# Pre-Training Autoencoder for Lung Nodule Malignancy Assessment Using CT Images
## 3 Results
### Malignancy Classification  
The classifier training convergence was achieved after 200 iterations. After this first training stage, fine-tuning was applied by unfreezing the encoder's last convolutional layer; finally, after the second training convergence, gradients were updated for the last two convolutional layers for a final training. This strategy obtained the best results by preventing the model to overfit, which occurred when it was tried to add one more convolutional layer for retraining.  
Mean values for each performance metric considered are presented in Table 4. By taking advantage of cross-validation data, the decision threshold was tuned for F-score maximization by the recall. This threshold optimization was employed by evaluating the precision-recall trade-off which, given the context, represents the cost of a missing malignant nodule (false negative) over a false suspicious of a benign tumor (false positive). Thus, as a missing malignant tumor should be a more penalized error, recall was maximized over precision in this classification task. With the TL approach, the mean value for  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Hyper-Parameter** & **Value** \\ \hline
**Learning Rate** & 0.001 \\
**Batch-size** & 8 \\
**Momentum** & 0.9 \\
**Weight decay** & 0.0001 \\
**Dropout** & 0.5 \\
**Hidden Layers** & 1 \\
**Hidden Neurons** & 64 \\
**Optimizer** & SGD 1 \\ \hline \hline \end{tabular}  
* Stochastic Gradient Descent.  
\end{table}
Table 3: Hyper-parameters values that achieved best performance.  
the classification threshold was 0.413 \(\pm\) 0.101, which clearly illustrates the necessity of choosing a value under 0.5, the default threshold value, to allow to increase the confidence in non-malignant predictions.  
Figure 4 shows the ROC curve for the binary classification between benign and malignant cases for our proposed method using the TL approach, with a maximum mean AUC of 0.936 \(\pm\) 0.009. The small gray shading in the figure shows the consistency of the results and the independence of the performance with the subsets selected for training and testing, given the small variation on the AUC obtained.  
To better understand the relationship between the success of a prediction and the output reconstruction of the correspondent nodule, Figure 5 shows one example for each case. Well and wrongly classified examples are depicted, alongside with the correspondent MSE value obtained by analysis of the CAE output. The reported MSE mean value for the successfully classified examples was 0.00162 \(\pm\) 0.00088, in contrast with the value 0.00337 \(\pm\) 0.00249, correspondent to wrong predictions. It was possible to verify that, in general, a correct prediction was associated with a reconstructed image with a lower pixel error, which might demonstrate the impact of the low-level features learning in the detection of more relevant patterns for classification.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Performance Metrics (Mean \(\pm\) Standard Deviation)**} \\ \hline
**Training Method** & **AUC** & **Precision** & **Recall** & **F-Score** \\ \hline Transfer Learning & 0.936 \(\pm\) 0.009 & 0.794 \(\pm\) 0.026 & 0.848 \(\pm\) 0.035 & 0.817 \(\pm\) 0.020 \\ \hline Trained from scratch & 0.928 \(\pm\) 0.027 & 0.842 \(\pm\) 0.035 & 0.789 \(\pm\) 0.069 & 0.808 \(\pm\) 0.022 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Lung nodule malignancy classification results.  
Figure 4: Averaged ROC curve for lung nodule malignancy classification using the transfer learning approach. The ROC curve is computed for each iteration, the arithmetic average is then calculated and represented by the blue line with a standard deviation represented by the gray shading area. The red dashed-line represents an at-chance classifier ROC curve.