Differential Privacy for Directional Data

Directional data is an important class of data where the magnitudes of the data points are negligible. It naturally occurs in many real-world scenarios: For instance, geographic locations (approximately) lie on a sphere, and periodic data such as time of day, or day of week can be interpreted as points on a circle. Massive amounts of directional data are collected by location-based service platforms such as Google Maps or Foursquare, who depend on mobility data from users' smartphones or wearable devices to enable their analytics and marketing businesses. However, such data is often highly privacy-sensitive and hence demands measures to protect the privacy of the individuals whose data is collected and processed. Starting with the von Mises-Fisher distribution, we therefore propose and analyze two novel privacy mechanisms for directional data by combining directional statistics with differential privacy, which presents the current state-of-the-art for quantifying and limiting information disclosure about individuals. As we will see, our specialized privacy mechanisms achieve a better privacy-utility trade-off than ex post adaptions of established mechanisms to directional data.