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b/text/evaluation/thething.tex index 487434c..b68bad5 100644 --- a/text/evaluation/thething.tex +++ b/text/evaluation/thething.tex @@ -14,28 +14,41 @@ Whereas, when each timestamp corresponds to a {\thething} we consider and protec \subsection{Experiments} +\label{sec:lmdk-expt} -\paragraph{Budget allocation schemes} +\subsubsection{Budget allocation schemes} Figure~\ref{fig:real} exhibits the performance of the three mechanisms: Skip, Uniform, and Adaptive. \begin{figure}[htp] \centering - \subcaptionbox{Geolife\label{fig:geolife}}{% - \includegraphics[width=.5\linewidth]{geolife}% + \subcaptionbox{Copenhagen\label{fig:copenhagen}}{% + \includegraphics[width=.5\linewidth]{copenhagen}% + }% + \hspace{\fill} + \subcaptionbox{HUE\label{fig:hue}}{% + \includegraphics[width=.5\linewidth]{hue}% }% \subcaptionbox{T-drive\label{fig:t-drive}}{% \includegraphics[width=.5\linewidth]{t-drive}% }% - \caption{The mean absolute error (in meters) of the released data for different {\thethings} percentages.} + \caption{The mean absolute error (a)~as a percentage, (b)~in kWh, and (c)~in meters of the released data for different {\thethings} percentages.} \label{fig:real} \end{figure} -For the Geolife data set (Figure~\ref{fig:geolife}), Skip has the best performance (measured in Mean Absolute Error, in meters) because it invests the most budget overall at every regular event, by approximating the {\thething} data based on previous releases. -Due to the data set's high density (every $1$--$5$ seconds or every $5$--$10$ meters per point) approximating constantly has a low impact on the data utility. -On the contrary, the lower density of the T-drive data set (Figure~\ref{fig:t-drive}) has a negative impact on the performance of Skip. -In the T-drive data set, the Adaptive mechanism outperforms the Uniform one by $10$\%--$20$\% for all {\thethings} percentages greater than $0$ and by more than $20$\% the Skip one. -In general, we can claim that the Adaptive is the best performing mechanism, if we take into consideration the drawbacks of the Skip mechanism mentioned in Section~\ref{subsec:lmdk-mechs}. Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive. +% For the Geolife data set (Figure~\ref{fig:geolife}), Skip has the best performance (measured in Mean Absolute Error, in meters) because it invests the most budget overall at every regular event, by approximating the {\thething} data based on previous releases. +% Due to the data set's high density (every $1$--$5$ seconds or every $5$--$10$ meters per point) approximating constantly has a low impact on the data utility. +% On the contrary, the lower density of the T-drive data set (Figure~\ref{fig:t-drive}) has a negative impact on the performance of Skip. +For the Copenhagen data set (Figure~\ref{fig:copenhagen}), Adaptive has a constant overall performance and performs best for $0$, $60$, and $80$\% {\thethings}. +The Skip model excels, compared to the others, at cases where it needs to approximate a lot ($100$\%). +The combination of the low range in HUE ($[0.28$, $4.45]$ with an average of $0.88$kWh) and the large scale in the Laplace mechanism results in a low mean absolute error for Skip(Figure~\ref{fig:hue}). +In general, a scheme that favors approximation over noise injection would achieve a better performance in this case. +However, the Adaptive model performs by far better than Uniform and strikes a nice balance between event- and user-level protection for all {\thethings} percentages. +In the T-drive data set (Figure~\ref{fig:t-drive}), the Adaptive mechanism outperforms the Uniform one by $10$\%--$20$\% for all {\thethings} percentages greater than $40$ and by more than $20$\% the Skip one. +The lower density (average distance of $623$ meters) of the T-drive data set has a negative impact on the performance of Skip. + +In general, we can claim that the Adaptive is the most reliable and best performing mechanism with minimal tuning, if we take into consideration the drawbacks of the Skip mechanism mentioned in Section~\ref{subsec:lmdk-mechs}. +Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive. \paragraph{Temporal distance and correlation}