Discussion of “Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan”

Abstract

We congratulate the authors for a very interesting and timely contribution to an important problem: using nonparametric functional data analysis methods for studying spatio-temporal observations with the aim to identify subregions in a spatial domain sharing similar patterns along time. The authors develop an efficient methodology to perform dimensional reduction of spatially dependent functional data based on treelet decompositions and an appropriate bagging Voronoi strategy that allows them to take into account the spatial dependency in the analysed data. Treelets were first introduced in Lee and Nadler (2007) and Lee et al. (2008) as a multi-scale basis that extends wavelets to unordered data. The method is fully adaptive. It returns orthonormal basis functions supported on nested clusters in a hierarchical tree. Unlike other hierarchical methods, the basis and the tree structure are computed simultaneously, and both reflect the internal structure of the data. Combination of treelets with a bagging Voronoi strategy for identifying subregions with similar patterns along time introduces numerical challenges that are efficiently tackled by the authors.