diff --git a/text/evaluation/thething.tex b/text/evaluation/thething.tex index ad5b659..01f934e 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -58,8 +58,11 @@ Moreover, designing a data-dependent sampling scheme \kat{what would be the main \subsection{Temporal distance and correlation} \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. -More particularly, we count for every event the total number of events between itself and the nearest {\thething} or the series edge. +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. +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] \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}. % 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}. +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. 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} \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}). -Furthermore, the behavior of the privacy loss is as expected regarding the temporal correlation degree. -Predictably, a stronger correlation degree generates higher privacy loss while widening the gap between the different distribution cases. +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. 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?}.