## 4 Results  
The experiments were carried out using signals from the MIT-BIH and AHA standard databases, Section 3.1. They were divided into four classes, namely _VF_, _VT_, _Normal_ and _Others_. The preprocessing stage carries out an 8 th order bandpass (1 Hz to 45 Hz) Butterworth IIR filter to denoise and reduce the baseline variation, Section 3.2, and calculates the window reference marks (WRM) of the signal, marks indicating the beginning and end of the 1.2 s time window from the temporal signals. At the feature extraction, we have proposed two different topological techniques to extract the parameters feeding the classifier: Topological Data Analysis (TDA) and Persistence Diagrams (PDI). In the case of the TDA method, each window of temporal signals were converted first into a Point Clouds representation, using delay embedding, and then into Persistence Diagrams, Persistence Landscapes, and Power Weighted Silhouettes. Finally, some parameters were extracted from these diagrams, Section 3.3, and then combined to create the features vector feeding the input of the classifier. Concerning the PDI method, the gaussian KDE was applied to the Persistence Diagram and the whole resulting image was used as a direct input to the classifier. The k-Nearest Neighbor (kNN) classifier was the only classifier used for both proposals. For each class, 67% of data was randomly selected for training and the remaining 33% for testing. The kNN training process was calculated and then the testing dataset was used to evaluate the classification performance by measuring the Sensibility (Se), Specificity (Sp), and Accuracy (Acc). This approach was repeated five times at random, and the performance of the classifiers was evaluated overall by taking this five iterations average. This number of iterations was chosen after some trials because it showed the lowest generalization error. Table 5 shows the confusion matrix for one of these iterations. It shows a great classification performance. Nevertheless, the values represented in the following tables (Tables 6-9) indicate the average performance values obtained from the repeated random validation used in this work. Thus, Tables 6-9 show the testing classification results for TDA and PDI feature selection methods. As it can be seen, the TDA method shows better classification results than the PDI. On the one hand, the PDI method results in values of accuracy above 92% for all classes, having better accuracy values for _VT_ and _Other_ classes (97.38% and 96.19%, respectively), but curiously falling to 92.65% for the detection of _Normal_ sinus rhythms. The sensitivity widely varies depending on the case, ranging from 82.25% for _VT_ to 93.09% for the _Normal_ classes, being more sensitive to _Normal_ and _Other_s classes (around 93%) than to _VT_ and _VF_ (around 84%). Except for the _Normal_ case, the global specificity (Spe) becomes greater than sensitivity, reaching the value of 98.53% for the _VT_ class. On the other hand, the TDA method results in very high results of accuracy, around 99% for all classes, with little differences between them. The sensitivity remains above 97% except for the _VT_ class, falling to 92.72% and getting the maximum sensitivity value for the _Normal_ case (99.05%), with 97.07% for the _VF_ class. Finally, the global specificity achieves high values: near 99% for the _Normal_ class and above 99% for the rest of the classes, hitting a maximum of 99.53% for the _VT_ class. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Type**} & \multicolumn{5}{c}{**VF**} \\ \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{2}{c}{**Sensitivity\%**} & \multicolumn{3}{c}{**Specificity\%**} & \multicolumn{3}{c}{**Accuracy\%**} \\ \cline{2-7}  & **VF** & **Global** & **VT** & **Other** & **N** & **Total** \\ \hline TDA & 97.07 & 99.25 & 93.78 & 99.90 & 99.68 & 98.68 \\ PDI & 84.34 & 96.77 & 89.70 & 99.14 & 96.68 & 94.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results obtained for _VF_ class classification in testing.