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Clustering Functional Data via Variational Inference

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.