## 7 Results
### Comparative Study for the Method of Combined Classifiers
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{4}{c}{\(ANN\_K\_KNN\_ANN\)} & \multicolumn{4}{c}{\(ANN\_K\_KNN\_L2 RLR\)} \\ \cline{2-9}  & \(V\!F\) & \(V\!T\) & _Others_ & _Normal_ & _VF_ & _VT_ & _Others_ & _Normal_ \\ \hline \(VF\) & 1667 & 56 & 3 & 26 & 1662 & 60 & 7 & 23 \\ \(VT\) & 33 & 612 & 0 & 11 & 38 & 606 & 1 & 11 \\ \(Others\) & 12 & 0 & 1941 & 44 & 12 & 0 & 1919 & 66 \\ \(Normal\) & 19 & 2 & 27 & 4955 & 18 & 2 & 59 & 4924 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Confusion matrix for classification of \(VF\), \(VT\), \(Others\), and \(Normal\) using the \(ANN\_K\_KNN\_ANN\) and \(ANNC\_KNN\_L2 RLR\) combined classifiers in HM topology. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(\Lambda\)NNC\_KNN\_L2 RLR(\%) & \(\Lambda\)NNC\_KNN\_BAGG(\%) & \(\textbf{BAGG\_KNN\_12 RLR(\%)}\) & \(\textbf{ANNC\_ANN\_L2 RLR(\%)}\) \\ \hline AUC(VF) & 98.28 & 98.72 & 98.70 & 98.36 \\ AUC(VT) & 95.03 & 97.18 & 98.44 & 97.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: AUC for VMM combination methods in detection of \(VF\) and \(VT\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(\Lambda\)NNC\_KNN\_L2 RLR(\%) & \(\Lambda\)NNC\_KNN\_BAGG(\%) & \(\textbf{BAGG\_KNN\_12 RLR(\%)}\) & \(\textbf{ANNC\_ANN\_L2 RLR(\%)}\) & \(\textbf{ANNC\_ANN\_L2 RLR(\%)}\) \\ \hline AUC(VF) & 98.08 & 97.28 & 98.44 & 97.12 \\ AUC(VT) & 95.03 & 97.18 & 98.44 & 97.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: AUC for HM classification combination methods in detection of \(VF\) and \(VT\). Figure 8: ROC curve for heirarchical method (HM) classification combination methods in detection of \(VF\) (**a**) and \(VT\) (**b**). Figure 7: Receiver operating characteristic (ROC) curve for voting majority method (VMM) combination methods in detection of \(VF\) (**a**) and \(VT\) (**b**). Additionally, the structural risk of the classifier is important in order to determine the training robustness. A risk test is proposed by the A-test where multiple z-fold cross-validation are performed in order to assess how classification error evolves. In this case, we have also tested 9-fold cross validation for comparison purposes with 5-fold. Figure 9 shows that very similar results are obtained for the same classifier. Specially in case of HM combined classifers, z-5 provides a slightly higher classification ratio. In any case, differences between z-5 and z-9 in the same classifier do not exceed 1% in classification value. Since correct detection and classification of \(VF\) and \(VT\) is of pivotal importance for an automatic external defibrillation and patient monitoring, they should be able to distinguish \(VF\) and \(VT\) accurately. If \(VT\) was misinterpreted as \(VF\), a high-energy defibrillation would be delivered, which could damage the heart. If \(VT\) is misinterpreted as \(VF\), the low-energy cardioversion may not return the heart to its normal sinus rhythm, which could be fatal [34]. However, clear distinction between ventricular arrhythmia rhythms and normal or other arrhythmias is required, preventing the patient to be unnecessarily exposed to an electrical cardioversion. As previous results show, the proposed methods obtain a high accuracy, not only in \(VF\) and \(VT\) separation but also in \(Normal\) and \(Others\). This fact leads to further separate the \(Others\) class into other sub-classes where different heart pathologies could also be detected: Premature Ventricular Complex (PVC) in bigeminy or trigeminy, hypertrophy, idioventricular Rhythms, asystoles, etc. Thus, using a new classifier level, all rhythms detected as \(Others\) could enter into a new classification process in order to discern among other cardiac pathologies. Table 18 compares results with different studies in the bibliography to check to what extent the obtained data support our hypothesis.