Zipf Distribution Model for Quantifying Risk of Re-identification from Trajectory Data

Abstract

In this paper, we propose a new mathematical model for evaluating a given anonymized dataset that risks being re-identified. Many anonymization algorithms have been proposed in the area called privacy-preserving data publishing (PPDP), but, no anonymization algorithms are suitable for all scenarios because many factors, e.g., a requirement of accuracy, a domain of attributes, a size of dataset, and sensitivities of attributes, are involved. In order to address the issues of anonymization, we propose a new mathematical model based on the Zipf distribution. Our model is simple, but it fits well with the real distribution of trajectory data. We demonstrate the primary property of our model and we extend it to a more complex environment. Using our model, we define the theoretical bound for reidentification, which yields the appropriate optimal level for anonymization.