Two-dimensional Categorical Data Collection Mechanism Satisfying Differential Privacy

In this paper, we propose a differentially private data collection mechanism for two-dimensional categorical data that is easy to implement. The mechanism is mainly composed of coding, noise addition, integer approximation, modulo and decoding. The method of round, round toward zero, ceil and floor are adopted to convert the data into decimal integer. We use accuracy rate, the ratio of the output data which is the same as the input data in the total output, to measure the utility of the mechanism. For privacy-preserving level, the measurement is based on local differential privacy. We define the privacy-preserving level of a randomized mechanism M which satisfies ϵ-local differential privacy as the minimum ϵ. We compare and analyze the utility and privacy-preserving level of each approximation method with the addition of relative noises to improve our mechanism. We find that round is the best approximation method for our mechanism and the utility and privacy-preserving level are related to the correlation coefficient of noises.