Quality assessment and community detection methods for anonymized mobility data: Clustering Italy in the time of Covid

Abstract:

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movement: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test-case, we consider the movement of Italians before and during the SARS-Cov2 pandemics, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methodes, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.