论文标题
计数价值张量数据的多维异质性学习，以及应用程序，用于现场目标尝试分析NBA播放器
Multidimensional heterogeneity learning for count value tensor data with applications to field goal attempt analysis of NBA players
论文作者
论文摘要
我们提出了一种多维张量聚类方法，用于研究专业篮球运动员的投篮命中率如何在法庭位置和比赛时间内变化。与大多数仅研究连续值张量或必须沿不同张量方向采用相同的簇结构的方法不同，我们提出了一个贝叶斯非参数模型，该模型涉及计数值张力张量，并将播放器之间的异质性投射到张量尺寸上，同时允许群集结构在方向上不同。我们的方法是完全概率的。因此，可以同时推断簇数和群集配置。我们提出了一种有效的后验抽样方法，并建立了后验分布的大样本收敛性。模拟研究表明该方法的经验表现出色。最后，在2017-2018常规赛期间收集了从191名NBA球员收集的射击图表数据，并揭示了一些有趣的篮球分析见解。
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.
