## 5 Bayesian Regularized Feed-Forward Neural Network (BR-FNN)  
We used the Bayesian regularization [36] proposed by [PERSON] in 1992 for training the NN. This regularization technique minimizes the linear combination of squared errors and weights so that, at the end of the training the resulting network has good generalization qualities. Later in 1997 [PERSON] and [PERSON] [37] proposed optimization using the Levenberg-Marquardt (LM) algorithm in the BR-FNN to reduce computational overhead. It reduces the linear arrangement of squared errors and weights and finally produces a good, generalized network after iterative training. The Bayesian regularization takes place within the Levenberg-Marquardt algorithm. This can be summarized using the following equations. For training the sets of the form \(\{x_{1}\,t_{1}\ \}\), \(\{x_{2}\,t_{2}\ \}\ldots\ \{x_{n}\,t_{n}\ \}\), where \(\{x_{i}\,t_{i}\ \}\) represents the input value and the corresponding target for the \(i\)th term. The sum of squared error during training is represented by:  
\[E_{D}=\sum_{i}^{n}(t_{i}-y_{i})^{2} \tag{4}\]  
Here, \(t_{i}\) are the target values and \(y_{i}\) is the predicted response by the neural network during the process of training for \(n\) number of training inputs. The objective function for Bayesian optimization and regulation exhibits a standard form as:  
\[F(w)=\beta E_{D}+\alpha E_{W} \tag{5}\]  
Here, \(E_{W}\) is the sum of squares of the network weights and the \(E_{D}\) error calculated from (4). Optimization parameters \(\alpha\) and \(\beta\) are calculated as in Equations (6) and (7), respectively. \[\alpha=\frac{\gamma}{2E_{W}(W)} \tag{6}\]  
\[\beta=\frac{n-\gamma}{2E_{D}(W)} \tag{7}\]  
Figure 8: Data processing result before and after Gaussian-weighted smoothing average filter, window size, shown for 14 th out of 18 features from ROI_CL. Blue colored curve is the raw data whereas orange and red curve represents the smoothened data for \(w=9\) and \(w=5\) respectively. Initially, \(\alpha=0\) and \(\beta=1\) such that \(F(w)=E_{D}\), where \(\gamma\) is the effective number of parameters, calculated using the Gauss-Newton approximation to the Hessian matrix available in the LM training algorithm until final convergence is met [37; 38]. We first randomly initialized a 2-layer feed-forward NN with the inputs connected to the first hidden layers and the second layer is the output layers with only two output values for binary classification. Here, the Nguyen-Widrow [39] method is used to initialize the weights and bias values for each hidden layer so that the active regions of the layer's neurons are distributed almost evenly over the input space. Hyperbolic tangent sigmoid [40] is used as an activation function in hidden layers to generate squashed outputs between [\(-1\) 1] for input vectors whereas in the output layer it is a linear purelin function. Random partition of training and testing (7:3) was performed manually on the whole set of features so that only the partitioned training set participates in training BR-NN, while the test set remains untouched. Later once the BR-NN model is trained, the test set is fed into the NN to find out the testing accuracy. To obtain the optimal number of hidden layers, the network was trained for a different number of hidden layers starting from 1 to 20, initialized each time randomly. The classification performance parameter was tested iteratively ten times for each number of hidden layers such that the average performance is calculated each time; the resulting graph is shown in Figure 9. Here, training will yield us, 10 independent models, for each hidden layer i.e., when tested for up to 20 hidden layers in total 10 \(\times\) 20 = 200 models were developed. Out of which every 10 models with the same number of hidden layers were passed iteratively for untouched test features, the average of ten iterations is then reported. Later the best performance was observed for 17 hidden layers. Table 10 in the appendix shows the result of each iteration.