A Study on c-Regression Model Based on Gaussian Process

Abstract

We proposed fuzzy c-regression (FCRM) based Gaussian process regression (GPRM) for the purpose of obtaining a complex regression model. FCRM is a method to perform clustering and regression at the same time, and can obtain cluster partition and regression models as a result. FCRM generally provides a linear regression model, and is difficult to obtain non-linear regression model. On the other hand, GPRM obtains a non-linear regression model, which is not obtained from a FCRM. Therefore, we present a method to obtain a complex regression model by performing GPRM based on the cluster partitioning obtained from the FCRM. In the numerical experiments, we compare the regression model by the GPRM with conventional one, and evaluate the cluster partitioning obtained. We also consider the effect of the kernel functions used in the Gaussian process (GP), and show the effectiveness of the proposed method.