lmdk-expt: New results and discussion

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}}{%
+  \subcaptionbox{Copenhagen\label{fig:copenhagen}}{%
-    \includegraphics[width=.5\linewidth]{geolife}%
+    \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.
+% 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.
+% 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.
+% 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.
+For the Copenhagen data set (Figure~\ref{fig:copenhagen}), Adaptive has a constant overall performance and performs best for $0$, $60$, and $80$\% {\thethings}.
-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.
+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}