A low cost and un-cancelled laplace noise based differential privacy algorithm for spatial decompositions

Abstract

Differentially private spatial decompositions split the whole domain into sub-domains recursively to generate a hierarchical private tree and add Laplace noise to each node’s points count. However the Laplace distribution is symmetric about the origin, the mean of a large number of queries may cancel the Laplace noise and reveal privacy. Existing methods take the solution by limiting the number of queries. But in private tree the points count of intermediate node may be real since the summation of all its descendants may cancel the Laplace noise. To address these problems of differentially private spatial decompositions, we propose a more secure algorithm to make the Laplace noise not be canceled. That splits the domains depending on its real points count not noisy, and only adds indefeasible Laplace noise to leaves. That the i th randomly selected leaf of one intermediate node is added noise by $\frac {\left (\upbeta -i+1 \right )+1+\upbeta }{(\upbeta -i+1)+\upbeta }Lap(\lambda )$. We also propose the definition of Lapmin(λ) whose absolute value is not greater than Sensitivity(f). It is proved that adding Lapmin(λ) noise to query answer guarantees both differential privacy and minimal relative error comparing with unlimited Laplace noise. The experiment results show that our algorithm performs better both on synthetic and real datasets with higher security and data utility, and the noises costs is highly decreased.