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With recent advancements in technology, the threats of privacy violations ofindividuals' sensitive data are surging. Location data, in particular, havebeen shown to carry a substantial amount of sensitive information. A standardmethod to mitigate the privacy risks for location data consists in adding noiseto the true values to achieve geo-indistinguishability (geo-ind). However,geo-ind alone is not sufficient to cover all privacy concerns. In particular,isolated locations are not sufficiently protected by the state-of-the-artLaplace mechanism (LAP) for geo-ind. In this paper, we focus on a mechanismbased on the Blahut-Arimoto algorithm (BA) from the rate-distortion theory. Weshow that BA, in addition to providing geo-ind, enforces an elastic metric thatmitigates the problem of isolation. Furthermore, BA provides an optimaltrade-off between information leakage and quality of service. We then proceedto study the utility of BA in terms of the statistics that can be derived fromthe reported data, focusing on the inference of the original distribution. Tothis purpose, we de-noise the reported data by applying the iterative Bayesianupdate (IBU), an instance of the expectation-maximization method. It turns outthat BA and IBU are dual to each other, and as a result, they work welltogether, in the sense that the statistical utility of BA is quite good andbetter than LAP for high privacy levels. Exploiting these properties of BA andIBU, we propose an iterative method, PRIVIC, for a privacy-friendly incrementalcollection of location data from users by service providers. We illustrate thesoundness and functionality of our method both analytically and withexperiments.

PRIVIC: A privacy-preserving method for incremental collection of location data