Abstract
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
Highlights
Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with power-law distributed jump size
We propose to explain the Levy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus
We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution
Summary
Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with power-law distributed jump size. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Previous research has shown that trajectories in human mobility have statistically similar features as Levy Walks by studying the traces of bank notes[14], cell phone users’ locations[15] and GPS16–19 According to the this model, human movement contains many short flights and some long flights, and these flights follow a power-law distribution. The short flights are associated with walking and the second short-distance taxi trip, whereas the long flights are associated with the subway and the initial taxi trip Based on this simple example, we observe that the flight distribution of each transportation mode is different. We demonstrate that the mixture of these transportation mode distributions is a power-law distribution based on two new findings: first, there is a significant positive correlation between consecutive flights in the same transportation mode, and second, the elapsed time in each transportation mode is exponentially distributed
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