzy clustering in order to characterize each cluster considering mutual relation among categories. While optimal scaling has been used for handling categorical observations, categorical observations often have ambiguity of natural language categories. In this paper, a modified FCM-type switching regression is performed by considering tolerance of quantified category observations in conjunction with optimal scaling.