Numerical Data Collection under Input-Discriminative Local Differential Privacy

Input-discriminative local differential privacy (ID-LDP) protects user data with a different range of values, which improves the utility of the estimated data compared to traditional LDP. However, the existing ID-LDP methods are used for categorical data and cannot be directly applied to numerical data. In this paper, we propose a numerical data collection (NDC) framework with ID-LDP to provide discriminative protection for the data with different inputs. This framework uses a piecewise mechanism to divide the numerical data into several segments and designs two perturbation methods to minimize the mean value of numerical data based on values submitted by users. We first create an NDC-UE method that encodes the raw data into a binary vector. This method sets the uploaded data bit as 1 and the rest as zero and perturbs each bit with a given probability. We further propose an NDC-GRR algorithm to perturb the numerical data with an optimal privacy budget. To reduce the complexity of NDC-GRR, we apply a greedy algorithm-based spanner to shorten the computation time and improve the accuracy. Theoretical analysis proves that our schemes satisfy the definition of ID-LDP. Experimental results based on two real-world datasets and a synthetic dataset show that the proposed schemes have less mean square error compared with the benchmarks.