Nonparametric clustering for longitudinal functional data with the application to H-NMR spectra of kidney transplant patients. Longitudinal functional data clustering.

Longitudinal functional data are increasingly common in the health domain. The motivated dataset for this paper comprises H-NMR spectra of kidney transplant patients [8]. Our aim is to cluster patients into different clinical outcome subgoups to reveal the success of the transplantation. The NMR spectra of each patient at each time point are functional data and the data are longitudinally collected at up to nine different time points. Existing methods are available for functional data collected at one time point, but not for longitudinal functional data collected at a grid of time points subject to missingness. We therefore first apply a method to extract the same number of functional feactures for each subject. Next we propose a novel nonparametric clustering method for mulitivariate functional data. We applied our proposed clustering method to the kidney transplant dataset both to a subset of the raw data with only two time points and the extacted functional features. It appeared that the proposed method achieves better clustering performance on the extracted functional features than on the subset of raw data. A data simulation study was performed to further evaluate the method. The design mimiced the kidney transplant dataset but with a larger sample size. Scenarios which have different levels of noise were considered. The simulation study showed the accuarcy of our proposed method.