From d0dcc654ba3d0a24f4f54ce5500544aebdc395db Mon Sep 17 00:00:00 2001
From: Manos <manos@delkappa.com>
Date: Wed, 13 Oct 2021 09:34:10 +0200
Subject: [PATCH] evaluation: Updated sel-utl

---
 text/evaluation/theotherthing.tex | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/text/evaluation/theotherthing.tex b/text/evaluation/theotherthing.tex
index b17a808..e82136b 100644
--- a/text/evaluation/theotherthing.tex
+++ b/text/evaluation/theotherthing.tex
@@ -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}