  Physical activity levels are an important predictor of cardiovascular health
and increasingly being measured by sensors, like accelerometers. Accelerometers
produce rich multivariate data that can inform important clinical decisions
related to individual patients and public health. The CHAMPION study, a study
of youth with chronic inflammatory conditions, aims to determine the links
between heart health, inflammation, physical activity, and fitness. The
accelerometer data from CHAMPION is represented as 4-dimensional arrays, and a
finite mixture of multidimensional arrays model is developed for clustering.
The use of model-based clustering for multidimensional arrays has thus far been
limited to two-dimensional arrays, i.e., matrices or order-two tensors, and the
work in this paper can also be seen as an approach for clustering D-dimensional
arrays for D > 2 or, in other words, for clustering order-D tensors.
