  Functional data analysis (FDA) is an important modern paradigm for handling
infinite-dimensional data. An important task in FDA is model-based clustering,
which organizes functional populations into groups via subpopulation
structures. The most common approach for model-based clustering of functional
data is via mixtures of linear mixed-effects models. The mixture of linear
mixed-effects models (MLMM) approach requires a computationally intensive
algorithm for estimation. We provide a novel Gaussian mixture model (GMM)
characterization of the model-based clustering problem. We demonstrate that
this GMM-based characterization allows for improved computational speeds over
the MLMM approach when applied via available functions in the R programming
environment. Theoretical considerations for the GMM approach are discussed. An
example application to a dataset based upon calcium imaging in the larval
zebrafish brain is provided as a demonstration of the effectiveness of the
simpler GMM approach.
