# Applying ANN and TM to Build a Prediction Model for the Site Selection of a Convenience Store
## 4 Case Study
### TM Analytical Results  
In this study, the \"bigger-the-best\" characteristic was employed, as the MD between the normal and abnormal groups was the \"larger-the-better\" in order to be significantly distinguished. For each test, followed by the factor setting in the orthogonal array (as in Table 6), an S/N ratio was obtained (listed in Table 8). The factorial effect of each factor was hence calculated and shown in Table 9. A total of three folders were created, and three sets of data were used to calculate the S/N (signal-to-noise ratio) value. The root-mean-square error (RMSE) of the results of each experiment was calculated using the RMSE of the test set; ten-folder cross validation for the ANN was then used repeatedly to calculate the S/N. In total, 16 experiments were conducted, as shown in Table 8, to respectively record the errors of the simulation results for the BPN network. The RMSE of the test data was used to obtain the average value of the error, and the S/N ratio in each experiment was obtained based on the STB characteristic (see Table 8). According to Table 8, the highest S/N ratio (23.6575) was observed in the third experiment and involved factors _A1_, _B3_, _C3_, _D3_, and _E3_. However, from the S/N ratio factor response list (Table 9), the transfer function was mostly affected by effect and rank factors and levels, followed by the learning rate. As shown in Table 9, the optimal parameter combination consisted of _A3_, _B2_, _C3_, _D2_, and _E3_. According to the combination of _A3_, _B2_, _C3_, _D2_, and _E3_, we split the training network data in Table 5 into three sets in the order 1-25, 26-50, 51-75, and carried out the optimal combination of BPN three times. The S/N ratio was 16.2946 and the 95% confidence interval was calculated as 14.253997-18.415372, which was confirmed to be within the confidence interval. The data are shown in Table 10. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Level**Factor** & **Neural Network Design (_A_)** & **Learning** & **Learning** & **Momentum** & **Transfer** \\  & & **Iteration (_B_)** & **Rate (_C_)** & **Term (_D_)** & **Function (_E_)** \\ \hline Level 1 & Five nodes, one hidden layer & 1000 & 0.1 & 0.1 & Sigmoid \\ Level 2 & Ten nodes, one hidden layer & 3000 & 0.4 & 0.4 & Gaussian \\  & Five nodes in the first hidden layer; & & & & Hyperbolic \\  & three nodes in the second hidden layer & & & & Tangent \\  & Ten nodes in the first hidden layer; & & & & Hyperbolic \\  & three nodes in the second hidden layer & & & & Secant \\ \hline \end{tabular}
\end{table} 
Table 7: Distribution list of the levels of factors of the neural network. Therefore, to verify the combination of the optimal parameters, we utilized the two combinations to obtain the S/N ratio (see Table 11). As shown in Table 11, we found that the combination of \(A3\), \(B2\), \(C3\), \(D2\), and \(E3\) had a larger S/N ratio. Therefore, the optimal parameter combination consisted of \(A3\), \(B2\), \(C3\), \(D2\), and \(E3\), respectively, including the neural network design (five nodes in the first hidden layer and three nodes in the second hidden layer), learning iterations (3000), learning rate (0.7), momentum term (0.4), and transfer function (hyperbolic tangent), respectively. Based on the above optimal parameter design result of the BPN, the network architecture was, therefore, designed (see Figure 2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment** & **Fold 1** & **Fold 2** & **Fold 3** & **Average** & **St. Dev** & **S/N** \\ \hline Combination of \(A3\):\(B2\):\(C3\):\(D2\):\(E3\) & 0.15075 & 0.197292 & 0.236022 & 0.194688 & 0.042696 & 19.3049 \\ Combination of \(A1\):\(B3\):\(C3\):\(D3\):\(E3\) & 0.257151 & 0.242185 & 0.203655 & 0.23433 & 0.027599 & 17.7922 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: S/N ratio of reverification.