Group Sparsity Tensor Factorization for Re-Identification of Open Mobility Traces

Re-identification attacks based on a Markov chain model have been widely studied to understand how anonymized traces are linked to users. This approach is known to enable users to be re-identified with high accuracy when an adversary trains a personalized transition matrix for each target user using a large amount of training data, and when all of the anonymized traces are from the target users. In reality, however, the amount of training data for each target user can be very small, since many users disclose only a small amount of their location information to the public. In addition, many of the anonymized traces are from “non-target” users, whose personalized transition matrices cannot be trained in advance. This paper aims to quantify the risk of re-identification in the realistic situation explained earlier. We first utilize the fact that spatial data can form a group structure, and propose group sparsity tensor factorization to effectively train the personalized transition matrices from a small number of training traces. We second formulate a re-identification attack in an “open” scenario, where many of the anonymized traces are from non-target users. Specifically, we regard this type of attack as a biometric verification (or identification) task, and propose a framework and an algorithm for performing this task using a population transition matrix, which is computed from personalized transition matrices. Our experimental results using three real data sets show that a training method using tensor factorization significantly outperforms the maximum likelihood estimation method, and is further improved by incorporating group sparsity regularization.