# An Intelligent Radomic Approach for Lung Cancer Screening
## 3 Results
### Model Optimization  
For this experiment, 51 (85%) patients of the dataset described in Section 2.1 were randomly selected for the optimization of models. This training set had 8 benign and 43 malignant nodules. The search space for optimizing network architectures given in Table 4 together with their hyperparameters was the following: (1) \(N_{h}\in[6,7,\ldots,16,17]\); (2) optimizer: SGD, Adam, RMSprop; (3) learning rate: 0.01, 0.001, 0.0001; (4) weight initialization: Normal, Xavier, Kaiming, Orthogonal; (5) epochs: 500, 1000, 1500. For each embedding (None, \(N_{i}=24\), Reproducibility, \(N_{i}=14\) and \(t\)-test, \(N_{i}=19\)), we use a grid search to optimize networks and the best configuration was selected according to the criteria given in Section 2.6. Table 6 shows the selected architectures and Table 7 shows the best hyperparameters. Table 8 reports the diagnostic metrics defined in Section 2.6 with top performance highlighted in boldface. For all architectures, the proposed embedding (corresponding to Models 3, 6, 9 and 12) is the one that achieves better metrics with 100% of diagnostic sensitivity and specificity. Among them, the one with highest Slice Diagnostic Index is Model3, which is the one with the simplest architecture. \begin{table}
\begin{tabular}{c c} \hline \hline
**Class** & **Feature** \\ \hline \hline \multirow{2}{*}{\begin{tabular}{c} Fist Order \\ \end{tabular} } & Entropy \\  & TotalEnergy \\  & Uniformity \\ \hline \multirow{4}{*}{\begin{tabular}{c} GLCM \\ \end{tabular} } & Inverse Difference \\  & Inverse Difference Moment \\  & Joint Energy \\  & Joint Entropy \\  & Maximum Probability \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} GLDM \\ \end{tabular} } & Dependence Non Uniformity Normalized \\  & Dependence Variance \\  & Large Dependence Emphasis \\ \hline \multirow{2}{*}{
\begin{tabular}{c} GLRLM \\ \end{tabular} } & Run Length Non Uniformity Normalized \\  & Run Percentage \\ \multicolumn{1}{c}{Short Run Emphasis} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Features from the study [31]. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Radiomic** & **Arch.** & \multicolumn{2}{c}{**Arch.**} & \multirow{2}{*}{**Architecture**} & \multirow{2}{*}{**\# Param.**} \\  & **Embedding** & **Num.** & \multicolumn{2}{c}{**Setting**} & & \\  & & & \(N_{t},N_{h}\) & & \\ \hline Model 1 & None & 1 & 24, 6 & [(24,6),(6,6),(6,2)] & 206 \\ Model 2 & Reproducibility & 1 & 14, 8 & [(14,8),(8,8),(8,2)] & 210 \\ Model 3 & \(t\)-test & 1 & 19, 9 & [(19,9),(9,9),(9,2)] & 290 \\ \hline Model 4 & None & 2 & 24, 9 & [(24,9),(9,9),(9,4),(9,2)] & 365 \\ Model 5 & Reproducibility & 2 & 14, 9 & [(14,9),(9,9),(9,4),(9,2)] & 275 \\ Model 6 & \(t\)-test & 2 & 19, 9 & [(19,9),(9,9),(9,4),(9,2)] & 320 \\ \hline Model 7 & None & 3 & 24, 8 & [(24,8),(8,8),(8,8),(8,4),(4,2)] & 382 \\ Model 8 & Reproducibility & 3 & 14, 9 & [(14,9),(9,9,(9,9),(9,4),(4,2)] & 362 \\ Model 9 & \(t\)-test & 3 & 19, 9 & [(19,9),(9,9),(9,9),(9,4),(4,2)] & 407 \\ \hline Model 10 & None & 4 & 24, 8 & [(24,8),(8,7)(7,6)(6,5),(5,4),(4,2)] & 305 \\ Model 11 & Reproducibility & 4 & 14, 14 & [(14,14),(13,13),(13,12),(12,11), (11,10),(10,2)] & 745 \\ Model 12 & \(t\)-test & 4 & 19, 8 & [(19,8),(8,7),(7,6),(6,5),(5,4),(4,2)] & 270 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Architecture of best models.