Functional fuzzy clusterwise regression analysis

We propose a functional extension of fuzzy clusterwise regression, which estimates fuzzy memberships of clusters and regression coefficient functions for each cluster simultaneously. The proposed method permits dependent and/or predictor variables to be functional, varying over time, space, and other continua. The fuzzy memberships and clusterwise regression coefficient functions are estimated by minimizing an objective function that adopts a basis function expansion approach to approximating functional data. An alternating least squares algorithm is developed to minimize the objective function. We conduct simulation studies to demonstrate the superior performance of the proposed method compared to its non-functional counterpart and to examine the performance of various cluster validity measures for selecting the optimal number of clusters. We apply the proposed method to real datasets to illustrate the empirical usefulness of the proposed method.