diff --git a/tables/micro.tex b/tables/micro.tex index d391cfb..b8c5794 100644 --- a/tables/micro.tex +++ b/tables/micro.tex @@ -44,7 +44,10 @@ \cite{primault2015time} & (sequential) & & & & & & \\ \hdashline \hyperlink{gursoy2018differentially}{\textbf{\emph{DP-Star}}} & finite & batch & global & user & linkage & perturbation & differential \\ - \cite{gursoy2018differentially} & (sequential) & & & & & (Laplace) & privacy \\ + \cite{gursoy2018differentially} & (sequential) & & & & & (Laplace) & privacy \\ \hdashline + + \hyperlink{ou2018optimal}{\textbf{\emph{FGS-Pufferfish}}} & finite & batch & local & event & dependence & perturbation & differential \\ + \cite{ou2018optimal} & (sequential) & & & & (temporal) & (Laplace) & privacy \\ \midrule diff --git a/text/bibliography.bib b/text/bibliography.bib index 6e34dd0..d812fc8 100644 --- a/text/bibliography.bib +++ b/text/bibliography.bib @@ -1310,6 +1310,16 @@ Accessed on November 11, 2020} } +@article{ou2018optimal, + title = {An optimal pufferfish privacy mechanism for temporally correlated trajectories}, + author = {Ou, Lu and Qin, Zheng and Liao, Shaolin and Yin, Hui and Jia, Xiaohua}, + journal = {IEEE Access}, + volume = {6}, + pages = {37150--37165}, + year = {2018}, + publisher = {IEEE} +} + @inproceedings{ozccep2015stream, title = {Stream-query compilation with ontologies}, author = {{\"O}z{\c{c}}ep, {\"O}zg{\"u}r L{\"u}tf{\"u} and M{\"o}ller, Ralf and Neuenstadt, Christian}, diff --git a/text/main.tex b/text/main.tex index ced4581..502b125 100644 --- a/text/main.tex +++ b/text/main.tex @@ -98,110 +98,6 @@ \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}