Treelet Analysis and Independent Component Analysis of Milan Mobile-Network Data: Investigating Population Mobility and Behavior

The metropolitan area of Milan is the fifth largest in Europe, it includes the provinces of Milan, Bergamo, Como, Lecco, Lodi, Monza-e-Brianza, Novara, Pavia, and Varese, and it is characterized by a high concentration of both working and residential activities. The OECD identifies housing, transport, and congestion as the bottlenecks to the future growth of the area. Indeed they seem to badly affect the well-being of the city from many perspectives: pollution (Milan is the second most air-polluted city in Europe), economy (the difficulty in managing people and goods mobility is estimated to damp more than 4% the output of the area), and society (while the population of the metropolitan area is growing, the population of the municipality of Milan is decreasing). In recent years a lot of initiatives have been undertaken to address these problems. The Green Move project, which the present research is part of, is among these initiatives. Green Move is an interdisciplinary research project financed by Regione Lombardia involving different research groups at the Politecnico di Milano and regarding the development of a vehicle sharing system based on the concept of “little, electric and shared vehicles”. Our contribution to the project is to provide information about people mobility to find optimal places where to locate the docking stations. To this aim, we exploit the Telecom Italia database. In this database the metropolitan area of Milan is parted according to a uniform lattice of several thousands of sites of size 232m × 309m. In each site, the average number of mobile phones simultaneously using the network for calling at a given time is provided every 15 minutes for 14 days. At a first approximation, this quantity can be considered proportional to the number of active people in that site at that time, and thus able to provide information about people mobility. The data set at hand can be genuinely considered an instance of spatially-dependent functional data, because of the high within-unit sample size and the very high signal-to-noise ratio. Indeed two different functional data analyses are performed and the corresponding results thoroughly compared: a Treelet analysis and an Independent Component Analysis. Both analyses aim at describing the data set by a time-varying linear combination of a reduced number of time-invariant basis surfaces. Time-varying coefficients represent basic profiles of mobile network use recurring over the map, while site-evaluations of the surfaces measure the contribution of the corresponding basic profile to the signal observed in that site. We expect spatial dependence to be non-stationary and non-isotropic, being strongly related to the underlying road network. It is thus treated in a non-parametric way which relies on several random Voronoi tessellations of the investigated area, providing several sets of local representatives that are separately analyzed and then bagged together in a final aggregation step. The results of the two analyses are complementary disclosing both common and analysis-specific patterns amenable of a clear spatiotemporal interpretation such as: average population density, working and residential activities, universities, shopping, leisure, and morning/evening road/railways commuting.