# Using 2D CNN with Taguchi Parametric Optimization for Lung Cancer Recognition from CT Images
## 2 Methods
### Taguchi Method  
The Taguchi method is a statistical approach using an orthogonal array (OA), consisting of factors and levels, to classify the results to optimize process parameters [16]. In the Taguchi method, the experimental design using OA tables enables the optimization process. The results are converted to a signal-to-noise (S/N) ratio to determine the combination of control factor levels to improve system stability and reduce quality loss. In this study, considering the factors that were found to be effective on the 2D CNN parameter design, the parameters with eight factors and three levels are listed in Table 1. To reduce the number of experiments and improve the reliability of experiments, the L\({}_{36}\)(211,312) OA was selected for the experimental design, and 36 experimental runs generated by Minitab(r) 19 (Scientific Formosa Inc, Taipei, Taiwan) are given in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Columns** & **Abbreviations** & **Factors** & **Level 1** & **Level 2** & **Level 3** \\ \hline A & C1\_S & conv1\_Stride & 1 & 2 & \\ B & C1\_P & conv1\_padding & 0 & 1 & \\ C & C2\_S & conv2\_Stride & 1 & 2 & \\ D & C2\_P & conv2\_padding & 0 & 1 & \\ E & C1\_KS & conv1\_Kernel size & 3 & 5 & 7 \\ F & C1\_F & conv1\_Filter & 4 & 6 & 12 \\ G & C2\_KS & conv2\_Kernel size & 3 & 5 & 7 \\ H & C2\_F & conv2\_Filter & 8 & 16 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Levels of control factors. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Exp. No** & **C1\_S** & **C1\_P** & **C2\_S** & **C2\_P** & **C1\_KS** & **C1\_F** & **C2\_KS** & **C2\_F** \\  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** \\ \hline
1 & 1 & 0 & 1 & 0 & 3 & 4 & 3 & 8 \\
2 & 1 & 0 & 1 & 0 & 5 & 6 & 5 & 16 \\
3 & 1 & 0 & 1 & 0 & 7 & 12 & 7 & 32 \\
4 & 1 & 0 & 1 & 0 & 3 & 4 & 3 & 8 \\
5 & 1 & 0 & 1 & 0 & 5 & 6 & 5 & 16 \\
6 & 1 & 0 & 1 & 0 & 7 & 12 & 7 & 32 \\
7 & 1 & 0 & 2 & 1 & 3 & 4 & 5 & 32 \\
8 & 1 & 0 & 2 & 1 & 5 & 6 & 7 & 8 \\
9 & 1 & 0 & 2 & 1 & 7 & 12 & 3 & 16 \\
10 & 1 & 1 & 1 & 1 & 3 & 4 & 7 & 16 \\
11 & 1 & 1 & 1 & 1 & 5 & 6 & 3 & 32 \\
12 & 1 & 1 & 1 & 1 & 7 & 12 & 5 & 8 \\
13 & 1 & 1 & 2 & 0 & 3 & 6 & 7 & 8 \\
14 & 1 & 1 & 2 & 0 & 5 & 12 & 3 & 16 \\
15 & 1 & 1 & 2 & 0 &According to the Taguchi optimization and the S/N ratio to quantify the output quality, the S/N ratio was selected as the optimization criterion. The best experimental results obtained by the calculation of average S/N ratio for each factor and the optimal level of the process parameters were indicated by the level with the largest S/N ratio. We analyzed the S/N ratio using three different performance characteristics: larger-is-better, nominal-is-better, and smaller-is-better [17]. In this study, 'larger-is-better' performance characteristics were preferred. \[\text{S/N}=-10\log\!\left(1/n\sum\
olimits_{i=1}^{n}\frac{1}{y_{i}^{2}}\right) \tag{1}\]  
where \(n\) is the total number of replications of per test run and \(y_{i}\) is the accuracy of the 2D CNN in the replication experiment for lung cancer recognition \(i\) executed under the same experimental conditions per test run. We used analysis of variance (ANOVA) on the experimental data from the Taguchi method to determine the significance of process parameters statistically affecting extraction and the measurements [18].