The Levy Flight of Cities: Analyzing Social-Economical Trajectories with Auto-Embedding

It has been found that human mobility exhibits random patterns following the Levy flight, where human movement contains many short flights and some long flights, and these flights follow a power-law distribution. In this paper, we study the social-economical development trajectories of urban cities. We observe that social-economical movement of cities also exhibit the Levy flight characteristics. We collect the social and economical data such as the population, the number of students, GDP and personal income, etc. from several cities. Then we map these urban data into the social and economical factors through a deep-learning embedding method Auto-Encoder. We find that the social-economical factors of these cities can be fitted approximately as a movement pattern of a power-law distribution. We use the Stochastic Multiplicative Processes (SMP) to explain such movement, where in the presence of a boundary constraint, the SMP leads to a power law distribution. It means that the social-economical trajectories of cities also follow a Levy flight pattern, where some years have large changes in terms of social-economical development, and many years have little changes.