diff --git a/recommender.tex b/recommender.tex
index 36946e20d37e355bf9fd2ffbd1ab79f2200fa496..10bc2221d2cfd78ab037067940cc39c3f00c921b 100644
--- a/recommender.tex
+++ b/recommender.tex
@@ -20,7 +20,7 @@ Figure \ref{fig:cf} shows a sketch of the general operation of the \textit{colla
 
 \input{content-based-collaborative-filtering-comparison}
 
-\subsection{Matrix-Factorization}
+\subsection{Matrix-Factorization}\label{sec:mf}
 The core idea of \textit{matrix factorization} is to supplement the not completely filled out \textit{rating-matrix} $\mathcal{R}$. For this purpose the \textit{users} and \textit{items} are to be mapped to a joined \textit{latent feature space} with \textit{dimensionality} $f$. The \textit{user} is represented by the vector $p_u \in \mathbb{R}^{f}$ and the item by the vector $q_i \in \mathbb{R}^{f}$. As a result, the \textit{missing ratings} and thus the \textit{user-item interaction} are to be determined via the \textit{inner product} $\hat{r}_{ui}=q_i^Tp_u$ of the corresponding vectors \citep{Kor09}. In the following, the four most classical matrix factorization approaches are described in detail. Afterwards, the concrete learning methods with which the vectors are learned are presented. In addition, the \textit{training data} for which a \textit{concrete rating} is available should be referred to as $\mathcal{B} = \lbrace(u,i) | r_{ui} \in \mathcal{R}\rbrace$.
 
 \subsubsection{Basic Matrix-Factorization}
@@ -48,3 +48,9 @@ Thus, \textit{implicit data} can also be included.
 First of all, it should be mentioned that \textit{temporary dynamics} can also be included.
 On the one hand, it is not realistic that a \textit{user} cannot change his taste. On the other hand, the properties of an \textit{item} remain constant. Therefore, \textit{missing ratings} can also be determined \textit{time-based}. A \textit{missing rating} is then determined by $\hat{r}_{ui}=\mu + b_i(t) + b_u(t) + q_i^{T}p_u(t)$ \citep{Kor09}.
 As a second possibility, \textit{implicit influence} can be included. This can involve the \textit{properties} of the \textit{items} a \textit{user} is dealing with. A \textit{missing rating} can be determined by $\hat{r}_{ui}=\mu + b_i + b_u + q_i^{T}(p_u + |\mathcal{I}_u|^{-\frac{1}{2}}\sum_{i \in \mathcal{I}_u}{y_i})$. $y_i \in \mathbb{R}^{f}$ describes the \textit{feature vectors} of the \textit{items} $i \in \mathcal{I}_u$ which have been evaluated by \textit{user} $u$. The corresponding \textit{minimization problems} can be adjusted as mentioned in the sections above \citep{Kor08}.
+
+\subsection{Optimization and Learning}
+An important point that does not emerge from the above points is the question of how the individual components $p_u, q_i, b_u, b_i$ are constructed. In the following, the three most common methods are presented.
+
+\subsubsection{Stochastic Gradient Descent}
+The best known and most common method when it comes to \textit{machine learning} is \textit{stochastic gradient descent (SGD)}. The goal of \textit{SGD} is to \textit{minimize} the \textit{error} of a given \textit{objective function}. Thus the estimators mentioned in section \ref{sec:mf} can be used as \textit{objective functions}. In the field of \textit{recommender systems}, \citet{Funk06} presented a \textit{modified} variant of \textit{SGD} in the context of the \textit{Netflix Challenge}. This can be applied to \textit{regulated matrix-factorization} with \textit{bias} as well as without \textit{bias}. This method can be described by the following pseudo code:
\ No newline at end of file
diff --git a/references.bib b/references.bib
index a391b459d67f74023cf0a68941ddf473250fcbb3..88581aa95b68e0ed1a3a227e8ec49850d1c915fe 100644
--- a/references.bib
+++ b/references.bib
@@ -79,4 +79,23 @@ pages = {426-434},
 title = {Factorization meets the neighborhood: A multifaceted collaborative filtering model},
 journal = {Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD'08).},
 doi = {10.1145/1401890.1401944}
+}
+@inproceedings{Kor11,
+author = {Yehuda Koren and Robert Bell},
+year = {2011},
+month = {01},
+pages = {145--186},
+title = {Advances in Collaborative Filtering},
+booktitle = {Recommender Systems Handbook},
+editor = {P.B. Kantor and F. Ricci and L. Rokach and B. Shapira},
+publisher={Springer},
+doi = {10.1007/978-0-387-85820-3_4}
+}
+@misc{Funk06,
+  author = {Simon Funk},
+  title = {Netflix Update: Try This at Home},
+  howpublished = {\url{https://sifter.org/~simon/journal/20061211.html}},
+  note = {Accessed: 2019-12-12},
+  year = {2006},
+  month = {12}
 }
\ No newline at end of file
diff --git a/submission.pdf b/submission.pdf
index 4255cb7c64b34e284853306b1928a10b18358a61..bec9a7f5524dbafdf42b131cc3625dd70b574300 100644
Binary files a/submission.pdf and b/submission.pdf differ
diff --git a/submission.tex b/submission.tex
index 6ec8f08af01ae4bee1d7b50762c8e6f9c4c44fb3..5fd0b2aa88c8da1ce7a595bc6fee7692cced1fef 100644
--- a/submission.tex
+++ b/submission.tex
@@ -48,7 +48,7 @@
 \hypersetup{
   colorlinks,
   citecolor=hhuUniBlau,
-  linkcolor=hhuUniBlau,
+  linkcolor=black,
   urlcolor=hhuUniBlau}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -62,6 +62,9 @@ A Study on Recommender Systems}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{document}
 \input{frontpage}
+\newpage
+\tableofcontents
+\newpage
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 % Hier beginnt der Inhalt!                                       %
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