Analysis of a Fast LZ-Based Entropy Estimator for Mobility Data

Randomness in people's movements might serve to detect behavior anomalies. The concept of entropy can be used for this purpose, but its estimation is computational intensive, particularly when processing long movement histories. Moreover, disclosing such histories to third parties may violate user privacy. With a goal to keep the mobility data in the mobile device itself yet being able to measure randomness, we propose three fast entropy estimators based on Lempel-Ziv (LZ) prediction algorithms. We evaluated them with 95 movement histories of real users tracked during 9 months using GSM-based mobility data. The results show that the entropy tendencies of the approaches proposed in this work and those in the literature are the same as time evolves. Therefore, our proposed approach could potentially detect variations in the mobility patterns of the user with a lower computational cost. This allows to unveil shifts in the users mobility behavior without disclosing their sensible location data.