FunCWM: Functional Cluster-Weighted Models and Their Applications to Climatological Functional Data

Cluster-weighted models (CWMs) are a powerful approach in model-based clustering, widely used for capturing complex relationships in regression data. We proposed a new class of CWMs to accommodate functional data, addressing the regression of a functional response on one or more functional predictors across different groups of subjects. Each functional random variable can be modeled as a Gaussian or Student’s T process. Projecting the response curve and functional predictors onto their eigenspaces simplifies the new regression model into a structure similar to classical CWMs. By imposing constraints on the covariance matrices of these projected data, we develop a family of parsimonious models. It leads to the proposed functional cluster-weighted model (FunCWM) approach. The maximum likelihood estimation of parameters is facilitated through an expectation-maximization (EM) algorithm. The consistency properties of these estimates are examined. The FunCWM approach is evaluated on several simulated and real datasets, and the results confirm its efficiency.