From 8d5310ae1e2e3e5f65f9e3063444ca8b7d696c59 Mon Sep 17 00:00:00 2001
From: feger <marc.feger@hhu.de>
Date: Wed, 11 Dec 2019 17:12:45 +0100
Subject: [PATCH] Add more text for recommender systems

---
 recommender.tex |   2 +-
 submission.pdf  | Bin 220277 -> 220281 bytes
 2 files changed, 1 insertion(+), 1 deletion(-)

diff --git a/recommender.tex b/recommender.tex
index 4e1e933..36946e2 100644
--- a/recommender.tex
+++ b/recommender.tex
@@ -42,7 +42,7 @@ Here $\mu_u$ denotes the \textit{average} of all \textit{assigned ratings} of th
 Thus $b_u$ indicates the \textit{deviation} of the \textit{average assigned rating} of a \textit{user} from the \textit{global average}. Similarly, $b_i$ indicates the \textit{deviation} of the \textit{average rating} of an item from the \textit{global average}.
 In addition, the \textit{minimization problem} can be extended by the \textit{bias}. Accordingly, the \textit{minimization problem} is then $\min_{p_u, q_i}{\sum_{(u,i) \in \mathcal{B}} (r_{ui} - \hat{r}_{ui})^{2}} + \lambda(\lVert q_i \rVert^2 + \lVert p_u \lVert^2 + b_u^2 + b_i^2)$. Analogous to the \textit{regulated matrix-factorization}, the values $b_u$ and $b_i$ are penalized in addition to $\lVert q_i \rVert, \lVert p_u \rVert$. In this case $b_u, b_i$ are penalized more if they assume a large value and thus deviate strongly from the \textit{global average}.
 
-\subsection{Advanced Matrix-Factorization}
+\subsubsection{Advanced Matrix-Factorization}
 This section is intended to show that there are \textit{other approaches} to \textit{matrix-factorization}.
 Thus, \textit{implicit data} can also be included.
 First of all, it should be mentioned that \textit{temporary dynamics} can also be included.
diff --git a/submission.pdf b/submission.pdf
index 81b080d59625d2f5f6108bd185d0ba094e2df2d6..4255cb7c64b34e284853306b1928a10b18358a61 100644
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