Supervised Multiscale Dimension Reduction for Spatial Interaction Networks

In modern applications, we frequently encounter complex object-type data, such as functions (Ramsay and Silverman, 2006), trees (Wang and Marron, 2007), shapes (Srivastava et al., 2011), and networks (Durante et al., 2017). In many instances, such data are collected repeatedly under different conditions, with an additional response variable of interest available for each replicate. This has motivated an increasingly rich literature on generalizing regression on vector predictors to settings involving more elaborate object-type predictors with special characteristics, such as functions (James, 2002), manifolds (Nilsson et al., 2007), tensors (Zhou et al., 2013), and undirected networks (Guha and Rodriguez, 2018). Complex objects are often built recursively from simpler parts. In this article, we introduce a new class of object data, denoted composite objects (CO), which are structured data composed of primitive objects (POs). Many common data types can be seen as instances of the CO family, such as a collection of time-stamped events, connections between regions of the brain, or basketball shots on the court. The component POs in COtype data can be enormous and mostly distinctive from one another across replicates, presenting new challenges for data exploration, analysis, and visualization. We are interested in identifying the association between the patterns of coordinated interactions among individual units in a group and the performance of the group. In this article, we focus on analyzing the FIFA World Cup 2018 data collected by StatsBomb.