diff --git a/tables/micro.tex b/tables/micro.tex index a7d912a..d391cfb 100644 --- a/tables/micro.tex +++ b/tables/micro.tex @@ -85,7 +85,7 @@ \cite{cao2017quantifying,cao2018quantifying} & & & & ($w$-)event & (temporal) & (Laplace) & privacy \\ \hdashline \hyperlink{naim2019off}{\emph{ON-OFF privacy}} & infinite & streaming & local & event & dependence & randomization & - \\ - \cite{naim2019off, ye2019preserving} & & & & & (serial) & & \\ + \cite{naim2019off, ye2019preserving} & (sequential) & & & & (serial) & & \\ \cite{ye2020off, ye2021off} & & & & & & & \\ \bottomrule diff --git a/tables/statistical.tex b/tables/statistical.tex index 2ab01cd..7629f7d 100644 --- a/tables/statistical.tex +++ b/tables/statistical.tex @@ -79,15 +79,15 @@ \cite{chen2017pegasus} & & & & & & (Laplace) & privacy \\ \hdashline \hyperlink{errounda2018continuous}{\textbf{Errounda et al.}} & infinite & streaming & local & $w$-event & linkage & randomization (ran- & differential \\ - \cite{errounda2018continuous} & & & & & & domized response), & privacy \\ + \cite{errounda2018continuous} & (sequential) & & & & & domized response), & privacy \\ & & & & & & perturbation & \\ & & & & & & (Laplace) & \\ \hdashline \hyperlink{wang2018privacy}{\textbf{\emph{DP-PSP}}} & infinite & streaming & global & $w$-event & linkage & perturbation (ex- & differential \\ - \cite{wang2018privacy} & & & & & & ponential, Laplace) & privacy \\ \hdashline + \cite{wang2018privacy} & (sequential) & & & & & ponential, Laplace) & privacy \\ \hdashline \hyperlink{ma2019real}{\textbf{\emph{RPTR}}} & infinite & streaming & global & $w$-event & linkage & perturbation & differential \\ - \cite{ma2019real} & & & & & & (Laplace) & privacy \\ \hdashline + \cite{ma2019real} & (sequential) & & & & & (Laplace) & privacy \\ \hdashline \hyperlink{farokhi2020temporally}{Farokhi} & infinite & streaming & global & - & linkage & perturbation & differential \\ \cite{farokhi2020temporally} & & & & & & (Laplace) & privacy \\ \hdashline diff --git a/text/main.tex b/text/main.tex index 502b125..ced4581 100644 --- a/text/main.tex +++ b/text/main.tex @@ -98,6 +98,110 @@ \input{theotherthing/main} \input{conclusion/main} +% An Optimal Pufferfish Privacy Mechanism for Temporally Correlated Trajectories +% - microdata +% - finite (sequential) +% - batch +% - dependence (temporal) +% - local +% - event +% - differential privacy +% - perturbation (randomized response, Laplace) +\hypertarget{ou2018optimal}{Ou et al.}~\cite{ou2018optimal} + +\emph{FGS-Pufferfish} + +temporally correlated trajectory data + + +First, a Laplace noise mechanism is realized through geometric sum of noisy Fourier coefficients of temporally correlated daily trajectories. + +We achieve better data utility for a given privacy budget by solving a constrained optimization problem of the noisy Fourier coefficients via the Lagrange multiplier method. + + +generation of Laplace noise via the Fourier coefficients' geometric + + +We present an analytical formula of the optimized Fourier coefficients noise for the constrained optimization problem of achieving a better data utility for a given privacy budget. + +We provide theoretical analysis of the data utility and privacy, as well as the posterior-to-prior knowledge gain of an adversary. + + + + + +we quantify the temporal correlation in a rigorous mathematics way. + +by adding noise to the Fourier coefficients through geometric sum. + +The discrete Fourier transform transforms a user's daily trajectory + +into a set of sine and cosine waves +of different frequencies and corresponding Fourier coefficients + +In this paper, we assume that both the real part and the imaginary part of the Fourier coefficient follow the same Gaussian distribution + + + +The constrained optimization problem is a strategy of finding the local extrema (maxima and minima) of a function f (b) subject to equality constraint g(b) = 0 + + +The user's mobility pattern can be described by the conditional probability of the next i-th location from the current n-th location + + +A user's temporal correlation depicts the relation +between two locations at current time slot tn and its following i-th time slots tn+i + + +the Pufferfish secrets set consists of temporal correlations of all users + +A correlation secrets pair consists of two temporal correlations of any two users in the same database + +the Fourier coefficients of the temporal correlation are closely related to those of the daily trajectory. +Thus it is natural to add noise to the Fourier coefficients of the trajectory + + +we propose to optimize the Fourier coefficients noise for the problem of temporal correlation privacy. + +First, we add the noise in the Fourier coefficients + +the noisy temporal correlation is obtained from the noisy daily trajectory + + +we propose to achieve the optimal data utility for a given privacy budget + +Here we consider two utilities, including the location utility and the correlation utility + +For the location utility, we want the average noisy location deviates from its raw location as small as possible + +The correlation utility is the average of the deviation of the noisy correlation from its raw value + + + + +Our goal is to prevent an adversary from mining a user's privacy through analyzing the user's temporal correlation based on the adversary’s prior knowledge about the user. + + + +First, we define the constrained optimization problem of achieving a better data utility for a given privacy budget given by the Laplace scale parameter +Next, we solve the constrained optimization problem via the LM method and obtain the optimal obtained Laplace scale parameter for the noisy Fourier coefficients +Then, the FGS-Pufferfish privacy mechanism adds noise to the Fourier coefficients and obtain the noisy Fourier coefficients +At last, we obtain the sanitized daily trajectories with the noisy Fourier coefficients + + +we design an algorithm to release temporally correlated trajectories in order to protect individuals' privacy. +Because our goal is to protect the temporal correlation of a user’s daily trajectory, we first calculate the Fourier coefficients of a daily trajectory which is related to the Fourier coefficients of its temporal correlation. +Then, to achieve the Laplace distribution of the noisy temporal correlation through the Fourier coefficients noise mechanism, i.e., adding noise to Fourier coefficients, with following the geometric distribution. +Furthermore, we obtain the optimal Laplace scale parameters for the noisy Fourier coefficients. Finally, we use IDFT to obtain the noisy loca- tions of the sanitized daily trajectory + + +We propose a Laplace noise mechanism based on the noisy Fourier coefficients' geometric sum, satisfying Pufferfish privacy, i.e., the FGS-Pufferfish privacy mechanism, to protect the temporal correlation of a user's daily trajectories. +The optimal noisy Fourier coefficients are obtained by solving the constrained optimization problem via the LM method to achieves a better data utility for a given privacy budget. +Experiments with both simulated and real-life data show that our FGS-Pufferfish privacy mechanism achieves better data utility and privacy compared to the existing approach. +Although we only deal with daily trajectories with a constant time interval, our proposed mechanism can be readily modified for time-series data with irregular time intervals + + + \backmatter \bibliographystyle{alpha} diff --git a/text/related/statistical.tex b/text/related/statistical.tex index 85621ac..ad72dd1 100644 --- a/text/related/statistical.tex +++ b/text/related/statistical.tex @@ -373,7 +373,7 @@ approach of differential privacy. % Privacy-protected statistics publication over social media user trajectory streams % - statistical -% - infinite +% - infinite (sequential) % - streaming % - linkage % - global @@ -392,7 +392,7 @@ From the implementation, it is not clear how DP-PSP takes into consideration all % Real-Time Privacy-Preserving Data Release Over Vehicle Trajectory % - statistical -% - infinite +% - infinite (sequential) % - streaming % - linkage % - global