Clustering functional data via variational inference

Among different 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 curve. In this work, we develop a novel variational Bayes (VB) algorithm for clustering and smoothing functional data simultaneously via a B-spline regression mixture model with random intercepts. We employ the deviance information criterion to select the best number of clusters. The proposed VB algorithm is evaluated and compared with other methods (k-means, functional k-means and two other model-based methods) via a simulation study under various scenarios. We apply our proposed methodology to two publicly available datasets. We demonstrate that the proposed VB algorithm achieves satisfactory clustering performance in both simulation and real data analyses.