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@ -58,8 +58,11 @@ Moreover, designing a data-dependent sampling scheme \kat{what would be the main
\subsection{Temporal distance and correlation} \subsection{Temporal distance and correlation}
\label{subsec:lmdk-expt-cor} \label{subsec:lmdk-expt-cor}
Figure~\ref{fig:avg-dist} shows a comparison of the average temporal distance of the events from the previous/next {\thething} or the start/end of the time series for various distributions in synthetic data. As previously mentioned, temporal correlations are inherent in continuous publishing, and they are the cause of supplementary privacy leakage in the case of privacy preserving data publication.
More particularly, we count for every event the total number of events between itself and the nearest {\thething} or the series edge. In this section, we are interested in studying the effect that the distance of the {\thethings} from every event have on the leakage caused by temporal correlations.
Figure~\ref{fig:avg-dist} shows a comparison of the average temporal distance of the events from the previous/next {\thething} or the start/end of the time series for various distributions in our synthetic data.
More specifically, we model the distance of an event as the count of the total number of events between itself and the nearest {\thething} or the series edge.
\begin{figure}[htp] \begin{figure}[htp]
\centering \centering
@ -72,6 +75,7 @@ We observe that the uniform and bimodal distributions tend to limit the regular
This is due to the fact that the former scatters the {\thethings}, while the latter distributes them on both edges, leaving a shorter space uninterrupted by {\thethings}. This is due to the fact that the former scatters the {\thethings}, while the latter distributes them on both edges, leaving a shorter space uninterrupted by {\thethings}.
% and as a result they reduce the uninterrupted space by landmarks in the sequence. % and as a result they reduce the uninterrupted space by landmarks in the sequence.
On the contrary, distributing the {\thethings} at one part of the sequence, as in skewed or symmetric, creates a wider space without {\thethings}. On the contrary, distributing the {\thethings} at one part of the sequence, as in skewed or symmetric, creates a wider space without {\thethings}.
This study provides us with different distance settings that we are going to use in the subsequent temporal leakage study.
Figure~\ref{fig:dist-cor} illustrates a comparison among the aforementioned distributions regarding the overall privacy loss under (a)~weak, (b)~moderate, and (c)~strong temporal correlation degrees. Figure~\ref{fig:dist-cor} illustrates a comparison among the aforementioned distributions regarding the overall privacy loss under (a)~weak, (b)~moderate, and (c)~strong temporal correlation degrees.
The line shows the overall privacy loss---for all cases of {\thethings} distribution---without temporal correlation. The line shows the overall privacy loss---for all cases of {\thethings} distribution---without temporal correlation.
@ -93,9 +97,8 @@ The line shows the overall privacy loss---for all cases of {\thethings} distribu
\label{fig:dist-cor} \label{fig:dist-cor}
\end{figure} \end{figure}
In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} even distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation. In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} event \kat{it was even, I changed it to event but do not know what youo want ot say} distance in a distribution can result into greater overall privacy loss under moderate and strong temporal correlation.
This is due to the fact that the backward/forward privacy loss accumulates more over time in wider spaces without {\thethings} (see Section~\ref{sec:correlation}). This is due to the fact that the backward/forward privacy loss accumulates more over time in wider spaces without {\thethings} (see Section~\ref{sec:correlation}).
Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree. Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree: a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases.
Predictably, a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases.
On the contrary, a weaker correlation degree makes it harder to differentiate among the {\thethings} distributions. On the contrary, a weaker correlation degree makes it harder to differentiate among the {\thethings} distributions.
The privacy loss under a weak correlation degree converge. The privacy loss under a weak correlation degree converge \kat{with what?}.