Generalization and Enhancement of Piecewise Mechanism for Collecting Multidimensional Data

As the amount of data in society increases, the importance of collecting and storing data while protecting privacy also increases. In particular, protecting personal numeric data is essential for crowdsourcing and big data analytics. Although various methods have been proposed for specific analysis purposes such as mean estimation, methods for storing numeric values themselves are still lacking. Furthermore, no method that can flexibly collect all data information with multiple attributes exists. Therefore, this study first generalizes the piecewise mechanism (PM), the state-of-the-art method in collecting a single numeric value, and proposes a new mechanism that achieves a truly smaller variance of the collected private values than the original one. Subsequently, we enhance our generalized PM for collecting multidimensional numeric data while considering a situation in which each attribute information has its own privacy level. The proposed mechanism is optimal in terms of privacy guarantees for the entire dataset, and is highly advisable for collecting all information with high privacy assurance. We further evaluate our mechanism both theoretically and experimentally and show that it outperforms existing methods. We measure the accuracy of the collected private values using real census data as well, demonstrating the utility of our mechanism. Overall, this study is an important step toward the safe and accurate collection of numeric data. The codes for the experiments are available at https://eithub.com/ay0408/Generalized-PM.