###### Abstract  
A rapid and accurate detection of ventricular arrhythmias is essential to take appropriate therapeutic actions when cardiac arrhythmias occur. Furthermore, the accurate discrimination between arrhythmias is also important, provided that the required shocking therapy would not be the same. In this work, the main novelty is the use of the mathematical method known as Topological Data Analysis (TDA) to generate new types of features which can contribute to the improvement of the detection and classification performance of cardiac arrhythmias such as Ventricular Fibrillation (VF) and Ventricular Tachycardia (VT). The electrocardiogram (ECG) signals used for this evaluation were obtained from the standard MIT-BIH and AHA databases. Two input data to the classify are evaluated: TDA features, and Persistence Diagram Image (PDI). Using the reduced TDA-obtained features, a high average accuracy near 99% was observed when discriminating four types of rhythms (98.68% to VF; 99.05% to VT; 98.76% to normal sinus; and 99.09% to Other rhythms) with specificity values higher than 97.16% in all cases. In addition, a higher accuracy of 99.51% was obtained when discriminating between shockable (VT/VF) and non-shockable rhythms (99.03% sensitivity and 99.67% specificity). These results show that the use of TDA-derived geometric features, combined in this case this the k-Nearest Neighbor (kNN) classifier, raises the classification performance above results in previous works. Considering that these results have been achieved without preselection of ECG episodes, it can be concluded that these features may be successfully introduced in Automated External Definition (AED) and Implantable Cardioverter Defibrillation (ICD) therapies. Electrocardiography analysis; ventricular arrhythmia detection; ventricular fibrillation detection; ventricular tachycardia detection; ECG signal classification; Topological Data Analysis; representation of point cloud; persistent diagram representation; landscape representation; silhouette representation +
Footnote †: journal: Medical Imaging  
0000-0001-999-2248-227  
To revert VF, the current protocol is the electrical defibrillation of the heart using an Automatic External Defibrillator (AED) [1], which can be commonly found nowadays in public places such as airports, shopping centers, sports arenas, etc. This process involves an external application of a high-energy electrical shock through the chest wall of the patient to allow the reinstatement of the normal rhythm. Some studies [2; 3; 4] have established that defibrillation success is conversely proportional to the time interval between the start of the Ventricular Fibrillation episode and the time when the electrical discharge is applied. However, similar pathologies exist, like Ventricular Tachycardia (VT), requiring a different treatment than VF. In these cases, the signal may share some characteristics (lack of organization, irregularity, etc.) with VF, but the administration of an electrical shock to a patient not suffering VF could result in serious injuries or even bring about VF itself. This is why an accurate detection and classification of ventricular arrhythmias is so relevant. The electrocardiogram (ECG) is an inexpensive and noninvasive tool used in the diagnosis of cardiac conduction disorders. It enables the analysis of the heart rate and morphology of different cardiac electrical waves, which, in turn, may permit the identification of various types of heart diseases. Because of this, ECG signals are considered an important and reliable source of information [5; 6]. Many statistical methods have been applied to detect VF or VT using ECG data. However, following these manual methods, it is difficult to make a feature extraction capable of capturing the deep characteristics of ventricular arrhythmias. This is the reason why machine learning techniques have been effectively applied for the recognition of cardiac arrhythmias. In this sense, [PERSON] et al.