Clustering of longitudinal curves via a penalized method and EM algorithm

A new algorithm is proposed for clustering longitudinal curves. The mean curves and the principal component functions are modeled using B-spline. The clusters of the mean curves are identified through a concave pairwise fusion method. The EM algorithm and the alternating direction method of multiplier algorithm are combined to estimate the group structure, mean functions and the principal components simultaneously. The proposed method also allows to incorporate the prior neighborhood information to have more meaningful groups by adding pairwise weights in the pairwise penalties. In the simulation study, the performance of the proposed method is compared to two existing clustering methods in terms of the accuracy for estimating the number of subgroups and mean functions. The results suggest that ignoring covariance structure will have a great effect on the performance of estimating the number of groups and estimating accuracy. The effect of including pairwise weights is also explored in a spatial lattice setting to take consideration of the spatial information. The results show that incorporating spatial weights will improve the performance. An example is used to illustrate the algorithm.