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rewrite parts of concept chapter

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30_Thesis/sections/40_concept.tex
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@@ -159,8 +159,6 @@ Now the recommendation procedure looks as follows:
\subsection{Scoring Function}
\label{subsec:Concept:SolutionGeneration:ScoringFunction}
\todo[inline]{rewrite and fix information}
\emph{Group configuration scoring function} includes preferences and current configuration state. This function gives a score for a finished configuration (while using the current configuration state and all user preferences):
\begin{equation}
score_{group}: S \times P \times S_F \to \mathbb{R}
@@ -171,14 +169,14 @@ An example group configuration scoring function is $score_{group}$ with
score_{group}(\overline{s},\ \overline{p},\ s) = score(\overline{p},\ s) \cdot penalty(\overline{s},\ s)
\end{equation}
This thesis will use multiple scoring functions. Among those are ones for least misery, average and multiplicative which all are implemented by $score$. Average and multiplicative yield good results among the studies presented by \citeauthor{Masthoff2015} \cite{Masthoff2015}. Strategies can also be combined, one example here is average without misery. The scoring functions used for this thesis all combine $penalty$ and $score$ by multiplication. However it is possible to use other combination strategies here too and it is possible to combine multiple scoring functions into one group scoring function. This thesis will use simpler scoring functions that are not combined but improvement he is possible.
This thesis will use multiple scoring functions. Among those are ones for least misery, average and multiplicative which all are implemented by $score$. Average and multiplicative yield good results among the studies presented by \citeauthor{Masthoff2015} \cite{Masthoff2015}. Strategies can also be combined, one example here is average without misery. The scoring functions used for this thesis all combine $penalty$ and $score$ by multiplication. However it is possible to use other combination strategies and it is possible to combine multiple scoring functions into one group scoring function. This thesis will use simpler scoring functions that are not combined but improvement here is possible.
\subsubsection{Preference Scoring}
\todo[inline]{rewrite and fix information}
\todo[inline]{possibly remove distance from average scoring from thesis}
All of the aggregation functions mentioned in \autoref{subsec:Concept:SolutionGeneration:ScoringFunction} use one preference per user per product. Therefore to use them as is, a score for the whole configuration per user has to be calculated.
This thesis proposes different scoring functions. First to use the difference from the selected feature compared to the average rating of all characteristics. This approach includes all preferences of a user meaning a preference is also seen relative to others.
All of the aggregation functions mentioned in \autoref{subsec:Concept:SolutionGeneration:ScoringFunction} have one preference per product. For configuration where a preference for all characterises exists there needs to be a function that combines the preferences of one user into her configuration score. After one score has been calculated per user the mentioned preference aggregation strategies can be used.
This thesis proposes two different scoring functions. First, to use the difference from the selected characteristic compared to the average rating of all characteristics of the corresponding feature. This approach includes all preferences of a user meaning a preference is also seen relative to other preferences.
As an example a feature could be
\begin{equation}
@@ -204,6 +202,11 @@ on the other hand results in a feature score of $0.9-0.3=0.6$. For this user cha
As scores should be kept as percentages and not in the interval $[-1,1]$ a normalisation is applied by adding one and dividing by two. Therefore the respective scores are $0.7$ for user one and $0.95$ for user two. A configuration usually consists of more than one feature therefore an average rating over all features is taken to get the score one user gives to a configuration. Based on that score the in \autoref{subsec:Concept:SolutionGeneration:ScoringFunction} mentioned aggregation functions can be used.
The second simpler scoring function approach is to use the the preference for each characteristic that is part of the configuration and then use the average. This approach is more transparent because the preference of a user is directly translated into the score and no weighting is done. It means that a configuration score is more simple to understand and to calculate. However, if needed, for example to give one group member more power, it allows relative weighting too. This can be done with preprocessing of preferences. Moreover, an approach like this ensures that through preprocessing feature weights can be added. It is therefore possible that a user gives different importances to features. Also, other means of weighting ratings is possible. For example the ratings of one group member who has more knowledge in an area can be increased by multiplication with a factor or alternatively the preferences for all other users can be decreased.
The example above would not result in different feature scores for $P_1$ and $P_2$. Both would result in a score of $0.9$. Therefore there is a more direct link between a users preference and the score.
The simplicity of the second approach in combination with transparency is why it is the approach that will be used in further chapters in this thesis, especially as trust in a recommendation system is important.
\subsubsection{Cofiguration Change Penalty}
\label{subsubsec:Concept:SolutionGeneration:ScoringFunction:Penalty}