# Optimal Histopathological Classification Factors for Deep Learning-Based Breast Cancer Prediction
## 5 Results
### Training Loss and Validation Loss
Figure 10 shows that the model achieves the highest accuracy when using 200x magnification, followed by a 400x magnification factor. The model performs worse when employing 100x and 40x magnification factors. This conclusion shows that the model learns more effectively from 200x and 400x magnification factors than from 100x and 40x. Precision, recall, and F1-scare metrics are used to further emphasize the differences in prediction performance among the four magnification factors. The model performs better using 200x and 400x magnification factors, as shown in precision, recall, and F-score measurements, as shown in Figure 11. Noticeably, 200x slightly outperforms 400x in all of the used performance metrics. Furthermore, it is crucial to note that the model performs better at predicting cancerous cells than healthy cells. Figure 12 displays the weighted average accuracy difference among the various magnification factors. The model achieves high accuracy by using a 200x magnification factor followed by a 400x magnification factor. These findings imply that the model accomplishes a higher learning rate from 200x and 400x magnifications factors. Figure 11: _Cont._  
Figure 10: Benign or malignant prediction accuracy for the various magnification factors. The softmax function at the CNNs' output layer predicts a class (i.e., benign or malignant) with a specified probability value. Table 3, for example, displays the prediction probability values for samples chosen at random from the testing pool. For instance, rows 3, 4, and 6 are predicted correctly as cancerous samples with a high probability, i.e., 0.8, 0.94, and 0.99, respectively. Similarly, the sample in row 9 is correctly predicted but with a probability of 0.53. The samples in rows 3, 4, and 6 have higher prediction probability values than those in row 9. In other words, the model is more certain about the former than the latter. The model's prediction probabilities at various magnification factors are highlighted (via using Kernel Density Estimator (KDE) ) to assess the model performance difference at various magnification factors. KDE is a method to estimate the Probability Density Function (PDF) from a finite dataset. KDE is a non-parametric method used ( in this study) to display the prediction probability across all magnification factors. KDE is similar to histograms but utilizes other properties such as smoothness or continuity by using the right kernel. Figure 13 shows the KDE of the four magnification factors. Figure 11: Accuracy difference using precision, recall, and F1-score. (**A**) Precision. (**B**) Recall. (**C**) F1-score. Figure 12: Weighted average accuracy difference. The gray area in the figures represents the area where there is a confusion, benign tumors are mistaken for malignant tumors or vice versa, resulting in inaccurate predictions. Those samples on the left of the border line are predicted non-cancerous cells while they are cancerous; those samples on the right of the border line are denoted as cancerous cells while they are not. Comparing the confusion areas of the different magnifcation factors (displayed in Figure 13A-D, the magnification factor of 200x has a minor area followed by a 400x magnification factor. It is evident that the prediction probability of cancerous cells is higher than those of non-cancerous cells; this is shown in all magnification factors of