diff --git a/recommender.tex b/recommender.tex
index 95c43ab9fc0df1b25e3e1d58ed143dfb8dddfc09..98106d84769a6ee3b062fdea28b47ca49759ae8b 100644
--- a/recommender.tex
+++ b/recommender.tex
@@ -11,7 +11,7 @@ In the following, the two main approaches of \textit{collaborative-filtering} an
 \textit{Content-based} \textit{recommender systems (CB)} work directly with \textit{feature vectors}. Such a \textit{feature vector} can, for example, represent a \textit{user profile}. In this case, this \textit{profile} contains informations about the \textit{user's preferences}, such as \textit{genres}, \textit{authors}, \textit{etc}.  This is done by trying to create a \textit{model} of the \textit{user}, which best represents his preferences. The different \textit{learning algorithms} from the field of \textit{machine learning} are used to learn or create the \textit{models}. The most prominent \textit{algorithms} are: \textit{tf-idf}, \textit{bayesian learning}, \textit{Rocchio's algorithm} and \textit{neural networks} \citep{Lops11, Dacrema19, DeKa11}. Altogether the built and learned \textit{feature vectors} are compared with each other. Based on their closeness, similar \textit{features} can be used to generate \textit{missing ratings}. Figure \ref{fig:cb} shows a sketch of the general operation of \textit{content-based recommenders}.
 
 \subsection{Collaborative-Filtering}
-Unlike the \textit{content-based recommender (CF)}, the \textit{collaborative-filtering recommender} not only considers individual \textit{users} and \textit{feature vectors}, but rather a \textit{like-minded neighborhood} of each \textit{user}.
+Unlike the \textit{content-based recommender}, the \textit{collaborative-filtering recommender (CF)} not only considers individual \textit{users} and \textit{feature vectors}, but rather a \textit{like-minded neighborhood} of each \textit{user}.
 Missing \textit{user ratings} can be extracted by this \textit{neighbourhood} and \textit{networked} to form a whole. It is assumed that a \textit{missing rating} of the considered \textit{user} for an unknown \textit{item} $i$ will be similar to the \textit{rating} of a \textit{user} $v$ as soon as $u$ and $v$ have rated some \textit{items} similarly. The similarity of the \textit{users} is determined by the \textit{community ratings}. This type of \textit{recommender system} is also known by the term \textit{neighborhood-based recommender} \citep{DeKa11}. The main focus of \textit{neighbourhood-based methods} is on the application of iterative methods such as \textit{k-nearest-neighbours} or \textit{k-means}.
 A \textit{neighborhood-based recommender} can be viewed from two perspetives: The first and best known problem is the so-called \textit{user-based prediction}.  Here, the \textit{missing ratings} of a considered \textit{user} $u$ are to be determined from his \textit{neighborhood} $\mathcal{N}_i(u)$. 
 $\mathcal{N}_i(u)$ denotes the subset of the \textit{neighborhood} of all \textit{users} who have a similar manner of evaluation to $u$ via the \textit{item} $i$. The second problem is that of \textit{item-based prediction}. Analogously, the similarity of the \textit{items} are determined by their received \textit{ratings}.
diff --git a/submission.pdf b/submission.pdf
index 825e0e6e07c35d9f8810b4b33bf9533b57d25569..e3a9f7e83c782b37d3f6273c2f239b125407ab8d 100644
Binary files a/submission.pdf and b/submission.pdf differ