Abstract

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling a variety of function features, such as jump points, branching, and periodicity. Functional ANOVA is employed to further decompose multivariate functions in a reproducing kernel Hilbert space and provide associated notions of main effect and interaction. Parsimonious random effects are used to capture various corre-lation structures. The mixed-effect models are nested under a general mixture model, in which the heterogeneity of functional data is characterized. We pro-pose a penalized Henderson’s likelihood approach for model-fitting and design a rejection-controlled EM algorithm for the estimation. Our method selects

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