On the use of instantaneous entropy to measure the momentary predictability of human mobility

Algorithms that can reliably predict the next location visited by a user can enable a large number of applications. The accuracy that can be achieved by these algorithms depends on the inherent characteristics of the mobility pattern of the user, i.e., on its predictability. Recent studies have shown the theoretical limits of human predictability and have provided a sound mathematical framework to compute predictability bounds using the entropy of the sequence of locations visited by the user. However, most of the existing results focus on the characterization of the predictability over long periods of time, e.g., a few weeks. For several applications, though, knowledge of the momentary predictability, i.e., the predictability at a given time instant k is required. To this end, a novel metric called Instantaneous Entropy (IE) has been introduced in the literature. In this paper, we investigate the actual suitability of the IE metric to characterize the momentary predictability. We provide quantitative results to show that IE can estimate the momentary predictability of human mobility only to a limited extent, i.e., as long as unfavorable situations do not appear in the sequence of historical locations visited by the user. Our analysis is based on both real human mobility traces and synthetically generated data.