# FACES: A Deep-Learning-Based Parametric Model to Improve Rosacea Diagnoses
## 3 Materials and Methods
### Analysis of Four Performance Parameters  
The accuracy, sensitivity, specificity, and precision of each model were calculated based on the confusion matrix containing true negative (TN), false negative (FN), true positive (TP), and false positive (FP) (Figure 2 and Table 3) to evaluate performance. Figure 4: Confusion matrix and accuracy with respect to \(\alpha\) for the quadratic function. Figure 3: Confusion matrix and accuracy with respect to \(\alpha\) for the linear function. In particular, the orange and blue colors denote true negative (TN) and true positive (TP), respectively. For the quadratic function, there are two stagnant areas showing constant TN, FN, TP, and FP: 0.1-0.3 and 0.5-0.7 (Figure 4). The best accuracy (92.27%) value is found to be at 0.8 of \(\alpha\), where 10% (11/110) of resacea and 5.45% (6/110) of normal skin are misclassified as normal skin and rosacea, respectively. Overall, TN and FN tend to increase more gradually with the increasing evaluation factor compared to the linear function, while TP and FP tend to decrease. For the cubic function, there are two large stagnant regions: the first region ranging from 0.1 to 0.4 and the second region ranging from 0.5 to 0.9 (Figure 5). The confusion matrix showed constant accuracy for each of the first and second stagnant areas at 89.09% and 92.27%, respectively. It should be noted that the TP of the first region is higher than that of the second region, while TN is the opposite, showing a lower value in the first region. Figure 5: Confusion matrix and accuracy with respect to \(\alpha\) for the cubic function. Figure 6: Confusion matrix and accuracy with respect to \(\alpha\) for the biquadratic function. At the region of highest accuracy (91.82%), 10% (11/110) of rosacea and 6.36% (7/110) of normal skin are misinterpreted as normal skin and rosacea, respectively. For the biquadratic function, a single \(\alpha\) (0.5) shows the best accuracy (92.27%), while two stagnant regions (0.1-0.4 and 0.6-0.9) reveal accuracy values at 89.09% and 91.82%, respectively (Figure 6). At the confusion matrix of highest accuracy (92.27%, \(\alpha\) = 0.5), 9.09% (10/110) of rosacea and 5.45% (6/110) of normal skin are misinterpreted as normal skin and rosacea, respectively. The confusion matrix created by the majority rule yields 90.45% accuracy as well as TN (106), which is the second largest, following ResNet-101 (91.36% for accuracy and 107 for TN) (Figure 7). In addition, in the majority rule, 15.45% (17/110) of rosacea and 3.64% (4/110) of normal skin are misinterpreted as normal skin and rosacea, respectively. On the basis of the results from the confusion matrices, accuracy is shown as a function of \(\alpha\) for each function. The results show that there is a significant impact of the evaluation factor on the accuracy, but their distribution depends highly on the degree of function (Figure 8a). To be more specific, for the linear function (n = 1), accuracy tends to increase up to 0.4 of \(\alpha\) continually but decreases after that. For the quadratic, cubic, and biquadratic functions (n = 2, 3, and 4), the accuracy drastically increases to 0.3 or 0.4 of \(\alpha\) and remains almost constant after 0.5 of \(\alpha\). The average accuracy values are 0.853, 0.907, 0.906, and 0.906 for the linear, quadratic, cubic, and biquadratic functions, respectively. The highest accuracy is 92.27% (\(\alpha\) = 0.4), 92.27% (\(\alpha\) = 0.8), 91.82% (\(\alpha\) \(\geq\) 0.5), and 92.27% (\(\alpha\) = 0.5) for the linear, quadratic, cubic, and biquadratic functions, respectively. When both the highest and average accuracy are considered, the quadratic function can be selected as the best performing function. Noticeably, all four performance parameters driven by FACES are at least greater than or equal to 0.9, while those by other models are not. We compared the performance of the FACES with that of individual CNN-based models and the majority rule.