FCM-type switching regression with alternating least squares method

Abstract

Fuzzy c-Regression Models (FCRM) performs switching regression based on a Fuzzy c-Means (FCM)-like iterative optimization procedure, in which regression errors are also used for clustering criteria. 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 nominal variables (categorical observations) are quantified so that they suit the current model, and has been applied to FCM-type fuzzy clustering in order to characterize each cluster considering mutual relation among categories. This paper proposes two new algorithms for handling mixed measurement situations in FCM-type switching regression based on the alternating least squares method. The iterative algorithms include additional optimal scaling steps for calculating numerical scores of categorical variables.