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\section{Results}
\begin{frame}
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	\begin{figure}
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		\frametitle{Evaluation of PageRank}
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		\centering
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		\includegraphics[width=\linewidth]{bilder/PageRankComparison.png}
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		\caption{Direct comparison of the different PageRank against the approach of \cite{wachsmuth:2017a}.}
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	\end{figure}
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\end{frame}
\begin{frame}
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	\frametitle{Baseline Evaluation}
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	\begin{figure}
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		\centering
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		\includegraphics[width=\linewidth]{bilder/PairwiseResultComparison.png}
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		\caption{Direct comparison of all baseline values reported by \cite{wachsmuth:2017a} with all results obtained in this paper.}
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	  \end{figure}
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\end{frame}
\begin{frame}
	\frametitle{Detailed Results}
	\begin{table}[hbp!]
		\centering
		\resizebox{\textwidth}{!}{
			\begin{tabular}{llrrrcrrrcrrrcrrrcrrr}
				\toprule
				\multirow{3}{*}{\textbf{\#}} &
				\multirow{3}{*}{\textbf{Approach}} &
				\multicolumn{3}{c}{\textbf{(a) Minimum}}& &
				\multicolumn{3}{c}{\textbf{(b) Average}} & &
				\multicolumn{3}{c}{\textbf{(c) Maximum}} & &
				\multicolumn{3}{c}{\textbf{(d) Sum}} & &
				\multicolumn{3}{c}{\textbf{(e) Best results}} \\
				\cline{3-5}  \cline{7-9}  \cline{11-13} \cline{15-17} \cline{19-21} & & $\tau$ & \textit{best} & \textit{worst} & & $\tau$ & \textit{best} & \textit{worst} & & $\tau$ & \textit{best} & \textit{worst} & & $\tau$ & \textit{best} & \textit{worst} & & $\tau$ & \textit{best} & \textit{worst}\\
				\midrule
				\small 1  & PageRank 						& 0.01 				& 8 				& 6 				& & 0.02 				& 9 				& 7 				& & 0.11 				& 8 				& 6 				& & 0.28 				& 11 				& 5 				& & 0.28 				& 11 				& 5 \\
				\small 2  & Frequency 						& -0.10 			& 2 				& 8 				& & -0.03 				& 3 				& 9 				& & -0.01 				& 2 				& 8 				& & 0.10 				& 6 				& 8 				& & 0.10 				& 6 				& 8 \\
				\small 3  & Similarity 						& -0.13 			& 4 				& 11 				& & -0.05 				& 5 				& 11 				& & 0.01 				& 6 				& 10 				& & 0.02 				& 6 				& 10 				& & 0.02 				& 6 				& 10 \\
				\small 4  & Sentiment 						& 0.01 				& 6 				& 7 				& & 0.11 				& 9 				& 4 				& & 0.12 				& 6 				& 4 				& & 0.12 				& 9 				& 4 				& & 0.12 				& 9 				& 4 \\
				\small 5  & Most premises 					& n/a 				& n/a 				& n/a 				& & n/a 				& n/a 				& n/a 				& & n/a 				& n/a 				& n/a 				& & 0.19 				& 3 				& 3 				& & 0.19 				& 3 				& 3 \\
				\small 6  & Random 							& n/a 				& n/a 				& n/a 				& & n/a 				& n/a 				& n/a 				& & n/a 				& n/a 				& n/a 				& & 0.00 				& 5 				& 7 				& & 0.00 				& 5 				& 7 \\
				\midrule
				\small 7  & SNN 	 						& 0.12 				& 10 				& 6 				& & 0.24 				& 11 				& 5 				& & 0.31 				& 12 				& 5 				& & 0.30 				& 13 				& 5 				& & 0.31 				& 13 				& 5 \\
				\small 8  & GWP 							& \textbf{0.22} 	& 12 				& 5 				& & \textbf{0.28}		& 13 				& \textbf{3}		& & \textbf{0.39}		& \textbf{14} 		& \textbf{2} 		& & \textbf{0.47} 		& \textbf{16} 		& \textbf{1} 		& & \textbf{0.47} 	& \textbf{16} & \textbf{1} \\
				\small 9  & GWOP 							& -0.06 			& 5 				& 9 				& & 0.00 				& 6 				& 7 				& & 0.14 				& 8 				& 6 				& & 0.20 				& 8 				& 4 				& & 0.20 				& 8 				& 4 \\
				\small 10 & EWP 							& 0.03 				& 6 				& 9 				& & 0.08 				& 7 				& 8 				& & 0.11 				& 8 				& 8 				& & 0.28 				& 9 				& 5 				& & 0.28 				& 9 				& 5 \\
				\small 11 & EWOP 							& -0.04 			& 5 				& 9 				& & 0.03 				& 6 				& 8 				& & 0.07 				& 7 				& 8 				& & 0.23 				& 9 				& 6 				& & 0.23 				& 9 				& 6 \\
				\small 12 & BWP 							& -0.09 			& 6 				& 9 				& & -0.02 				& 7 				& 8 				& & 0.05 				& 9 				& 8 				& & 0.24 				& 10 				& 5 				& & 0.24 				& 10 				& 5 \\
				\small 13 & BWOP 							& -0.06 			& 6 				& 9 				& & -0.01 				& 7 				& 8 				& & 0.07 				& 9 				& 8 				& & 0.26 				& 10 				& 5 				& & 0.26 				& 10 				& 5 \\
				\small 14 & MKBM 							& 0.10 				& 5 				& 7 				& & 0.08 				& 13 				& 6 				& & 0.24 				& 12 				& 8 				& & 0.34 				& 11 				& 9 				& & 0.34 				& 13 				& 6 \\
				\small 15 & AKBM 							& 0.15 				& \textbf{14}		& \textbf{4} 		& & 0.26 				& \textbf{14} 		& 4 				& & 0.38 				& 11 				& 7 				& & 0.40 				& 13 				& 7 				& & 0.40 				& 14 				& 4 \\
				\bottomrule
			\end{tabular}
		}
		\vspace*{0mm}
		\caption{Comparison of the approaches of \cite{wachsmuth:2017a} (1-6) with those used in this study (7-15). For each aggregation (a-d) the average agreement $\tau$ and the cases in which the respective approach performed best or worst over the 32 conclusions of the 110 arguments are given. (e) shows the best results of an aggregation.}
	\label{tab:results}
	\end{table}
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\end{frame}