## 4 Experiments and Results
### PCA as Fragmentation-Wave Enhancement Tool
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & **Frag 1** & **Frag 2** & **Frag 3** & **Frag 4** & **Frag 5** & **Frag 6** & **Frag 7** & **Frag 8** & **Frag 9** & **Frag 10** & **Frag 11** & **Frag 12** \\ \hline ctrl 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ ctrl 2 & 0 & 0.998 & 0.002 & 0 & 0 & **0** & **0** & **0** & **0** & **0** & **0** & **0** \\ ctrl 3 & 0 & 0.002 & 0.986 & 0.005 & 0 & **0** & **0** & **0** & **0** & **0.002** & **0** & **0** & 0.002 \\ ctrl 4 & 0 & 0 & 0.012 & 0.959 & 0.012 & **0.005** & 0.002 & 0 & 0 & 0.002 & **0.005** & 0.002 \\ ctrl 5 & 0 & 0 & 0 & 0.036 & 0.906 & **0.031** & 0.002 & 0.002 & 0.002 & 0.007 & **0.007** & 0.005 \\ ctrl 6 & 0 & 0 & 0 & 0 & 0.077 & **0.834** & 0.039 & 0.029 & 0.002 & 0.002 & 0.01 & 0.007 \\ ctrl 7 & 0 & 0 & 0 & 0 & 0.005 & **0.123** & 0.773 & 0.053 & 0.019 & 0.007 & 0.012 & 0.007 \\ ctrl 8 & 0 & 0 & 0 & 0 & 0 & 0.007 & 0.176 & 0.728 & 0.048 & 0.017 & 0.017 & 0.007 \\ ctrl 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.178 & 0.713 & 0.075 & **0.024** & 0.01 \\ ctrl 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0.002 & 0.005 & 0.195 & 0.728 & **0.058** & 0.012 \\ ctrl 11 & 0 & 0 & 0 & 0 & 0 & 0 & **0.005** & 0.002 & 0.007 & **0.159** & **0.781** & 0.046 \\ ctrl 12 & 0 & 0 & 0 & 0 & 0 & **0** & **0** & **0** & **0** & **0.002** & **0.01** & **0** & **0.087** & 0.901 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Normalized confusion matrix of PCA for 12-lead ECG. 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. \[aVR =-\frac{I+II}{2}\] \[aVL =\frac{I-II}{2} \tag{5}\] \[aVF =II-\frac{I}{2}\] \[III =II-I\]  
Therefore, and due to the fact that leads _III_, _aVF_, _aVR_, and _aVL_ add nothing more than redundant information to the rest of the leads, we could explore the fragmentation isolation capabilities of the suggested methodology when these leads are not considered in this process. Results of this experiment are shown in Table 2, where a lower dispersion rate can be observed compared with Table 1. Similar results are observed in terms of dispersion coefficient, which is reduced to 0.07. However, the findings in Table 2 are even more illustrative and relevant, confirming that only three components presented figures lower than 0.90, hence narrowing the uncertainty of PCA output components. Figure 3 shows an example of relevant component in-and-out cross-signal-transference applying this technique. An exceptional and singular case could be found in Panels (2,3) of said figure, where this swap is due to the non-physiological case of the prominent amplitude of the additive fragmented wave, the magnitude of which positively compares to the T-wave. In order to _highlight fragmentation in PCA transformed components_, we also operated with the previously defined database, but only taking into account the independent leads, namely, \(I\), _II_, _V1_, _V2_, _V3_, _V4_, _V5_ and _V6_, by following the methodology described hereafter: First, PCA was computed for control and subrogated records; Then, the root mean square error (_RMSE_) was calculated for control (_RMSE_ECG) and subrogated (_RMSE_PCA) signals; and finally, coefficient \(\rho_{RMSE}\) was evaluated.