Differentially private data publishing via cross-moment microaggregation

Abstract

Differential privacy is one of the most prominent privacy notions in the field of anonymization. However, its strong privacy guarantees very often come at the expense of significantly degrading the utility of the protected data. To cope with this, numerous mechanisms have been studied that reduce the sensitivity of the data and hence the noise required to satisfy this notion. In this paper, we present a generalization of classical microaggregation, where the aggregated records are replaced by the group mean and additional statistical measures, with the purpose of evaluating it as a sensitivity reduction mechanism. We propose an anonymization methodology for numerical microdata in which the target of protection is a data set microaggregated in this generalized way, and the disclosure risk limitation is guaranteed through differential privacy via record-level perturbation. Specifically, we describe three anonymization algorithms where microaggregation can be applied to either entire records or groups of attributes independently. Our theoretical analysis computes the sensitivities of the first two central cross moments; we apply fundamental results from matrix perturbation theory to derive sensitivity bounds on the eigenvalues and eigenvectors of the covariance and coskewness matrices. Our extensive experimental evaluation shows that data utility can be enhanced significantly for medium to large sizes of the microaggregation groups. For this range of group sizes, we find experimental evidence that our approach can provide not only higher utility but also higher privacy than traditional microaggregation.