## 4 Experiments and Results
### PCA as Fragmentation-Wave Enhancement Tool
The first experiment of this set will determine if the _presence of fragmentation in the ECG_ could change the order in the PCA-components output. To do so, we proposed the use of a subrogated database to compare the principal component output under a controlled situation. We proceeded as follows for the control ECG and for their synthetically fragmented copies. First the beat templates were created according to the method described before. Then, we compared the principal component of the control and synthetically fragmented beat templates by using the signal correlation. We the used the PCC or Pearson correlation coefficient to test whether the PCA components position is maintained when fragmentation is synthetically added to the signal. This analysis was performed for each region individually. Results are summarized in the confusion matrices presented in Table 3a-c. The dispersion coefficient for each region are 0.009 in antero-septal region, 0.034 in lateral region, and 0 in inferior region. These results are much better than the achieved by the independent-lead case in terms of PCA component mismatching. Given that the order in the position of the principal components provided apparently better results in a regional approach than the previously evaluated independent-lead model, we again moved forward to quantify the enhancement using this approach. To do so, this experimental setup was similar to the used in the independent-leads model. First, we extracted the principal components for control ECG and fragmented ECG using PCA. Finally, we computed the coefficient \(\rho_{RMSE}\), and we derived the enhancement ratio as the portion of cases where \(\rho_{RMSE}>0\). Figures 7a, 8a and 9a show the distribution of \(\rho_{RMSE}\) for each region and component. As it can be observed, the distributions did not improve the results obtained by PCA over independent-lead model. The value of RMSE measured in the ECG was greater than the value of RMSE measured in principal components. Figures 7b, 8b and 9b show the enhancement ratio for each component, which is also lower than the value achieved in the independent-lead model. Finally, Figures 7c, 8c and 9c show the joint enhancement ratios that again did not outperform the independent-lead model. Therefore, we should elaborate the use of the regionalization in the detection of fragmentation using PCA does not provide better results than the use of the independent leads. Table 4 summarizes the most relevant results of this set of experiments. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} & \multicolumn{3}{c}{**(b)**} & \multicolumn{3}{c}{**(c)**} \\ \hline  & **Frag 1** & **Frag 2** & **Frag 3** & **Frag 4** & **Frag 1** & **Frag 2** & **Frag 3** & **Frag 4** & **Frag 1** & **Frag 2** & **Frag 3** \\ \hline Ctrl 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ Ctrl 2 & 0 & 0.993 & 0 & 0.007 & 0 & 0.986 & 0.007 & 0.007 & 0 & 1 & 0 \\ Ctrl 3 & 0 & 0.007 & 0.986 & 0.007 & 0 & 0.014 & 0.935 & 0.051 & 0 & 0 & 1 \\ Ctrl 4 & 0 & 0 & 0.014 & 0.986 & 0 & 0 & 0.058 & 0.942 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Normalized confusion matrix for each heart region, (a) antero-septal, (b) lateral region, and (c) inferior region by using PCA. For each one, the _ij_ value of the table represent the ratio of _i_-th component of control patient that is paired with the _j_-th component of synthetically fragmented patient according to the value of PCC. Figure 8: _Cont._  
Figure 7: Different measurements for PCA over antero-septal heart region. (**a**) Distribution of \(\rho_{RMSE}\) coefficient for each independent component, values lower than zero represents cases where the RMSE measured over the ECG is greater than RMSE measured over the independent component. (**b**) Ratio of fragmentation wave enhancement for each independent component, this ratio is computed as cases where the \(\rho_{RMSE}\) value is greater than zero.