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lmdk-expt: Reviewed all graphs for synthetic

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Manos Katsomallos
2021-10-09 13:27:16 +02:00
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text/evaluation/thething.tex
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@ -51,7 +51,8 @@ In general, we can claim that the Adaptive is the most reliable and best perform
Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive.
\paragraph{Temporal distance and correlation}
\subsubsection{Temporal distance and correlation}
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.
We observe that the uniform and bimodal distributions tend to limit the regular event--{\thething} distance.
@ -61,33 +62,33 @@ On the contrary, distributing the {\thethings} at one part of the sequence, as i
\begin{figure}[htp]
\centering
\includegraphics[width=.5\linewidth]{avg-dist}%
\includegraphics[width=.5\linewidth]{evaluation/avg-dist}%
\caption{Average temporal distance of the events from the {\thethings} for different {\thethings} percentages within a time series in various {\thethings} distributions.}
\label{fig:avg-dist}
\end{figure}
Figure~\ref{fig:dist-cor} illustrates a comparison among the aforementioned distributions regarding the overall privacy loss under moderate (Figure~\ref{fig:dist-cor-mod}), and strong (Figure~\ref{fig:dist-cor-stg}) 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.
We skip the presentation of the results under a weak correlation degree, since they converge in this case.
In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event-{\thething} 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{subsec:correlations}).
In combination with Figure~\ref{fig:avg-dist}, we conclude that a greater average event--{\thething} 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.
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.
\begin{figure}[htp]
\centering
\subcaptionbox{Weak correlation\label{fig:dist-cor-wk}}{%
\includegraphics[width=.5\linewidth]{dist-cor-wk}%
\includegraphics[width=.5\linewidth]{evaluation/dist-cor-wk}%
}%
\hspace{\fill}
\subcaptionbox{Moderate correlation\label{fig:dist-cor-mod}}{%
\includegraphics[width=.5\linewidth]{dist-cor-mod}%
\includegraphics[width=.5\linewidth]{evaluation/dist-cor-mod}%
}%
\subcaptionbox{Strong correlation\label{fig:dist-cor-stg}}{%
\includegraphics[width=.5\linewidth]{dist-cor-stg}%
\includegraphics[width=.5\linewidth]{evaluation/dist-cor-stg}%
}%
\caption{Privacy loss for different {\thethings} percentages and distributions, under weak, moderate, and strong degrees of temporal correlation.
\caption{Privacy loss for different {\thethings} percentages and distributions, under (a)~weak, (b)~moderate, and (c)~strong degrees of temporal correlation.
The line shows the overall privacy loss without temporal correlation.}
\label{fig:dist-cor}
\end{figure}