## 5 Experimental Evaluations and Results
### Performance Evaluation and Comparison  
For binary deep learning models, the confusion matrix is used to describe the prediction results on labeled test data. There are four possible outcomes of such a test: true-positive (TP), false-positive (FP), true-negative (TN), and false-negative (FN). The true-positive represents the infected cells correctly diagnosed as infected and the true-negative denotes the number of uninfected cells correctly diagnosed as uninfected. The uninfected cells incorrectly diagnosed as infected are considered false-positive, and the infected cells incorrectly diagnosed as uninfected are false-negatives. Different parametric and non-parametric statistical measures are used in performance evaluation, including Specificity, Sensitivity, Precision, Accuracy, F\({}_{1}\) score, Matthews correlation coefficient (MCC), and Cohen's kappa (\(\kappa\)) [75; 76; 77].  
Specificity calculates the proportion of actual negatives out of total negative observations that are predicted by an algorithm. It is also known as the true negative rate and is computed as  
\[Specificity=\frac{TN}{TN+FP} \tag{4}\]  
Sensitivity is the ability of an algorithm to correctly predict the true positives out of total positive observations. It is also known as true positive rate or Recall.  
\[Sensitivity=\frac{TP}{TP+FN} \tag{5}\]  
Precision shows the extent of correctness of the an algorithm in terms of positive results. It is computed as actual positives out of total positive observations.  
\[Precision=\frac{TP}{TP+FP} \tag{6}\]  
The ability of an algorithm to differentiate between healthy and infected subjects flawlessly is called accuracy. In the case of the malaria diagnosis model, if an infected cell image is predicted correctly by the model as infected and vice-versa, then the model has high accuracy.  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{7}\]  
The F\({}_{1}\) score is the weighted harmonic mean of precision and recall measures. It provides an overall accuracy of the model using both positive and negative predictions. It is considered to be a more reliable performance measure than accuracy and precision metrics that can be delusive when the data are highly unbalanced [78; 79]. For balancing the classification model with precision and recall, the F\({}_{1}\) score of the model on test data should be high.  
\[F_{1}\,score=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{8}\]The Matthews correlation coefficient (MCC) evaluates the performance of a binary classification model with a range of \(-1\) to \(+1\). The minimum value \(-1\) indicates a poor classifier while the maximum value \(+1\) indicates a correct classifier. The MCC is regarded as a balanced measure because it considers both positive and negative observations. A recent research [80] showed that MCC is a more informative and realistic measure than other parametric statistical measures. It is computed as:  
\[MCC=\frac{(TP\times TN)-(FP\times FN)}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}} \tag{9}\]  
[PERSON]'s kappa (\(\kappa\)) measures the agreement between total accuracy and random accuracy of a model. Kappa value, computed as Equation (10), ranges from 0 to 1. The lowest value 0 means no agreement and the highest value 1 means complete agreement  
\[\kappa=\frac{p_{o}-p_{e}}{1-p_{e}} \tag{10}\]  
where \(p_{o}\) is the accuracy of the model (Equation (7)) and \(p_{e}\) is the hypothetical probability of chance agreement, computed as  
\[p_{e}=\frac{(TP+FN)(TP+FP)+(FP+TN)(FN+TN)}{\left(TP+TN+FP+FN\right)^{2}}\]  
All these performance metrics are computed for each deep learning architecture and the results are summarized in Table 3. The results reveal that the proposed malaria detection algorithm performs better than the compared deep learning models. The proposed method achieves more than 0.96 accuracy and F1 score, and more than 0.93 score in both MCC and \(\kappa\). The malaria detector based on the VGG19 architecture also achieves appreciative results with an F1 and \(\kappa\) score of 0.9592 and 0.9185, respectively.