Abstract
Clustering functional data aims to identify unique functional patterns in the entire domain, but this can be challenging due to phase variability that distorts the observed patterns. Curve registration can be used to remove this variability, but determining the appropriate level of warping flexibility can be complicated. Curve registration also requires a target to which a functional object is aligned, typically the cross-sectional mean of functional objects within the same cluster. However, this mean is unknown prior to clustering. Furthermore, there is a trade-off between flexible warping and the number of resulting clusters. Removing more phase variability through curve registration can lead to fewer remaining variations in the functional data, resulting in a smaller number of clusters. Thus, the optimal number of clusters and warping flexibility cannot be uniquely identified. We propose to use external information to solve the identification issue. We define a cross validated Kullback-Leibler information criterion to select the number of clusters and the warping penalty. The criterion is derived from the predictive classification likelihood considering the joint distribution of both the functional data and external variable and penalizes the uncertainty in the cluster membership. We evaluate our method through simulation and apply it to electrocardiographic data collected in the Chronic Renal Insufficiency Cohort study. We identify two distinct clusters of electrocardiogram (ECG) profiles, with the second cluster exhibiting ST segment depression, an indication of cardiac ischemia, compared to the normal ECG profiles in the first cluster.