## 4 Application
### Performance: Proposed Models and AUC Values
Therefore, the total number of parameters for the network architecture \(3721\times 2=7442\) parameters. The test set performance, measured by the AUC, is 98.5% for Model 1. **Model 2. ** This model builds upon the architecture of Model 1. The only difference is that there is one hidden layer with 64 units (or neurons). We fully connect each variable in the 1 st Conv. Layer with each neuron in the hidden layer; afterward, we fully connect the hidden layer with the output layer. This means that from the 1 st Conv. Layer to the hidden layer, there are \(3721\times 64=238,144\) parameters. From the hidden layer of 64 neurons to output layer with two units, there are \(64\times 2=128\) parameters. This means that, in total, there are \(238,144+128=238,272\) parameters. The performance of this architecture is 99.7%. The design of this one hidden layer with 64 units reduced the error rate from 1.5% in Model 1 to 0.3% in Model 2, which is an 80% error reduction. **Model 3. ** This model has two interaction-based convolutional layers. The 1 st Conv. Layer uses the set of parameters in \(\triangle\) and the 2 nd Conv. Layer uses the set of parameters in \(\square\). From the 1 st Conv. Layer in Model 1, we are left with \(61\times 61=3721\) variables. Using the parameters in \(\square\), we have new matrix with size \(\lfloor(61-1-2+1)/2+1\rfloor\times\lfloor(61-1-2+1)/2+1\rfloor=30\times 30=900\) variables. These 900 variables can be the input layer and we can directly pass these 900 variables into the output layer for making predictions. In other words, the output layer has \(900\times 2=1800\) parameters. The test set AUC value is 97.0%. **Model 4. ** This model is the deepest amongst all six models. Model 4 has two interaction-based convolutional Llyers and one hidden layer. From the 2 nd Conv. Layer in Model 3, we are left with 900 variables. The architecture has one hidden layer with 64 units. The 900 variables are fully connected with the hidden layer, which creates \(900\times 64=57,600\) variables. From the hidden layer with 64 units to the output layer with 2 units, there are \(64\times 2=128\) parameters. In total, there are \(57,600+128=57,728\) parameters. The prediction performance is 99.6% on the test set. **Model 5. ** Both Models 5 and 6 have wider convolutional layers instead of aiming for depth. Model 5 has a concatenated of features from both convolutional layers. This means the architecture takes the 7442 variables from the 1 st Conv. Layer and 900 variables from the 2 nd Conv. Layer from the previous models together as one large convolutional layer. In other words, Model 5 has a 1 st Conv. Layer with \(3721+900=4621\) variables. These 4621 variables can be directly used to be fed into the output layer with two units. In total, this architecture creates \(4621\times 2=9242\) parameters with a test set performance of 98.3%. **Model 6. ** The last model, Model 6, is just as wide as the previous Model 5. Model 6 also has a first convolutional layer that is a concatenation of features. It has \(3721+900=4621\) \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Proposed Work** & **1 st Conv.** & **2 nd Conv.** & **Hidden** & **Output Layer** & **Num. of Param.** & **AUC** \\ \hline Model 1 & \(\triangle\) & None & None & 2 & 7442 & 98.5\% \\ Model 2 & \(\triangle\) & None & IL (64 units) & 2 & 238,272 & 99.7\% \\ Model 3 & \(\triangle\) & \(\square\) & None & 2 & 1800 & 97.0\% \\ Model 4 & \(\triangle\) & \(\square\) & 1L (64 units) & 2 & 57,728 & 99.6\% \\ Model 5 & \(\triangle+\square\) & None & None & 2 & 9242 & 98.3\% \\ Model 6 & \(\triangle+\square\) & None & 1L (64 units) & 2 & 295,872 & 99.8\% \\ \hline Remark & \(\triangle\): & & & & & \\ Starting Point = 6 & Starting Point = 1 & & & & \\ Window Size: 2 by 2 & Window Size: 2 by 2 & & & & \\ Stride = 2 & Stride = 2 & & & & \\ Output: 61 by 61 & Output: 30 by 30 & & & & \\ \hline \hline \end{tabular}
\end{table}