# ECG Arrhythmia Classification using High Order Spectrum and 2D Graph Fourier Transform
## 1 Introduction  
According to the World Health Organization (WHO), about one third of the world's deaths are caused by cardiovascular disease every year statistically [1]. Cardiovascular disease has become one of the leading causes of death from non-infectious and non-transmissible diseases in the world [2]. Therefore, prevention and early diagnosis are key for a successful clinical management. Arrhythmia is an important group of diseases in cardiovascular disease. The diagnosis of arrhythmia mainly depends on the electrocardiogram (ECG). ECG is an important modern medical tool that can record the process of cardiac excitability, transmission, and recovery. It reflect the degree of myocardial cell damage, development process, functional structure of atrium and ventricle [3]. Detection of irregular heartbeats from ECG signals is a significant task for the automatic diagnosis of cardiovascular disease. The extraction of features from the ECG signal is a key step for ECG recognition, as it allows to greatly enhance and extract the characteristics of the signal. The quality of morphological features extraction in the ECG greatly affects the recognition and classification rate of ECG signals. Generally, the features in the time domain include the amplitude, the RR interval, the duration, and the shape of the clinical components (P-wave, QRS-complex, and T-wave) of ECG [4; 5; 6]. The features in the transformdomain embody different diagnostic features extracted by different signal processing techniques, such as the autoregressive model coefficients, principal component analysis, and geometric attributes based on an image [7; 8; 9; 10]. Those features can be fed into conventional machine learning models, for instance, decision trees, support vector machine, k nearest neighbor, and Bayesian algorithm [11; 12; 13; 14] to realize heartbeats classification. The high-order spectra (HOS) has been widely used in the analysis of bio-medical signals [15; 16]. The high order statistics method is insensitive to Gaussian noise, thus, becoming a suitable method for feature extraction. Bispectrum is the simplest high order spectra, sharing the characteristics of time shift invariance, phase retention and scale variability. Bispectrum and histogram have been used in the analysis of ECG signals [10; 17; 18]. A method for the automated identification of Coronary Artery Disease was proposed in [10], which achieved 98.99% accuracy with 31 cumulants features. [PERSON], [PERSON] et.al [17] proposed an Atrial Fibrillation (AF) identification system based on 57 features including bispectrum and histogram. They got an accuracy of 98.72%. A combination of both vertical and horizontal histogram and pattern based heuristic methods were used in [18] for the detection of P, Q, R, S and T waves. The detection accuracy for P and T wave were 92.2% and 96.7%, respectively. Over the past decade, the graph signal processing (GSP) based on spectral graph theory [19] has been proven to be a real promising method in many application areas [20; 21; 22]. Analogous to the Fourier transform (FT), GFT, as the foundation of GSP, is a data conversion method [23]. GSP visualizes spatiotemporal data as a 2D graph signal, [PERSON]. [PERSON] et al. developed a 3D-GFT model that renders better than its 2D counterpart [24]. This study intends to develop a new method which combines the insensitivity of the bispectrum and the merits of GFT. Features fed into the classifier are spectral flatness, spectral brightness and spectral roll-off [25]. To assess the performance of the proposed method and compare it with previous algorithms, confusion matrix, accuracy (_Acc_), error rate (_Err_), Macro-averaged F-score (_F - score_), sensitivity (_Sen_), specificity (_Spe_), and positive predictive rate (_Ppr_) are used to analyze quantitatively. The analysis results of experimental signals based on the widely recognized MIT-BIH Arrhythmia Database [26] indicated that the proposed method can effectively differentiate several beat types.