Add PageRank and WordNet to slides/methods.tex

references.bib

@@ -8,3 +8,41 @@
   	location = 	{Valencia, Spain},
   	url = 	{http://aclweb.org/anthology/E17-1105}
 }
+@techreport{PageRank1999,
+	number = {1999-66},
+	month = {November},
+	author = {Lawrence Page and Sergey Brin and Rajeev Motwani and Terry Winograd},
+	note = {Previous number = SIDL-WP-1999-0120},
+	title = {The PageRank Citation Ranking: Bringing Order to the Web.},
+	type = {Technical Report},
+	publisher = {Stanford InfoLab},
+	year = {1999},
+	institution = {Stanford InfoLab},
+	url = {http://ilpubs.stanford.edu:8090/422/}
+}
+@inproceedings{Mihalcea2006similarity,
+	author = {Mihalcea, Rada and Corley, Courtney and Strapparava, Carlo},
+	title = {Corpus-Based and Knowledge-Based Measures of Text Semantic Similarity},
+	year = {2006},
+	isbn = {9781577352815},
+	publisher = {AAAI Press},
+	booktitle = {Proceedings of the 21st National Conference on Artificial Intelligence - Volume 1},
+	pages = {775–780},
+	numpages = {6},
+	location = {Boston, Massachusetts},
+	series = {AAAI’06}
+}
+@misc{Wu1994distance,
+	author = {Wu, Zhibiao and Palmer, Martha},
+	title = {Verbs Semantics and Lexical Selection},
+	year = {1994},
+	publisher = {Association for Computational Linguistics},
+	address = {USA},
+	url = {https://doi.org/10.3115/981732.981751},
+	doi = {10.3115/981732.981751},
+	booktitle = {Proceedings of the 32nd Annual Meeting on Association for Computational Linguistics},
+	pages = {133–138},
+	numpages = {6},
+	location = {Las Cruces, New Mexico},
+	series = {ACL ’94}
+}
\ No newline at end of file

slides/methods.tex

 \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 T1 and T2 was used as a weakened variant
+	\end{itemize}
+\end{frame}
 \begin{frame}
 	\frametitle{Similarity}
 	\begin{itemize}
@@ -17,8 +63,6 @@ contextualized word representations,”}
 		      \end{itemize}
 	\end{itemize}
 \end{frame}
-
-
 \begin{frame}
 	\frametitle{Sentiment}
 	\begin{itemize}