@@ -42,7 +42,7 @@ Here $\mu_u$ denotes the \textit{average} of all \textit{assigned ratings} of th
...
@@ -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}.
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}.
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}.
This section is intended to show that there are \textit{other approaches} to \textit{matrix-factorization}.
Thus, \textit{implicit data} can also be included.
Thus, \textit{implicit data} can also be included.
First of all, it should be mentioned that \textit{temporary dynamics} can also be included.
First of all, it should be mentioned that \textit{temporary dynamics} can also be included.
