related: Added (sequential)

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

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

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}

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