# Automatic Breast Tumor Screening of Mammographic Images with Optimal Convolutional Neural Network
## 3 Experimental Results
### Multilayer CNN-Based Classifier Testing and Validation
The testing result of the abnormal pattern yields TP = 178 and FP = 6, while that of the normal pattern yields TN = 269 and FN = 13; these values can be used as variables in Table 2 to compute the four evaluation indices of the classifier. In this study, precision (%) = 96.74%, recall (%) = 93.19%, F1 score = 0.9493, and accuracy (%) = 95.92%. Precision (%) is the standard for predicting TP, and recall (%) is the true accuracy of TP. Both indicators may be greater than 80%. Recall (%) is also called the positive predictive value (PPV), which is the so-called TP in the detection case. The general PPV index is larger than 80%, which means the proposed classifier has promising predictive performance. The F1 score fuses the indicators of precision (%) and recall (%), and F1 score larger than 0.9000 generally indicates a good classification model. Youden's index (YI) is a fusion evaluation index of sensitivity (Sens) and specificity (Spec) [54], which reflects the performance of the classifier for detecting abnormalities. The larger the YI, the better the performance of the classifier for detection and validation and the greater its authenticity. The testing results show YI = 91.01% (Sens = 93.19%, Spec = 97.82%). Given that all evaluation indicators considered in this work exceed 90%, Model #1 indeed has an architecture that supports good classification accuracy and performance, as seen in the tenfold cross-validation (\(K_{f}\) = 10) for averages of precision (%), recall (%), accuracy (%), and F1 score in Table 8. Hence, we suggest Model #1 to carry out a multilayer CNN-based classifier for automatic breast tumor screening. In addition, as seen in Table 9, we also set 4, 8, 16, and 32 Kernel convolutional windows and 4, 8, 16, and 32 maximum pooling windows in second and third convolutional-pooling layers, respectively, for establishing four models (Models #1-1 to #1-4). With the tenfold cross-validation, trained feature patterns are randomly selected, the average training CPU time of Models #1-1 and #1-2 is less than Model #1-3 with 16 Kernel convolutional windows and 16 maximum pooling windows. It can be seen that Model #1-4 comprises 32 Kernel convolutional windows and 32 maximum pooling windows will increase the average training CPU time and complex computational processes at each cross-validation. With the tenfold cross-validation, untrained feature patterns are also randomly selected, as seen in Tables 10-13, the proposed architecture of multilayer classifier (Model #1-3) has promising classification accuracy and performance in terms of average precision (%), average recall (%), average accuracy (%), and average F1 score. Additionally, the proposed CNN architecture with different convolutional windows in the first convolutional layer, including fractional-order, Sobel (first-order), and Histeq convolutional windows, is used to test the performance of breast tumor screening model. Through the tenfold cross-validation, the CNN classifier with a fractional-order convolutional window in the first convolutional layer, as Model #1 in Table 14, has better classification accuracy (larger than 95%) than Model #2 (larger than 85%) and Model #3 (larger than 90%). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**ModelTest Fold** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **Average Accuracy** \\ \hline
1 & 96.14 & 97.43 & 98.07 & 97.96 & 98.93 & 98.07 & 96.35 & 95.60 & 96.89 & 98.28 & 97.37 \\ \hline
2 & 97.42 & 98.93 & 98.28 & 97.64 & 99.14 & 97.21 & 97.85 & 98.28 & 99.14 & 97.42 & 98.13 \\ \hline
3 & 96.14 & 97.64 & 98.50 & 98.71 & 99.14 & 97.85 & 97.64 & 95.06 & 97.21 & 99.57 & 97.75 \\ \hline
4 & 98.93 & 98.71 & 96.14 & 97.32 & 99.36 & 98.18 & 91.74 & 90.34 & 97.64 & 90.02 & 95.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Cross-validation results for different multilayer CNN models (\(K_{f}\) = 10).