Supervised Multiscale Dimension Reduction for Spatial Interaction Networks


We introduce a multiscale supervised dimension reduction method for SPatial Interaction Network (SPIN) data, which consist of a collection of interactions between units indexed by spatial coordinates. To facilitate regression analysis with SPIN predictors, we extend bag-of-words representations to more complex settings, in which each primitive variable being represented is essentially unique, so that it becomes necessary to group the variables in order to simplify the representation and enhance interpretability and statistical power. We propose an empirical Bayes approach called spinlets, which first constructs a partitioning tree to guide the reduction with mixed spatial granularities, and then refines the representation of predictors according to the relevance to the response. We consider an inverse Poisson regression model, regularized by a multiscale extension of the generalized double Pareto prior, induced via a novel tree-structured parameter expansion scheme. Our approach is motivated by an application in soccer analytics, in which we obtain spinlets visualizations of soccer passing networks under the supervision of team performance.