## 7 Experiments and Results
### Comparison to Other Approaches
Table 16 shows the best results, based on the g-mean scores in [34] and those of the two methods that are proposed in this work. It is clear that the proposed methods significantly improved the g-mean scores. According to these results, we noticed the benefits of applying cost-sensitive learning to our MHOANN, as well as the advantages that could be gained by using ensemble learning to improve financial distress prediction. Although the same dataset was used in this work and in [34], it is worth mentioning that there were some differences between the experiment setups: (1) in this work, we used a 66% to 34% split for the training and testing datasets, while the authors of [34] used a 10-fold cross-validation technique that meant that 90% of their data were used to train the model, but the approach that is proposed in this work still showed better results; (2) ten separate runs were performed in [34] for each combination, while we performed five separate runs per combination in this work. \begin{table}
\begin{tabular}{l l l} \hline  & **Classifier** & **G-Mean** \\ \hline Basic Classifiers & k-NN [34] & 0.367 \\  & MLP [34] & 0.427 \\  & Naive Bayes [34] & 0.402 \\  & Random Tree [34] & **0.602** \\  & J48 [34] & 0.583 \\  & Rep tree [34] & 0.336 \\ \hline Ensembles & Bag-J48/(10) [34] & 0.488 \\  & AB-J48(20) [34] & 0.609 \\  & Dec-J48/(10) [34] & 0.549 \\  & RF-J48(80) [34] & 0.509 \\  & Bag-Rep Tree/(80) [34] & 0.315 \\  & AB-Rep Tree (90) [34] & **0.602** \\  & Dec-Rep Tree/(10) [34] & 0.414 \\  & RF-Rep Tree (10) [34] & 0.094 \\  & Bag-Random Tree/(100) [34] & 0.491 \\  & AB-Random Tree/(10) [34] & 0.574 \\  & Dec-Random Tree/(20) [34] & 0.532 \\  & Rtf-Random Tree/(30) [34] & 0.518 \\  & RF/(50) [34] & 0.464 \\ \hline Proposed Methods & ENS\_PSONN\({}_{\text{cost}}\) & 0.877 \\  & ENS\_CSONN\({}_{\text{cost}}\) & **0.893** \\ \hline \end{tabular}
\end{table} 
Table 15: The results for the g-mean scores of the standard classifiers that were used in the related work compared to those of the two methods that are proposed in this work using the dataset of Spanish companies. The best g-mean result per classification approach is marked in boldface. In another study that used the dataset of Taiwanese companies [35], the authors established that the integration of financial ratios (FRs) and corporate governance indicators (CGIs) could enhance the performance of the classifiers when forecasting the financial health of Taiwanese firms. Following this combination, five feature selection methodologies were evaluated to see whether they could lower data dimensionality. Consequently, the best results were achieved using an SVM with the stepwise discriminant analysis (SDA) feature selection method, along with the combination of FRs and CGIs (FC). The g-mean was not used as an evaluation metric in that study. Instead, type I and type II errors were used. A type I error [53] is also known as the False Positive Rate (FPR). In binary classification tasks, the FPR quantifies the proportion of false positives among all of the positive samples. It is defined in Equation (15):  
\[\text{Type I error}=\frac{\text{FP}}{\text{TN}+\text{FP}}=1-\text{Specificity} \tag{15}\]  
A type II error [53] is also known as the False Negative Rate (FNR). In binary classification tasks, the FNR quantifies the proportion of false negatives among all of the negative samples. It is defined in Equation (16):  
\[\text{Type II error}=\frac{\text{FN}}{\text{TP}+\text{FN}}=1-\text{Sensitivity} \tag{16}\]  
Hence, the g-mean score could be extracted using Equation (17):  
\[\text{g-mean}=\sqrt{(1-\text{Type II error})\times(1-\text{Type I error})} \tag{17}\]  
Table 17 shows the best results for the calculated g-mean scores using the type I and type II errors in [35] and the two methods that are proposed in this work. It can be seen that both of the proposed methods produced higher g-mean scores.