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Abstract:
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There are at least a couple challenges in functional clustering due to the existence of phase variability in the functional data. The first challenge is related to the removal of phase variation through curve registration. Curve registration requires a target function that a functional curve is aligned to. However, since the cluster membership is unknown, methods that consider curve registration as a data preprocessing step or separate the curve registration and clustering steps typically do not work. We proposed an iterative method that performs curve registration and clustering simultaneously. The second challenge is related to the selection of the penalty parameter for the warping function and number of clusters in the data. Without the specification of a warping penalty, the number of clusters determined by the amplitude variability is not uniquely identified. We propose a unified criterion for simultaneously selecting the number of clusters and warping penalty. The criterion is derived from the predictive classification likelihood, evaluating the predictability of the cluster membership on an outcome while penalizing the cluster membership uncertainty.
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