## 3 Experimental Results
### MLP Architecture Selection
The main reason is the stochastic nature of the training process of an artificial neural network, which is introduced by the random initialization of the weights for each neuron, and the sampling process used to form the validation and training subsets. For the training stage of each possible architecture of the MLP, the back-propagation with the Levenberg-Marquardt optimization [22] are employed for the weights fitting, using the training set of 100 angiograms. After the training stage, the generalization performance of the artificial neural network is evaluated using the test set of 30 angiograms, and the area under the ROC curve as metric. The ROC analysis is used since the final detection response of the proposed method is provided in an unbounded continuous scale, which can be considered as a multiple level classifier for the pixels of the coronary angiograms. To illustrate the stochastic behavior of the generalization performance of the tested MLP architectures, Figure 5 presents the distribution of the performance achieved using 30 trials by each artificial neural network configuration. In addition, the Shapiro-Wilk test is applied to determine whether the behavior of the generalization performance of each tested configuration follows a normal distribution. The results of the Shapiro-Wilk test are presented in Table 1, where the analysis suggests that normality cannot be assumed for all MLP configurations with a significance level of 5%. Consequently, a non-parametric comparison approach is required to select the most appropriate MLP architecture. Figure 5: Distribution of the generalization performance of each MLP configuration, measured in terms of the area under the ROC curve obtained using the testing set of 30 images. \begin{table}
\begin{tabular}{l|l l l l l l l l l l l l} \hline  & [-,1] & [-,2] & [-,3] & [-,4] & [-,5] & [-,6] & [-,7] & [-,8] & [-,9] & [-,10] \\ \hline
[1,-] & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **0.0003** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** \\
[2,-] & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** \\
[3,-] & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** \\
[4,-] & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** \\
[5,-] & 0.1264 & **0.0175** & **<0.0001** & **<0.0001** & **<0.0005** & **<0.0305** & **<0.0002** & **<0.0001** & **<0.0001** & **<0.0001** \\
[6,-] & **0.0456** & **0.2161** & **0.3827** & **<0.0001** & **<0.0001** & **<0.0004** & **<0.0147** & **<0.0001** & **<0.0016** & **<0.0002** \\
[7,-] & 0.6347 & **<0.0001** & **0.1427** & **<0.0001** & **<0.0001** & **<0.0005** & **<0.0004** & **<0.0001** & **<0.0001** & **<0.0002** \\
[8,-] & 0.2948 & **0.0499** & **<0.0001** & **<0.0001** & **<0.0002** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** \\
[9,-] & 0.3329 & **<0.0001** & **0.0020** & **0.0011** & **0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0002** \\
[10,-] & 0.0643 & **0.0005** & **0.0699** & **0.012** & **<0.0001** & **0.0001** & **<0.0001** & **<0.0001** & **<0.0001** & **<0.0004** \\ \hline \end{tabular}
\end{table} 
Table 1: P-values of the Shapiro-Wilk test to determine normality distribution of the generalization performance of each MLP configuration, using the test set of 30 images. The configurations are presented as [\(i\), -] for configurations with \(i\) neurons in the first hidden layer, and [\(\cdot\),\(j\)] for configurations with \(j\) neurons in the second hidden layer. In literature, the Wilcoxon-Mann-Whitney test is the most common non-parametric technique used to compare the performance of two methods applied to independent samples.