# Prediction of High Capabilities in the Development of Kindergarten Children
## 4 Results and Discussion
### Results for Educational Data  
As we were dealing with an imbalanced dataset, with imbalance ratio IR = 8.1, we used as a classifier performance measure the Area under the ROC curve (AUC). AUC is a performance measure that takes into consideration the amount of correctly classified instances of positive and negative classes [27]. This characteristic makes AUC suitable for the evaluation of classifier performance in imbalanced datasets, due to its lack of bias in favor of the majority class. The AUC is based on the computation of two measures: the True Positive Rate (recall or sensitivity) and the True Negative Rate (specificity). \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Classified as**} \\ \hline
**Examples** & **Positive** & **Negative** \\ \hline Positive & True positive (\(\mathit{tp}\)) & False negative (\(\mathit{fn}\)) \\ Negative & False positive (\(\mathit{fp}\)) & True negative (\(\mathit{tn}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix for a two-class classification problem. Let us consider the confusion matrix of Table 7. The True Positive Rate (TPR) and True Negative Rate (TNR) are computed as follows:  
\[TPR=\frac{tp}{tp+fn} \tag{8}\]  
\[TNR=\frac{tn}{tn+fp} \tag{9}\]  
Accordingly, the Area under the ROC curve for a discrete classifier is computed as:  
\[AUC=\frac{TPR+TNR}{2} \tag{10}\]  
In addition to classifier performance, we computed the instance reduction rate and feature reduction rate. As the Nearest Neighbor classifier stores the training set in memory, and also compares the new instances to be classified with the ones stored in the training set, both instance and feature reduction measures indicate the amount of computational cost saved with the preprocessing algorithm. We compared FIS-SM with respect to previously reported algorithms. Several genetic based algorithms were selected [28], such as the Genetic Algorithm proposed by [PERSON] and [PERSON] (IN-GA) [29], the Genetic Algorithm proposed by [PERSON] and [PERSON] (KJ-GA) [30] and the Genetic Algorithm proposed by [PERSON], [PERSON] and [PERSON] (AKH-GA) [31]. The hybrid Evolutionary Instance Selection enhanced by Rough set based Feature Selection (EIS-RFS) algorithm [19] was also selected for comparison. In addition, the deterministic algorithm for instance and feature selection proposed by [PERSON] et al., the Testors and Compact set based Combined Selection (TCCS) [32] were considered in the comparison. We also computed the results of the NN classifier without any preprocessing (ONN). The parameters for the compared algorithms are shown in Table 8. We used the corresponding papers for such parameter configuration. In Table 9 we show the results of the compared algorithms over the kindergarten dataset. We highlight in bold the best results. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameters** \\ \hline \hline \multirow{4}{*}{AKH-GA} & Iterations: 20 \\  & Population count: 200 individuals \\  & Crossover probability: 0.7 \\  & Mutation probability: 0.1 per bit \\  & MAX\_EVALUATIONS: 10,000 \\  & Population count: 50 \\  & Crossover probability: 1.0 \\  & Mutation probability for features: 0.01 per bit \\  & Mutation probability for instances: \(p(1\to 0)=0.1\) and \(p(0\to 1)=0.01\) \\  & Iterations: 100 \\  & Population count: 10 individuals \\  & Crossover probability: 1.0 \\  & Mutation probability: 0.1 per bit \\  & No user-defined parameter \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters used by algorithms under comparison. The results show that the proposed FIS-SM increased the classifier performance according to the AUC measure, using fewer instances and features. FIS-SM obtained an AUC very close to the perfect classification, with less than 7% of instances and with almost 27% of features. Having a reduced set of instances and features decreased the computational cost of the Nearest Neighbor classifier, and reduced the execution time.