Functional clustering of accelerometer data via transformed input variables

The paper considers the clustering problem of physical activity data measured by a computerized accelerometer. Classical methods such as K‐means clustering and partitioning around medoids are not efficient in handling accelerometer data that are high dimensional with inherent multiscale structures. Existing functional clustering approaches do not naturally utilize the dynamic structures of accelerometer data that may be necessary to form homogeneous clusters in a meaningful way. The paper introduces new input variables for clustering the accelerometer data based on the rank‐based transformation and thick pen transformation, which reflect specific structures of the data such as the amount and the pattern of physical activity while preserving a functional form. The clustering methods proposed are obtained by coupling the transformed input variables with functional clustering that considers a marginal representation of the data for building clustering criteria. We suggest several clustering schemes using the proposed methods and apply the schemes to a real data set of 365 subjects. A simulation study is performed to evaluate the empirical performance of the methods proposed, which are shown to be superior to some existing methods.