# Prediction of High Capabilities in the Development of Kindergarten Children
## 4 Results and Discussion
### Results for Repository Data  
In addition to the excellent results obtained over the Cuban kindergarten dataset, we also consider that it was necessary to test the performance of the proposed algorithm over well-known repository datasets. To accomplish this task, we selected eight datasets from the UCI Machine Learning repository [33]. Table 10 gives the description of them. The IR column represents the imbalance ratio of the dataset, computed as the ratio between the instances in the majority and minority classes. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & **Nominal** & **Numeric** & \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**Classes**} & **Missing** & **Imbalance** \\  & **Attributes** & & & & **Values** & **Ratio** \\ \hline breast-w & 0 & 9 & 699 & 2 & & 1.90 \\ credit-a & 9 & 6 & 690 & 2 & x & 1.25 \\ diabetes & 0 & 8 & 768 & 2 & & 1.87 \\ heart-c & 7 & 6 & 303 & 5 & x & 1.20 \\ hepatitis & 13 & 6 & 155 & 2 & x & 3.87 \\ labor & 6 & 8 & 57 & 2 & & 1.86 \\ wine & 0 & 13 & 178 & 3 & x & 1.47 \\ zoo & 16 & 1 & 101 & 7 & & 10.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Description of repository databases. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **ONN** & **TCCS** & **EIS-RFS** & **AKH-GA** & **IN-GA** & **KJ-GA** & **FIS-SM** \\ \hline AUC & 0.94 & 0.94 & 0.93 & 0.87 & 0.64 & 0.76 & **0.95** \\ Instance Reduction & 0.00 & 0.70 & 0.44 & 0.45 & 0.21 & 0.68 & **0.93** \\ Feature Reduction & 0.00 & 0.52 & 0.00 & 0.71 & 0.52 & 0.43 & **0.73** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance of the algorithms to predict high capabilities in kindergarten children. To consider the imbalanced class scenario, we included five datasets having \(IR>1.5\). We also considered among the selected datasets seven having mixed numerical and categorical features, and five incomplete datasets. To apply the NN classifier over the repository data, we selected as the dissimilarity function the HEOM dissimilarity [34]. We used the five-fold cross validation procedure and averaged the results. We selected five-fold cross validation due to its suitability for handling the imbalanced nature of some of the datasets [35]. As in the previous experiment, we computed the instance reduction ratio and the feature reduction ratio for the Nearest Neighbor classifier. However, to compare the classifier performance we could not use the Area under the ROC curve measure. As the AUC is only applicable for a two class problems and we were dealing with several multiclass imbalanced data problems, and it is well known that classifier accuracy is biased to favor the majority class, we considered the computation of the average accuracy by classes (Avg_Acc) as a classifier performance measure [36]. Let be \(Y=\{Y_{1},\ \cdots,\ Y_{l}\}\) the set of classes the averaged accuracy by classes is computed by:  
\[Avg\_Acc=\frac{1}{|Y|}\sum_{Y_{i}\in Y}\frac{1}{|Y_{i}|}\sum_{x \in Y_{i}}well(x) \tag{11}\] \[well(x)=\left\{ \begin{array}{ll}1&\text{if $x$ is correctly classified}\\ 0&\text{otherwise}\end{array} \right.\]  
We considered that the computation of the average accuracy by classes eliminates the bias of the traditional classifier accuracy and allows us to compare the classifier performance over multiclass imbalanced datasets. This computation is also provided in the summary results of the Explorer module of the Weka software [37]. Table 11 offers the Avg_Acc results of the Nearest Neighbor classifier without preprocessing (ONN), as well as the results of TCCS, EIS-RFS and the proposed FIS-SM. Best results are highlighted in bold. The averaged accuracy results over the repository datasets favored the proposed FIS-SM, which obtained the best classifier performance in four datasets. We considered that this behavior was due to FIS-SM being designed to deal with imbalanced data, a key feature that allows it to maintain good classifications in the datasets.