Multidimensional heterogeneity learning for count value tensor data with applications to field goal attempt analysis of NBA players

We propose a multidimensional tensor clustering approach for studying how professional basketball players' shooting patterns vary over court locations and game time. Unlike most existing methods that only study continuous-valued tensors or have to assume the same cluster structure along different tensor directions, we propose a Bayesian nonparametric model that deals with count-valued tensors and projects the heterogeneity among players onto tensor dimensions while allowing cluster structures to be different over directions. Our method is fully probabilistic; hence allows simultaneous inference on both the number of clusters and the cluster configurations. We present an efficient posterior sampling method and establish the large-sample convergence properties for the posterior distribution. Simulation studies have demonstrated an excellent empirical performance of the proposed method. Finally, an application to shot chart data collected from 191 NBA players during the 2017-2018 regular season is conducted and reveals several interesting insights for basketball analytics.