Fuzzy Change-Point Algorithms for Regression Models

Abstract

Change-point (CP) regression models have been widely applied in various fields, where detecting CPs is an important problem. Detecting the location of CPs in regression models could be equivalent to partitioning data points into clusters of similar individuals. In the literature, fuzzy clustering has been widely applied in various fields, but it is less used in locating CPs in CP regression models. In this paper, a new method, called fuzzy CP (FCP) algorithm, is proposed to detect the CPs and simultaneously estimate the parameters of regression models. The fuzzy c -partitions concept is first embedded into the CP regression models. Any possible collection of all CPs is considered as a partitioning of data with a fuzzy membership. We then transfer these memberships into the pseudomemberships of data points belonging to each individual cluster, and therefore, we can obtain the estimates for model parameters by the fuzzy c -regressions method. Subsequently, we use the fuzzy c -means clustering to obtain the new iterates of the CP collection memberships by minimizing an objective function concerning the deviations between the predicted response values and data values. We illustrate the new approach with several numerical examples and real datasets. Experimental results actually show that the proposed FCP is an effective and useful CP detection algorithm for CP regression models and can be applied to various fields, such as econometrics, medicine, quality control, and signal processing.