## 4 Experiments and Results
### ICA as Fragmentation-Wave Enhancement Tool
\begin{table}
\begin{tabular}{l c 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 & 0.40 & 0.26 & 0.22 & 0.08 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Ctrl 2 & 0.19 & 0.31 & 0.23 & 0.18 & 0.06 & 0.02 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Ctrl 3 & 0.14 & 0.15 & 0.24 & 0.25 & 0.16 & 0.03 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Ctrl 4 & 0.10 & 0.11 & 0.12 & 0.26 & 0.27 & 0.11 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Ctrl 5 & 0.07 & 0.05 & 0.07 & 0.10 & 0.27 & 0.31 & 0.09 & 0.02 & 0.01 & 0.00 & 0.01 & 0.00 \\ Ctrl 6 & 0.04 & 0.04 & 0.04 & 0.05 & 0.07 & 0.31 & 0.37 & 0.05 & 0.01 & 0.01 & 0.00 & 0.00 \\ Ctrl 7 & 0.01 & 0.03 & 0.02 & 0.03 & 0.06 & 0.11 & 0 & 0.32 & 0.06 & 0.01 & 0.00 & 0.01 \\ Ctrl 8 & 0.01 & 0.01 & 0.01 & 0.02 & 0.03 & 0.04 & 0.07 & 0.42 & 0.32 & 0.05 & 0.01 & 0.01 \\ Ctrl 9 & 0.00 & 0.01 & 0.01 & 0.01 & 0.01 & 0.02 & 0.02 & 0.08 & 0.44 & 0.33 & 0.06 & 0.00 \\ Ctrl 10 & 0.01 & 0.00 & 0.01 & 0.01 & 0.02 & 0.01 & 0.02 & 0.03 & 0.07 & 0.48 & 0.27 & 0.07 \\ Ctrl 11 & 0.01 & 0.01 & 0.01 & 0.01 & 0.02 & 0.01 & 0.01 & 0.03 & 0.05 & 0.08 & 0.53 & 0.22 \\ Ctrl 12 & 0.01 & 0.02 & 0.02 & 0.01 & 0.01 & 0.02 & 0.03 & 0.04 & 0.03 & 0.03 & 0.11 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normalized confusion matrix of ICA for the twelve-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. information is spread over every independent component, but it this contribution is significantly higher in the components with lower kurtosis. This behavior follows previous PCA results, where fragmentation information was strongly present, and clearly in the components with lower variance. In next step and for statistical analysis purposes, we computed the ratio of cases in which the presence of fragmentation wave was enhanced in the corresponding components. For this purpose, when \(\rho_{RMSE}\) value is greater than zero, it is considered considered the existence of fragmentation-boost or enhancement in the selected component. Figure 10b shows the ratio of cases which presents fragmentation wave enhancement, and it can be observed that the greater values of improvement appear in the components with lower kurtosis, which is also like in case of PCA where they appeared in components with lower variance. Finally, we calculated the ratio of fragmentation wave enhancement depending of the number of independent components, in order to know the number of them that we must to take to achieve a complete detection of fragmentation, and as it can be observed, the optimal is reached by taking the last four components as shown in Figure 10c. In the subsequent experiment, we calculated the _dependency of \(\rho_{RMSE}\) with the variables which model the fragmentation wave_. We used the same parameter variation as in the preceding PCA parts, namely, amplitude of the wave from 1% to 50% of the maximum beat template amplitude, number of cycles of the wave from 0.5 to 25, width of the wave from 10 to 200 ms, and number of leads affected by fragmentation from 1 to 12. In this experiment, we worked with a subset of 50 cases from the control database. We created replications of these cases and we varied the fragmentation wave parameters according to previous values. Figure 11 shows the variation of \(\rho_{RMSE}\) with each parameter variation. As it can be observed, the parameters that induce major changes in the \(\rho_{RMSE}\) value are amplitude (Figure 11a) and width (Figure 11b) of the fragmentation wave. Unlike the PCA part, these two parameters present a decreasing curve because when they increase the sine, which models the fragmentation wave, it is more easily separable by ICA and the fragmentation information is isolated in only one component, which varies its position in the output.