We propose a method for clustering multivariate functional linear regression data. Our approach extends multivariate cluster weighted models \cite{DangPunzoMcNicholasIngrassiaBrowne:2017} to functional data with multivariate functional response and predictors, based on the ideas used by the funHDDC method \cite{SchmutzJacquesBouveyronChezeMartin:2020}. To add model flexibility, we consider several two-component parsimonious models by combining the parsimonious models used for funHDDC with the Gaussian parsimonious clustering models family in \cite{CeleuxGovaert:1995}. Parameter estimation is carried out within the expectation maximization (EM) algorithm framework. The proposed method outperforms funHDDC on simulated and real-world data.

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\bibitem{CeleuxGovaert:1995} Celeux G., Govaert G.: Gaussian parsimonious clustering models. Pattern

Recognition \textbf{28}, 781--793 (1995)

\bibitem{DangPunzoMcNicholasIngrassiaBrowne:2017}

Dang U.J., Punzo A., McNicholas P.D., et~al: Multivariate response and parsimony for {G}aussian cluster-weighted models. J. Classif \textbf{34}, 4--34 (2017)

\bibitem{SchmutzJacquesBouveyronChezeMartin:2020} Schmutz A., Jacques J., Bouveyron C., et~al: Clustering multivariate functional data in group-specific functional subspaces. Comput. Stat. \textbf{35}, 1101--1131 (2020)

\end{thebibliography}