# Analysis of the Learning Process through Eye Tracking Technology and Feature Selection Techniques
## 3 Results
### Study with Supervised Learning Machine Learning Techniques: Feature Selection  
A feature selection analysis was performed with the R programming package mclust, selecting from all possible variables those that received a positive ranking. The gain ratio, symmetrical uncertainty and chi-square algorithms were used for feature selection. Table 3 shows the best values found with each of them for feature selection.  
(a) The gain ratio is a feature selection method that belongs to the filtering methods. It relies on entropy to assign weights to discrete attributes based on their correlation between the attribute and a target variable (in this study, the results in solving the crossword puzzle). The gain ratio focuses on the information gain metric [57], traditionally used to choose the attribute at a node of a decision tree with the ID3 method. This is the one that generates a partition in which the examples are distributed less randomly among the classes. This method was improved by [PERSON] in 1993 [58], as he detected that the information gain was calculated with an unfair favouritism towards attributes with many results. To correct this, he added a value correction based on standardisation by the entropy of that attribute. If Y is the variable to be predicted, then the gain ratio standardises the gain by dividing by the entropy of X. Thus, the C4.5 decision tree construction method uses this measure. From a data mining point of view, this attribute selection could be understood as the selection of attributes as best candidates for the root of a decision tree, which in this study will predict the solving crossword puzzle variable. With H being the entropy, the gain ratio equation is as follows:  
\[gain\ ratio=\frac{H(Class)+H(Attribute)-H(Class,Attribute)}{H(Attribute)}\]  
Figure 4 shows the correlation matrix found with the gain ratio algorithm in the selection of best features.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Features** & **Gain Ratio** & **Symmetrical Uncertainty** & **Chi-Square** \\ \hline Previous Knowledge & 0.199 & 0.199 & 0.453 \\ Group Type & 0.238 & 0.171 & 0.421 \\ Employment Status & 0.238 & 0.171 & 0.421 \\ Gender & 0.108 & 0.067 & 0.372 \\ Level Degree & 0.100 & 0.082 & 0.263 \\ Knowledge Branch & 0.084 & 0.057 & 0.251 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Best performing features in the gain ratio, symmetrical uncertainty and chi-square feature selection algorithms.  
Figure 4: Relationship matrix on the selected features performed with the gain ratio algorithm.  
(b) Symmetrical uncertainty is a feature selection method which, as with the gain ratio, belongs to the filter methods and is also based on entropy. Symmetrical uncertainty normalises the values in the range [0, 1]. It also normalises the gain by dividing by the sum of the attribute and class entropies, where H is the entropy.  
\[\textit{symmetrical uncertainty}=2\times\frac{H(Class)+H(Attribute)-H(Class, Attribute)}{H(Attribute)+H(Class)}\]  
Figure 5 shows the correlation matrix found with the symmetrical uncertainty algorithm on the best features.  
(c) Chi-square is a feature selection algorithm that belongs to the filter type and tries to obtain the weights of each feature by using the chi-square test (in case the features are not nominal, it discretises them). The selection result is the same as [PERSON]'s V coefficient. The chi-square equation is as follows:  
\[\chi^{2}=\sum_{i=1}^{k}\frac{\left(Oi+Ei\right)^{2}}{Ei}\]  
where \(Oi\) is the observed or empirical absolute frequency and \(Ei\) is the expected frequency.  
Figure 6 shows the correlation matrix found with chi-square (\(\chi^{2}\)) [59].  
Figure 5: Relationship matrix on the selected features performed with the symmetrical uncertainty algorithm.