# Improved War Strategy Optimization with Extreme Learning Machine for Health Data Classification
## 7 Performance Evaluation  
In the experimental evaluation, the classification performance of the proposed model was assessed using five widely recognized metrics: accuracy, precision, sensitivity, specificity and the F1 score. These metrics provide a comprehensive understanding of the model's ability to classify medical data accurately and reliably [27]. Accuracy (Equation (17)) measures the proportion of correctly classified instances among all predictions and reflects the overall effectiveness of the model. Precision (Equation (18)) indicates the proportion of true positive predictions among all instances predicted as positive, providing insight into the model's correctness in identifying positive cases. Sensitivity (also known as True Positive Rate, Equation (19)) evaluates the model's ability to correctly identify actual positive instances. Specificity (Equation (20)) assesses the proportion of actual negative instances correctly classified as negative, which is critical for minimizing false alarms in clinical applications. F1 Score (Equation (21)) offers a harmonic mean between precision and sensitivity, presenting a balanced measure that is particularly useful when there is an uneven class distribution. The definitions of the metrics are based on the following components:  
TP (True Positives): The number of correctly predicted positive cases;  
TN (True Negatives): The number of correctly predicted negative cases;  
FP (False Positives): The number of negative cases incorrectly predicted as positive;FN (False Negatives): The number of positive cases incorrectly predicted as negative. \[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FP}+\text{FN}+\text{ TN}}\times 100 \tag{17}\]  
\[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{18}\]  
\[\text{Sensitivity}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{19}\]  
\[\text{Specificity}=\frac{\text{TN}}{\text{TN}+\text{FP}} \tag{20}\]  
\[\text{F1 Score}=2\times\frac{\text{Precision}\times\text{Sensitivity}}{ \text{Precision}+\text{Sensitivity}} \tag{21}\]  
In experimental studies, statistical evaluations are performed with the Wilcoxon rank sum and Friedman tests. In this study, an independent group is used to determine the accuracy results of 30 run trials for each algorithm. The Wilcoxon rank sum test, also known as the Mann-Whitney U test, is a non-parametric statistical technique employed to assess whether there is a significant difference between two independent samples. Unlike parametric methods, this test does not assume normality in the underlying data distribution, making it particularly advantageous in scenarios involving non-Gaussian or ordinal data. The procedure involves pooling the data from both groups, assigning ranks to the combined dataset, and computing the sum of ranks for each group. The test statistics are derived from these rank sums and are used to determine whether the observed difference between groups is likely to have occurred by chance. By relying on the ordinal properties of the data rather than their absolute values, the Wilcoxon rank sum test offers a robust and distribution-free approach for evaluating group differences, especially when classical parametric assumptions cannot be satisfied [27; 28]. The Friedman test is a widely used non-parametric method designed to evaluate whether there are statistically significant differences among multiple related groups. It is particularly appropriate when the same set of algorithms or treatments is assessed under consistent experimental conditions across different blocks, such as datasets or subjects. Unlike parametric alternatives, it does not require assumptions of normality or equal variances. The test operates by ranking the performance of each method within each block and analyzing the variability of these ranks across all methods. This rank-based approach provides a robust solution for analyzing repeated measures or matched designs, especially when parametric conditions are violated.