Fuzzy c-Regression with Partitioning of Categories

Abstract

Fuzzy c-Regression Models (FCRM) is a fuzzy clustering-based switching regression model where regression errors are also used for clustering criteria in a Fuzzy c-Means (FCM)-like iterative optimization procedure. In data mining applications, we often deal with databases consisting of mixed measurement levels. Optimal scaling is a technique for mixed measurement situations, in which nominal variables represented by categories are quantified so that they suit the current model and then the model is updated in a single numerical space using the current quantified scores. Honda et al. applied the technique to FCM-type fuzzy clustering in order to characterize each cluster considering mutual relation among categories. In this paper, we propose a new switching regression model that improves the interpretability of multiple regression models considering partition of categories. The new model uses a hybrid objective function of FCRM for numerical variables and FCM for categorical variables. The FCRM part is responsible for multiple regression model estimation while the FCM part tries to characterize each cluster by assigning corresponding categories.