# Nodule Detection with Convolutional Neural Network Using Apache Spark and GPU Frameworks
## 3 Our Proposed Methodology
### Pre-Processing
We evaluated our accuracy percentage based on the number of epochs. Similarly, for the ROC curve, training accuracy, validation accuracy, training loss, and validation loss number of epochs are taken as x-axis for better percentage comparison. The performance is improved by choosing the best hyperparameters, such as the number of nodes, size, and the number of the filter from cross-validation results. Classification diagnostic accuracy, sensitivity, specificity, and area under the receiver operator characteristic curve (AUC) of the model performance is compared with various neural network models, such as Convolutional Auto Encoder Deep Learning Framework (CAE-DLF), Convolutional Neural Network (CNN), and Deep Belief Network (DBN). The accuracy of the diagnostic exam in the medical field is determined by sensitivity and specificity. The former shows the number of patients with the disease, and the following measures the false positive rate, which is misdiagnosis. The classification is analyzed using the receiver operator characteristic curve and area under the receiver operator character curve [40]. \[Correntropy_{\sigma}(A,B)=E[k_{\sigma}(A-B)], \tag{2}\]1

\[Correntropy_{\sigma}(A,B)=E[k_{\sigma}(A-B)], \tag{2}\]2\[Correntropy_{\sigma}(A,B)=E[k_{\sigma}(A-B)], \tag{2}\]3

As mentioned earlier, we used four-fold cross-validation to choose optimal hyperparameters for our NG-CNN model. We ensured that training and testing datasets are from different patients to get an actual accuracy percentage. CNN, NG-CNN, CAE-DLF, and DBN are trained and tested with the same dataset. Figure 6 shows the validation and training loss for our proposed NG-CNN model in the top-left graph. The validation loss is 0.7256, which is higher than the training loss of 0.5148. The values are achieved after applying dropout to reach the minimum difference between training and validation loss. The bottom figures, Figure 6c,d, depict our proposed model's test accuracy and ROC curve with other deep models. The test accuracy for our model is 0.9452. This accuracy percentage is more significant than the convolutional neural network without any noise removal step. The test accuracy percentages for our proposed model NG-CNN and other comparative methods are given in \[Correntropy_{\sigma}(A,B)=E[k_{\sigma}(A-B)], \tag{2}\]4 Table 2 shows a comparison of the precision of NG-CNN with various neural network algorithms. Thus, it proves that medical images with visual noise reduction aim at better feature learning and accurate prediction of the lung cancer nodules. We compared the ROC curve for three deep neural models with our proposed model in Figure 6d. The x-axis indicates 1-Specificity, and the Y-axis indicates sensitivity. The figure represents the average graph of ROC achieved by four-fold cross-validation. Our proposed method, NG-CNN, has an AUC of 0.896, which performs better than other neural network models. Since higher AUC indicates maximum performance on average, NG-CNN gives less validation loss. Table 3 compares the sensitivity and false-positive rate with other models. \begin{table}
\begin{tabular}{c c c c c} \hline
**ep** & **NG-CNN** & **CAE-DLF** & **DBN** & **CNN** \\ \hline
50 & 0.5879 & 0.5124 & 0.5469 & 0.6789 \\
100 & 0.78632 & 0.6645 & 0.6214 & 0.7356 \\
150 & 0.8021 & 0.6987 & 0.6987 & 0.78541 \\
200 & 0.8432 & 0.7421 & 0.7548 & 0.8632 \\
250 & 0.9584 & 0.8952 & 0.79215 & 0.9452 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of classification test accuracy of NG-CNN with existing methods. \begin{table}
\begin{tabular}{c c c} \hline
**Methods** & **Sensitivity** & **Specificity** \\ \hline NG-CNN & 91.3974 & 90.325 \\ CAE-DLF & 84.8537 & 79.215 \\ DBN & 88.6088 & 75.215 \\ CNN & 89.2759 & 89.214 \\
[41] & 71.0 & 60.0 \\
[42] & 80.0 & 75.0 \\
[43] & 90.0 & 88.0 \\
[44] & 76.0 & 73.0 \\ \hline \end{tabular}
\end{table} 
Table 3: Performance summary of NG-CNN with existing methods. ### Performance Analysis

For uniform platform comparison, we carried out the experiments in Ubuntu 14.04 Linux OS, Apache Spark v2.3.0, and Python v3.