A Case Study on Spatially Dependent Functional Data: the Analysis of Mobile Network Data for the Metropolitan Area of Milan

43/2012

A Case Study on Spatially Dependent Functional Data: the Analysis of Mobile Network Data for the Metropolitan Area of Milan

Friday 19th October 2012

Secchi, P.; Vantini, S.; Vitelli, V.

We analyze geo-referenced high-dimensional data describing the use over time of the mobile-phone network in the urban area of Milan, Italy. Aim of the analysis is segmenting the metropolitan area of Milan into subregions sharing a similar pattern along time, possibly related to activities taking place in specific locations and/or times within the city. To tackle this problem, we develop a non-parametric method for the analysis of spatially dependent functional data, named Bagging Voronoi Treelet Analysis. Indeed, this novel approach integrates the treelet decomposition with a proper treatment of spatial dependence, obtained through a Bagging Voronoi strategy. The latter relies on the aggregation of different replicates of the analysis, each involving a set of functional local representatives associated to random Voronoi-based neighborhoods covering the investigated area. In the presence of spatial dependence the method appears to be both computationally and statistically efficient. Indeed results clearly point out some interesting temporal patterns interpretable both in terms of population density and mobility (e.g., daily work activities in the tertiary district, leisure activities in residential areas in the evenings and in the weekend, commuters movements along the highways during rush hours, and localized mob concentrations related to occasional events). Moreover we perform two simulation studies, aimed at investigating the properties and performances of the method.

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Journal of the American Stastistical Association