  We introduce a multiscale supervised dimension reduction method for SPatial
Interaction Network (SPIN) data, which consist of a collection of spatially
coordinated interactions. This type of predictor arises when the sampling unit
of data is composed of a collection of primitive variables, each of them being
essentially unique, so that it becomes necessary to group the variables in
order to simplify the representation and enhance interpretability. In this
paper, we introduce an empirical Bayes approach called spinlets, which first
constructs a partitioning tree to guide the reduction over multiple spatial
granularities, and then refines the representation of predictors according to
the relevance to the response. We consider an inverse Poisson regression model
and propose a new multiscale generalized double Pareto prior, which is induced
via a tree-structured parameter expansion scheme. Our approach is motivated by
an application in soccer analytics, in which we obtain compact vectorial
representations and readily interpretable visualizations of the complex network
objects, supervised by the response of interest.
