From 4f76ee51c42b389551c795351a3c67f5557c1684 Mon Sep 17 00:00:00 2001
From: feger <marc.feger@hhu.de>
Date: Thu, 28 Nov 2019 14:01:21 +0100
Subject: [PATCH] Add text for recommender systems

---
 recommender.tex |  10 ++++++++++
 references.bib  |  11 +++++++++++
 submission.pdf  | Bin 103822 -> 142618 bytes
 submission.tex  |   7 +++++--
 4 files changed, 26 insertions(+), 2 deletions(-)
 create mode 100644 recommender.tex

diff --git a/recommender.tex b/recommender.tex
new file mode 100644
index 0000000..3ff45f9
--- /dev/null
+++ b/recommender.tex
@@ -0,0 +1,10 @@
+\section{A Study on Recommender Systems}
+This section explains the basics of \textit{recommender systems} necessary for the essential understanding of the paper presented. Besides the general definition of the \textit{recommender problem}, the corresponding solution approaches are presented. Furthermore, the main focus will be on the solution approach of  \textit{matrix factorization}.
+
+\subsection{Recommender Problem}
+The \textit{recommender problem} consists of the entries of the sets $\mathcal{U}$ and $\mathcal{I}$, where $\mathcal{U}$ represents the set of all \textit{users} and $\mathcal{I}$ the set of all \textit{items}.
+Each of the \textit{users} in $\mathcal{U}$ gives \textit{ratings} from a set $\mathcal{S}$ of possible scores for the available \textit{items} in $\mathcal{I}$. The resulting \textit{rating-matrix} $\mathcal{R}$ is composed of $\mathcal{R} = \mathcal{U} \times \mathcal{I}$. The entries in $\mathcal{R}$ indicate the \textit{rating} from \textit{user} $u \in \mathcal{U}$ to \textit{item} $i \in \mathcal{I}$. This entry is then referred to as $r_{ui}$. Due to incomplete \textit{item-ratings}, $\mathcal{R}$ may also be incomplete. In the following, the subset of all \textit{users} who have rated a particular \textit{item} $i$ is referred to as $\mathcal{U}_i$. Similarly, $\mathcal{I}_u$ refers to the subset of \textit{items} that were rated by \textit{user} $u$. Since $\mathcal{R}$ is not completely filled, there are missing values for some \textit{user-item relations}. The aim of the \textit{recommender system} is to estimate the missing \textit{ratings} $\hat{r}_{ui}$ using a \textit{prediction-function} $p(u,i)$. The \textit{prediction-function} consists of $p: \mathcal{U} \times \mathcal{I} \rightarrow \mathcal{S}$ \citep{DeKa11}. In the further course of the work different methods are presented to determine $p(u,i)$.
+
+In the following, the two main approaches of \textit{collaborative-filtering} and \textit{content-based} \textit{recommender systems} will be discussed. In addition, it is explained how \textit{matrix factorization} can be integrated into the two ways of thinking.
+
+\subsection{Collaborative-Filtering}
\ No newline at end of file
diff --git a/references.bib b/references.bib
index 71e2152..5a3c6e9 100644
--- a/references.bib
+++ b/references.bib
@@ -27,3 +27,14 @@
   biburl    = {https://dblp.org/rec/bib/journals/corr/abs-1905-01395},
   bibsource = {dblp computer science bibliography, https://dblp.org}
 }
+@inproceedings{DeKa11,
+author = {Desrosiers, Christian and Karypis, George},
+year = {2011},
+month = {01},
+pages = {107--144},
+title = {A Comprehensive Survey of Neighborhood-Based Recommendation Methods},
+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}
+}
\ No newline at end of file
diff --git a/submission.pdf b/submission.pdf
index 1a19cab2d18e8f5381775cda9beea5fa47bce19e..f37eae4f5c4d863d89944736146a898a6f2bdde4 100644
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diff --git a/submission.tex b/submission.tex
index d98a497..b0c8b34 100644
--- a/submission.tex
+++ b/submission.tex
@@ -31,7 +31,10 @@
 \parindent 6pt
 \usepackage[]{titlesec}
 \titlespacing*{\section}
-{0pt}{0pt}{6pt}
+{0pt}{6pt}{6pt}
+\usepackage[]{titlesec}
+\titlespacing*{\subsection}
+{0pt}{6pt}{6pt}
 \usepackage{footmisc}
 \setlength{\abovedisplayskip}{0pt}
 \renewcommand{\footrulewidth}{0.5pt}
@@ -62,7 +65,7 @@ A Study on Recommender Systems}
 % Hier beginnt der Inhalt!                                       %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \input{introduction}
-
+\input{recommender}
 \newpage
 \bibliography{references}
 \bibliographystyle{plainnat}
-- 
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