## 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}{*}{**Class**} & \multicolumn{4}{c}{_VF_} & \multicolumn{4}{c}{_VT_} \\ \cline{2-10}  & **Sens \%** & **Spe \%** & **Acc \%** & **Pre \%** & **Sens \%** & **Spe \%** & **Acc \%** & **Pre \%** \\ \hline
**Combined Classification Algorithms (Cls, Cls, Cls)** & _VF_ & **Global** & **Global** & **Global** & **VT** & **Global** & **Global** & **Global** \\ \hline \(ANN\_CNN\_ANNC\) & & & & & & & & \\ Test & 95.13 \(\pm\) 0.06 & 99.10 \(\pm\) 0.04 & 98.41 \(\pm\) 0.04 & 96.38 \(\pm\) 0.19 & 92.32 \(\pm\) 0.66 & 99.33 \(\pm\) 0.07 & 98.91 \(\pm\) 0.02 & 91.38 \(\pm\) 0.84 \\ \hline _ANN\_CNN\_12 RLR_ & & & & & & & \\ Test & 94.89 \(\pm\) 0.56 & 99.08 \(\pm\) 0.20 & 98.32 \(\pm\) 0.27 & 96.02 \(\pm\) 0.87 & 92.37 \(\pm\) 2.46 & 99.27 \(\pm\) 0.10 & 98.78 \(\pm\) 0.23 & 90.71 \(\pm\) 1.38 \\ \hline _BAG\_CNN\_ANNNC_ & & & & & & & \\ Test & 95.58 \(\pm\) 0.40 & 99.31 \(\pm\) 0.08 & 98.6 \(\pm\) 0.04 & 98.25 \(\pm\) 0.29 & 94.02 \(\pm\) 0.58 & 99.31 \(\pm\) 0.08 & 99.14 \(\pm\) 0.43 & 98.59 \(\pm\) 0.09 \\ \hline _BAG\_CNN\_12 RLR_ & & & & & & & & \\ Test & 95.58 \(\pm\) 0.42 & 99.31 \(\pm\) 0.04 & 98.6 \(\pm\) 0.05 & 96.93 \(\pm\) 0.19 & 94.02 \(\pm\) 0.58 & 99.31 \(\pm\) 0.08 & 99.14 \(\pm\) 0.43 & 91.25 \(\pm\) 0.91 \\ \hline _I2 RLR\_KNN\_ANNC_ & & & & & & & & \\ Test & 93.33 \(\pm\) 0.31 & 98.93 \(\pm\) 0.07 & 97.88 \(\pm\) 0.12 & 95.30 \(\pm\) 0.96 & 92.01 \(\pm\) 0.58 & 99.22 \(\pm\) 0.09 & 98.71 \(\pm\) 0.03 & 90.06 \(\pm\) 1.37 \\ \hline _I2 RLR\_KNN\_12 RLR_ & & & & & & & & \\ Test & 93.54 \(\pm\) 0.31 & 98.01 \(\pm\) 0.07 & 97.98 \(\pm\) 0.12 & 95.65 \(\pm\) 0.35 & 92.95 \(\pm\) 0.58 & 99.26 \(\pm\) 0.08 & 98.82 \(\pm\) 0.03 & 90.70 \(\pm\) 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results for different hierarchical method (HM) combined classifier methods to detect _VF_ and _VT_ pathologies. Table 14 shows the average execution time of all the classification algorithms analyzed in this work. The execution time corresponds to the elapsed time between the input of a \(t_{w}\) window from the ECG signal to the generation of a classification result of the algorithm. Concerning individual classifiers, it can be appreciated that \(L2 RLR\) and \(ANN\) have a lower computational cost than other individual algorithms, with a run time of \(t=7\times 10^{-5}\) s and \(t=5\times 10^{-4}\) s, respectively. For \(KNN\) and \(BAGG\), \(t=0.17\) s and \(t=0.05\) s was attained, respectively. In case of the VMM combination methods, they are the slowest among HM and individual, ranging from \(t=190\) ms to \(t=290\) ms. This is normal since all three classifiers (\(Cla\), \(Clb\), \(Clc\)) must be computed, increasing the total computation time. Actually, any VMM combination method required more computation time than the slowest individual algorithm (\(KNN\)). In case of HM classification methods, we obtained different computation time depending on the executed classifier (\(Clb\) or \(Clc\)) depending on the results given by the first classifier (\(Cla\)). For this reason we obtained a minimum and maximum computation time, ranging from \(t=50\) ms to \(t=130\) ms. Thus HM combined methods provide a high classification, together with a reduced computation time, showing their feasibility for real-time classification systems. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{4}{c}{\(L2 RLR\_KNN\_ANN\)} & \multicolumn{4}{c}{\(L2 RLR\_KNN\_L2 RLR\)} \\ \cline{2-9}  & \(V\!F\) & \(V\!T\) & _Others_ & _Normal_ & _VF_ & _VT_ & _Others_ & _Normal_ \\ \hline \(VF\) & 1635 & 60 & 6 & 51 & 1639 & 56 & 12 & 45 \\ \(VT\) & 38 & 604 & 0 & 14 & 32 & 610 & 1 & 13 \\ \(Others\) & 9 & 0 & 1941 & 47 & 9 & 1 & 1911 & 76 \\ \(Normal\) & 32 & 7 & 30 & 4934 & 33 & 7 & 69 & 4894 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Confusion matrix for classification of \(VF\), \(VT\), \(Others\), and \(Normal\) using the \(L2 RLR\_KNN\_ANN\) and \(L2 RLR\_KNN\_L2 RLR\) combined classifiers in HM topology.