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Understanding individual human mobility patterns
M. C. Gonzalez, C. A. Hidalgo, A. -L. Barabasi
TL;DR
Human mobility patterns are difficult to characterize because time-resolved individual location data have been limited. This paper analyzes tracked human trajectories and finds strong regularity, with individual patterns collapsing into a common spatial probability distribution after rescaling.
Problem
Limited understanding of human diffusion and mobility patterns constrains knowledge of the basic regularities governing human motion.
Method
The study analyzes individual trajectories using anisotropic rescaling and density-based normalization to compare their spatial patterns.
Results
Human trajectories show strong temporal and spatial regularity, including high return probabilities to a few frequently visited locations and a shared spatial distribution after rescaling.
Takeaways & Limitations
Individual trajectories are largely indistinguishable after rescaling, indicating that diverse travel histories follow simple reproducible patterns.
Abstract
from arXiv · showhide
Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited thanks to the lack of tools to monitor the time resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six month period. We find that in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic length scale and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent based modeling.
R ∞
Human mobility is temporally regular, with strong returns to a few highly frequented locations, while individual spatial probability distributions become universal after anisotropic rescaling. The observed population-level jump statistics therefore reflect a convolution of individual motion and population heterogeneity.
- Population-level statistics: The observed jump-size distribution P(∆r) is the convolution of individual trajectory statistics P(∆rg|rg) and population heterogeneity P(rg), consistent with hypothesis C.The relation β = βr+α−1 is consistent, within error bars, with the measured exponents.
- Temporal recurrence: Return probabilities peak at 24 h, 48 h, and 72 h, revealing recurrence and temporal periodicity in human mobility.These peaks contrast with the ∼1/(t ln(t)^2) behavior expected for a two-dimensional random walk.
- Frequent locations: The location-rank probability follows P(L) ∼1/L, so people devote most of their time to a few locations and visit 5 to 50 others less regularly.The rank distribution is independent of the number of locations visited by the user.
- Universal spatial distribution: After anisotropic rescaling, users with different rg follow the same universal two-dimensional probability distribution ˜Φ(˜x, ˜y).The individual distributions are spatially anisotropic, and the anisotropy ratio S decreases monotonically with rg.
- Modeling implications: These findings establish ingredients for agent-based models: assign users according to population density, draw rg from P(rg), and use the predicted anisotropic rescaling with ˜Φ(x, y).The resulting framework can provide the likelihood of finding a user at any location.