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evaluation: Updated sel-utl

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Manos Katsomallos 2021-10-13 09:34:10 +02:00
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@ -26,11 +26,12 @@ Figure~\ref{fig:sel-dist} demonstrates the normalized distance that we obtain wh
\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.
% (0 + (0.25 + 0.25 + 0.3 + 0.3)/4 + (0.45 + 0.45 + 0.45 + 0.5)/4 + (0.5 + 0.5 + 0.7 + 0.7)/4 + (0.6 + 0.6 + 1 + 1)/4 + (0.3 + 0.3 + 0.3 + 0.3)/4)/6
% (0 + (0.15 + 0.15 + 0.15 + 0.15)/4 + (0.2 + 0.2 + 0.3 + 0.4)/4 + (0.3 + 0.3 + 0.6 + 0.6)/4 + (0.3 + 0.3 + 1 + 1)/4 + (0.05 + 0.05 + 0.05 + 0.05)/4)
The maximum difference is approximately $0.4$ for the former and $0.7$ for the latter between the bimodal and skewed {\thething} distribution.
While both methods share the same mean normalized distance of $0.4$, the Euclidean distance demonstrates a more consistent performance among all possible {\thething} distributions.
Therefore, we choose to utilize the Euclidean distance metric for the implementation of the privacy-preserving {\thething} selection in Section~\ref{subsec:lmdk-sel-sol}.
% (1 + (0.25 + 0.25 + 0.45 + 0.45)/4 + (0.25 + 0.25 + 0.3 + 0.3)/4 + (0.2 + 0.2 + 0.2 + 0.2)/4 + (0.15 + 0.15 + 0.15 + 0.15)/4)/6
% (1 + (0.1 + 0.1 + 0.25 + 0.25)/4 + (0.075 + 0.075 + .15 + 0.15)/4 + (0.075 + 0.075 + 0.1 + 0.1)/4 + (0.025 + 0.025 + 0.025 + 0.025)/4)/6
The maximum difference per {\thething} percentage is approximately $0.2$ for the former and $0.15$ for the latter between the bimodal and skewed {\thething} distributions.
Overall, the Euclidean achieves a mean normalized distance of $0.3$ and the Wasserstein $0.2$.
Therefore, and by observing Figure~\ref{fig:sel-dist}, the Wasserstein distance demonstrates a less consistent performance and less linear behavior among all possible {\thething} distributions.
Thus, we choose to utilize the Euclidean distance metric for the implementation of the privacy-preserving {\thething} selection in Section~\ref{subsec:lmdk-sel-sol}.
\subsection{Privacy budget tuning}