Mountain C-Regressions in Comparing Fuzzy C-Regressions

In fuzzy clustering, the fuzzy c-mean (FCM) is a most used algorithm. The embedding of FCM into switching regressions, called the fuzzy c-regression (FCR), was proposed by Hathaway and Bezdek in 1993. However, these FCRs always heavily depend on the initial values. In this paper, we propose mountain c-regressions (MCR) to solve the initial-value problem where the MCR is based on the modified mountain clustering method. We first transform the data set into a parameter space and then take a random sample from the transformed data set. We implement the modified mountain clustering on the random samples for switching regressions. The proposed MCR can form c estimated regression models for switching regression data sets without giving initials. Several examples show the accuracy and effectiveness of the proposed MCR method.