A Deep Gravity model for mobility flows generation

Abstract

The movements of individuals within and among cities influence critical aspects of our society, such as well-being, the spreading of epidemics, and the quality of the environment. When information about mobility flows is not available for a particular region of interest, we must rely on mathematical models to generate them. In this work, we propose Deep Gravity, an effective model to generate flow probabilities that exploits many features (e.g., land use, road network, transport, food, health facilities) extracted from voluntary geographic data, and uses deep neural networks to discover non-linear relationships between those features and mobility flows. Our experiments, conducted on mobility flows in England, Italy, and New York State, show that Deep Gravity achieves a significant increase in performance, especially in densely populated regions of interest, with respect to the classic gravity model and models that do not use deep neural networks or geographic data. Deep Gravity has good generalization capability, generating realistic flows also for geographic areas for which there is no data availability for training. Finally, we show how flows generated by Deep Gravity may be explained in terms of the geographic features and highlight crucial differences among the three considered countries interpreting the model’s prediction with explainable AI techniques.

Generating Synthetic Mobility Networks with Generative Adversarial Networks

“…We compare MoGAN with the Gravity and the Radiation models, two classical approaches for mobility flows' generation [11,9,15,21].…”

“…In our experiments, we try three error metrics: RMSE, CPC, and CD. The Root Mean Square Error (RMSE) [9,15] is defined as:…”

“…Note that RMSE is substantially equivalent to the Frobenious norm (see Supplementary Note 4). The Common Part of Commuters (CPC), also known as Sørensen-Dice index [11,15,44,15], a well-established measure to compute the similarity between real and generated, is defined as: [45] is based on the notion of cut weight, widely used in network theory [43], and measures how much a network is bipartite. The cut norm ||A|| C of a real matrix A = (a ij ), i ∈ R, j ∈ S with a set of rows indexed by R and a set of columns indexed by S, is the maximum over all I ⊂ R, J ⊂ S of the quantity | i∈I,j∈J a ij |.…”

“…In this regard, a particularly challenging task is generating realistic mobility flows, i.e., flows of people among a set of geographic locations given their demographic and geographic characteristics (e.g., population and distance) [9,15,11,10,16]. Traditionally, flow generation is addressed through the Gravity model [17,18,19,11,20], the Radiation model [21,11,10], and their variants [15,11,22,23]. The Gravity model assumes that the number of travelers between two locations (flow) increases with the locations' populations while decreasing with the distance between them.…”

Predicting the impact of urban change in pedestrian and road safety

“…With vast amounts of data about cities currently available, automated analysis has been recognized as a crucial tool to help urban planners in decision tasks [3][4][5][6] . While the link between the growth of urban open data and new computational techniques such as Deep Learning has been pointed out by several authors [7][8][9][10][11][12][13] , much work can still be done in leveraging these new technologies towards the end of achieving the ambitious goals of Vision Zero.…”