  Functional data analysis deals with data recorded densely over time (or any
other continuum) with one or more observed curves per subject. Conceptually,
functional data are continuously defined, but in practice, they are usually
observed at discrete points. Among different kinds of functional data analyses,
clustering analysis aims to determine underlying groups of curves in the
dataset when there is no information on the group membership of each individual
curve. In this work, we propose a new model-based approach for clustering and
smoothing functional data simultaneously via variational inference. We derive
coordinate ascent mean-field variational Bayes algorithms to approximate the
posterior distribution of our model parameters by finding the variational
distribution with the smallest Kullback-Leibler divergence to the posterior.
The performance of our proposed method is evaluated using simulated data and
publicly available datasets.
