\section{Methods}
\subsection{Baseline Methods}
\begin{frame}
	\frametitle{PageRank}
	\begin{columns}
		\column{0.6\textwidth}
		\begin{itemize}
			\item PageRank by \cite{PageRank1999} was originally used to evaluate relevant websites via their links
			\item Websites can be replaced by arguments
			\item Linking results due to the reuse of conclusions and premises
			\item In this work it was used:
			\begin{itemize}
				\item Custom-made PageRank
				\item NetworkX PageRank
				\item NetworkX-Scipy PageRank
			\end{itemize}
		\end{itemize}
		\begin{block}{Custom-made PageRank}
			\begin{equation*}
				p_t(c_i) = \left\{
				\begin{array}{lr}
						(1 - \alpha)\frac{1}{|D|} + \alpha \sum_{j}{\frac{p_{t-1}(c_j)}{|P'_j|}} & : t > 0\\
					\frac{1}{|D|} & : t = 0
				  \end{array}
			\right.
			\end{equation*}
		\end{block}
		\column{0.4\textwidth}
			\includegraphics[scale=0.25]{bilder/ExampleGraph.png}
		\end{columns}
\end{frame}
\begin{frame}
	\frametitle{WordNet}
	\begin{itemize}
		\item As knowledge based method $Sim(T_1, T_2)$ of \cite{Mihalcea2006similarity} was used
		\item $Sim(T_1, T_2)$ determines the semantic similarity of $T_1,T_2$ by mutually picking up highly similar concepts
		\item The concepts were determined via WordNet
		\item For $maxSim$ the $CoSim$ of \cite{Wu1994distance} was used
	\end{itemize}
	\begin{block}{$Sim(T_1, T_2)$}
		\begin{equation*}
			\frac{1}{2}(\frac{\sum_{w \in {T_1}}{maxSim(w, T_2)\cdot idf(w)}}{\sum_{w \in {T_1}}{idf(w)}}+\frac{\sum_{w \in {T_2}}{maxSim(w, T_1)\cdot idf(w)}}{\sum_{w \in {T_2}}{idf(w)}})
		\end{equation*}
	\end{block}
	\begin{itemize}
		\item Analogously, the average conceptual similarity between $T_1$ and $T_2$ was used as a weakened variant
	\end{itemize}
\end{frame}
\begin{frame}
	\frametitle{Similarity}
	\begin{itemize}
		\item For ranking the arguments, we measured the semantic similarity
		      between the premises and conclusions
		\item Argument were embedded word-wise in an averaged vector space
		\item The resulting similarity was calculated by using $Cos(c, p)$
	\end{itemize}
	\begin{block}{Embeddings used}
		BERT by \cite{devlin2018bert}

		ELMo by \cite{Peters:2018ELMo}

		GloVe by \cite{pennington2014glove}
	\end{block}
\end{frame}
\begin{frame}
	\frametitle{Sentiment}
	\begin{columns}
		\column{0.6\textwidth}
		\begin{itemize}
			\item As another approach we used to measure the positivity of the argument
			\item We used a neural network based on FastText by \cite{Armand:2017FastText}
			\item The neural network was trained to indicate the sentiment with IMDb film ratings
		\end{itemize}
		\column{0.4\textwidth}
			\includegraphics[scale=0.1]{bilder/pngfuel-friends.png}
		\end{columns}
\end{frame}