evaluation: Minor corrections and text

text/evaluation/theotherthing.tex

@@ -1,9 +1,36 @@
 \section{Selection of events}
 \label{sec:lmdk-sel-eval}
 
-In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets. 
-% With the experiments on the real data sets (Section~\ref{subsec:lmdk-expt-bgt}), we show the performance in terms of utility of our three {\thething} mechanisms.
-% With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}.
+In this section we present the experiments that we performed, to test the methodology that we presented in Section~\ref{subsec:lmdk-sel-sol}, on real and synthetic data sets.
+With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utiliy}) we show the normaziled distances for various {\thething} percentages.
+privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}.
+With the experiments on the real data sets (Section~\ref{subsec:sel-prv}), we show the performance in terms of utility of our three {\thething} mechanisms in combination with privacy preserving {\thething} that can be possibly applied to humans.
+
+
+\subsection{{\Thething} selection utility metrics}
+\label{subsec:sel-utl}
+
+Figure~\ref{fig:sel-dist} demonstrates the normalized distance that we obtain when we utilize either (a)~the Euclidean or (b)~the Wasserstein distance metric to obtain a set of {\thethings} including regular events.
+
+\begin{figure}[htp]
+  \centering
+  \subcaptionbox{Euclidean\label{fig:sel-dist-norm}}{%
+    \includegraphics[width=.5\linewidth]{evaluation/sel-dist-norm}%
+  }%
+  \subcaptionbox{Wasserstein\label{fig:sel-dist-emd}}{%
+    \includegraphics[width=.5\linewidth]{evaluation/sel-dist-emd}%
+  }%
+  \caption{The normalized (a)~Euclidean, and (b)~Wasserstein distance of the generated {\thething} sets for different {\thething} percentages.}
+  \label{fig:sel-dist}
+\end{figure}
+
+Comparing the results of the Euclidean distance in Figure~\ref{fig:sel-dist-norm} with those of the Wasserstein in Figure~\ref{fig:sel-dist-emd} we conclude that the Euclidean distance provides more consistent results for all possible distributions.
+The maximum difference is approximately $0.4$ for the former and $0.7$ for the latter between the bimodal and skewed {\thething} distribution.
+Therefore, we choose to utilize the Euclidean distance metric for the implementation of the privacy-preserving {\thething} selection.
+
+
+\subsection{Budget allocation and {\thething} selection}
+\label{subsec:sel-prv}
 
 Figure~\ref{fig:real-sel} exhibits the performance of Skip, Uniform, and Adaptive (see Section~\ref{subsec:lmdk-mechs}) in combination with the {\thething} selection component.
 
@@ -19,7 +46,7 @@ Figure~\ref{fig:real-sel} exhibits the performance of Skip, Uniform, and Adaptiv
   \subcaptionbox{T-drive\label{fig:t-drive-sel}}{%
     \includegraphics[width=.5\linewidth]{evaluation/t-drive-sel}%
   }%
-  \caption{The mean absolute error (a)~as a percentage, (b)~in kWh, and (c)~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 {\thething} percentages.}
   \label{fig:real-sel}
 \end{figure}