## 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{2-9}  & **Sens \%** & **Spe \%** & **Acc \%** & **Pre \%** & **Sens \%** & **Spe \%** & **Acc \%** & **Pre \%** \\ \hline
**Combined Classification Algorithms (Cla, Clb, Clc)** & _VF_ & **Global** & **Global** & **Global** & **Global** & **VT** & **Global** & **Global** \\ \hline \(\Delta\)NNC\_KNN\_l2 RLR_ & \(97.47\pm 0.13\) & \(99.09\pm 0.10\) & \(98.71\pm 0.06\) & \(96.12\pm 0.23\) & \(91.31\pm 0.88\) & \(99.97\pm 0.08\) & \(99.18\pm 0.01\) & \(96.26\pm 0.90\) \\ \hline \(\Delta\)NNC\_KNN\_BAGG_ & \(98.46\pm 0.06\) & \(98.98\pm 0.02\) & \(98.89\pm 0.01\) & \(96.04\pm 0.60\) & \(89.63\pm 0.30\) & \(99.86\pm 0.01\) & \(99.14\pm 0.02\) & \(97.64\pm 0.15\) \\ \hline \(\Delta\)G\_KNN\_l2 RLR_ & \(98.43\pm 0.16\) & \(98.98\pm 0.08\) & \(98.87\pm 0.04\) & \(95.79\pm 0.50\) & \(91.01\pm 0.68\) & \(99.83\pm 0.03\) & \(99.16\pm 0.02\) & \(97.51\pm 0.18\) \\ \hline
**BAGG\_ANNC\_l2 RLR_** & \(97.89\pm 0.08\) & \(98.84\pm 0.05\) & \(98.66\pm 0.04\) & \(95.33\pm 0.31\) & \(87.80\pm 1.21\) & \(99.88\pm 0.03\) & \(99.98\pm 0.06\) & \(97.61\pm 0.50\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results for the voting majority method (VMM) combination method using \(TRI\) as data input. Results correspond to detection of _VF_ and _VT_ pathologies. In the second analysis, the Hierarchical Method (HM) is applied to three individual algorithms (\(Cla\), \(Clb\), \(Clc\)) getting the \(Cla\_Clb\_Clc\) multiclassifier where \(Clb\) and \(Clc\) are in parallel and both cascaded after \(Cla\) (Figure 5). The obtained results are shown in Tables 9 and 10 with confusion matrices in Tables 11-13. Since \(KNN\) was the best individual algorithm in the detection and discrimination between \(VF\) and \(VT\), it was chosen as \(Clb\). The \(ANNC\), \(BAGG\), \(L2 RLR\) algorithms are taken as \(Cla\) for the discrimination between the classes \(VFVT\) and \(NormalOthers\) and the \(ANNC\) and \(L2 RLR\) algorithms are used as \(Clc\) for \(Normal\) and \(Others\) discrimination. Analyzing the results, it can be concluded that the combinational algorithms have a similar or better behavior than the individual \(KNN\) in the detection of \(VF\) in very large datasets and high dimensionality, with a reduced execution time. With all the results obtained, the use of combined algorithms can be recommended as the best method of classification. In addition, results obtained using the combination \(BAGG\_KNN\_ANNC\) using HM showed better classification ratio when compared to those obtained using the algorithms individually, and other multi classifiers. The \(BAGG\_KNN\_ANNC\) HM obtained a good behavior in the discrimination between the classes \(VF\), \(VT\), \(Normal\), and \(Others\), with a sensitivity of 95.58 \(\pm\) 0.4%, a global specificity of 99.31 \(\pm\) 0.08%, an accuracy of 98.6 \(\pm\) 0.04%, and an overall precision of 98.25 \(\pm\) 0.29% for \(VF\). For \(VT\), a sensitivity of 94.02 \(\pm\) 0.58%, a specificity of 99.31 \(\pm\) 0.08%, an accuracy of 99.14 \(\pm\) 0.43%, and a precision of 98.59 \(\pm\) 0.09% was obtained. It is interesting to note that the \(ANNC\) classifier obtained a good behavior in the discrimination between the classes \(Normal\) and \(Others\), and the \(BAGG\) classifier had a good behavior in the discrimination between the classes \(NormalOthers\) and \(VFVT\) with a fast execution time in comparison with the individual \(KNN\) algorithm.