# A Machine Learning Approach for Breast Cancer Risk Prediction in Digital Mammography +
## 3 Results
### Neural Networks  
Since machine learning does not provide good results in multiclass classification, it was thought to apply a neural network to the extracted features. First of all, the comparison between two structures was evaluated: a simple structure composed of only two dense layers and a more complex structure composed of many dense layers. For a network of only two dense layers and 500 nodes, the overfitting was reached after about 50 epochs and reached a maximum accuracy around epoch 30. Instead, for a network of six dense layers, after 60 epochs, the overfitting was not yet reached, but the epoch that performed best was around iteration 55. Based on the results obtained, it makes no sense to prefer a network with many layers; therefore, we tried to reduce the number of nodes of a structure made of only two layers. In particular, for a number of nodes equal to 250 for a single-layer network, it can be seen that after epoch 50, the overfitting on the data started testing, and that before this iteration, the maximum accuracy level was reached. A comparison of the overall accuracies of two methods with the same number of layers but a different number of nodes is shown in Table 4. The values of specificity, sensitivity, and accuracy of the two methods for the different classes is shown in detail in Table 5. Based on the results obtained, it can be concluded that better accuracy is achieved for a model with only two layers with 500 and 4 nodes respectively.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Algorithm** & **Accuracy (95\% CI)** & **Kappa** \\ \hline \multirow{6}{*}{**SMOTE**} & **SVM** & 0.43 (0.25–0.62) & 0.27 \\ \cline{2-4}  & **Rpart tree** & 0.33 (0.17–0.53) & 0.11 \\ \cline{2-4}  & **Nnet** & 0.50 (0.31–0.69) & 0.32 \\ \cline{2-4}  & **LDA** & 0.63 (0.44–0.80) & 0.49 \\ \cline{2-4}  & **RF** & 0.50 (0.31–0.69) & 0.33 \\ \hline \multirow{6}{*}{**ROSE**} & **SVM** & 0.37 (0.20–0.56) & 0.13 \\ \cline{2-4}  & **Rpart tree** & 0.50 (0.31–0.69) & 0.23 \\ \cline{2-4}  & **Nnet** & 0.57 (0.37–0.54) & 0.36 \\ \cline{2-4}  & **LDA** & 0.47 (0.28–0.66) & 0.29 \\ \cline{2-4}  & **RF** & 0.53 (0.34–0.72) & 0.25 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Overall classification evaluation metrics among four density classes applying SMOTE and ROSE oversampling.  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & **Algorithm** & \multicolumn{4}{c}{**Sensitivity**} & \multicolumn{4}{c}{**Specificity**} \\ \cline{3-10}  & & **A** & **B** & **C** & **D** & **A** & **B** & **C** & **D** \\ \hline \multirow{6}{*}{**SMOTE**} & **SVM** & 1.00 & 0.27 & 0.50 & 0.50 & 0.85 & 0.93 & 0.67 & 0.83 \\ \cline{2-10}  & **Rpart** & 0.33 & 0.20 & 0.50 & 0.50 & 0.85 & 0.73 & 0.70 & 0.79 \\ \cline{2-10}  & **Nnet** & 0.67 & 0.40 & 0.67 & 0.50 & 0.92 & 0.87 & 0.79 & 0.75 \\ \cline{2-10}  & **LDA** & 1.00 & 0.53 & 0.67 & 0.67 & 0.96 & 0.93 & 0.75 & 0.87 \\ \cline{2-10}  & **RF** & 1.00 & 0.33 & 0.67 & 0.50 & 0.89 & 0.87 & 0.75 & 0.83 \\ \hline \multirow{6}{*}{**ROSE**} & **SVM** & 0.33 & 0.50 & 0.33 & 0.33 & 0.85 & 0.73 & 0.75 & 0.79 \\ \cline{2-10}  & **Rpart** & 0.00 & 0.67 & 0.33 & 0.50 & 1.00 & 0.67 & 0.79 & 0.79 \\ \cline{2-10}  & **Nnet** & 0.33 & 0.67 & 0.50 & 0.50 & 0.92 & 0.80 & 0.83 & 0.83 \\ \cline{2-10}  & **LDA** & 0.67 & 0.33 & 0.83 & 0.33 & 0.85 & 0.87 & 0.67 & 0.92 \\ \cline{2-10}  & **RF** & 0.00 & 0.73 & 0.33 & 0.50 & 0.96 & 0.53 & 0.92 & 0.83 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Classification evaluation metrics relating individual four density classes applying SMOTE and ROSE oversampling.