In this study we analyze the travel patterns of 500,000 individuals in Cote d'Ivoire using mobile phone call data records. By measuring the uncertainties of movements using entropy, considering both the frequencies and temporal correlations of individual trajectories, we find that the theoretical maximum predictability is as high as 88%. To verify whether such a theoretical limit can be approached, we implement a series of Markov chain (MC) based models to predict the actual locations visited by each user. Results show that MC models can produce a prediction accuracy of 87% for stationary trajectories and 95% for non-stationary trajectories. Our findings indicate that human mobility is highly dependent on historical behaviors, and that the maximum predictability is not only a fundamental theoretical limit for potential predictive power, but also an approachable target for actual prediction accuracy. tudies of mobility patterns and predictions of individual mobility trajectories are important in many research fields, such as mobile computing, epidemic modeling, traffic planning and disaster response [1] [2] [3] . Real-time locations visited by individuals are typically collected through mobile devices equipped with global-positioning system (GPS) capability, mobile phone cell towers, or wireless local area network (WLAN) access points. Various methods have been proposed to forecast individual trajectories, including Markov chain (MC) models 4, 5 , neural networks 6 , Bayesian networks 7 , and finite automaton 8 . Prediction accuracy has been shown to vary according to the algorithm used and the context from which the location data come. For example, in an evaluation of next cell prediction based on more than 6000 users on Dartmouth's campus-wide Wi-Fi wireless network, it was found that the best predictor (the O 2 ð Þ-MC model) had an accuracy of about 65-72% . In another study where mobility traces of six researchers and GPS-locations of 175 individuals were used, the prediction accuracy was shown to be in the range of 70% to 95% with an O 2 ð Þ-MC model [10] [11] [12] . On the other hand, in an evaluation of MC models for pedestrian-movement prediction, the prediction accuracy was as low as 2%, 45% and 74.4% for the O 1 ð Þ-MC model, hidden-Markov model, and the mixed MC model, respectively 13 . The above studies investigated small numbers of individuals or special populations, and the results and practical feasibility of the proposed new predictive algorithms were therefore difficult to generalize to the general population. In addition, it was not clear how well these algorithms performed versus the best possible algorithm that could theoretically be constructed; i.e., what is, for the given data type, the best possible accuracy achievable and how well do the predictive algorithms perform versus such a benchmark? The highest potential accuracy of predictability, termed ''maximum predictability'' (P max ), is defined by the entropy of information of a person's trajectory (frequency, sequence of location visits, etc.). P max can be calculated by solving a limiting case of Fano's inequality (a relation derived from calculation of the decrease in information in a noisy information channel) [14] [15] [16]
Lu et al. refers to the above methods, and leverage Markov Chain to predict 500,000 user's behavior, whose average accuracy reaches 95% REF .
Approaching the Limit of Predictability in Human Mobility
Scientific Reports
Scientific Reports
Computer Science Medicine