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It has been found that human mobility exhibits random patterns following theLevy flight, where human movement contains many short flights and some longflights, and these flights follow a power-law distribution. In this paper, westudy the social-economical development trajectories of urban cities. Weobserve that social-economical movement of cities also exhibit the Levy flightcharacteristics. We collect the social and economical data such as thepopulation, the number of students, GDP and personal income, etc. from severalcities. Then we map these urban data into the social and economical factorsthrough a deep-learning embedding method Auto-Encoder. We find that thesocial-economical factors of these cities can be fitted approximately as amovement pattern of a power-law distribution. We use the StochasticMultiplicative Processes (SMP) to explain such movement, where in the presenceof a boundary constraint, the SMP leads to a power law distribution. It meansthat the social-economical trajectories of cities also follow a Levy flightpattern, where some years have large changes in terms of social-economicaldevelopment, and many years have little changes.

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