# ECG Arrhythmia Classification using High Order Spectrum and 2D Graph Fourier Transform
## 4 Experiments and Analysis
### Classification Results
#### 4.5.1 Cross-validation Test
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Class N** & **Class S** & **Class V** & **Class F** \\ \hline \multirow{4}{*}{**Average Classification Results**} & _Acc_ & Mean & 0.960 & 0.982 & 0.977 & 0.988 \\ \cline{2-6}  & _Err_ & Mean & 0.040 & 0.018 & 0.023 & 0.012 \\ \cline{2-6}  & _Acc / Err_ & SD & 0.009 & 0.003 & 0.002 & 0.001 \\ \cline{2-6}  & _Sen_ & Mean & 0.993 & 0.715 & 0.767 & 0.462 \\ \cline{2-6}  & _SD_ & 0.001 & 0.039 & 0.014 & 0.027 \\ \cline{2-6}  & _Sen_ & Mean & 0.719 & 0.993 & 0.992 & 0.999 \\ \cline{2-6}  & _SD_ & 0.052 & 0.002 & 0.002 & 0.003 \\ \hline \multirow{2}{*}{\(Ppr\)} & Mean & 0.963 & 0.826 & 0.869 & 0.910 \\ \cline{2-6}  & _SD_ & 0.420 & 0.502 & 0.504 & 0.503 \\ \hline \multirow{2}{*}{\(F-score\)} & Mean & 0.833 & 0.831 & 0.865 & 0.63 \\ \cline{2-6}  & _SD_ & 0.035 & 0.027 & 0.009 & 0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Average Metrics of ECG heartbeat classification results after bispectrum + 2D GFT in cross-validation. Data listed in Tables 10 and 11 is a more direct presentation of the proposed method compared with the results in the experiments conducted by [38; 39; 40; 41; 42; 43; 44]. All papers in Tables 10 and 11 use the cross-validation method. The methods mentioned in Table 10 all use feature-extraction-pattern, the ones in Table 11 are not. The recordings used in other references listed in Tables 10 and 11 are all from MIT-BIH database. However, the records and segments used in the training set and test set in each literature are not exactly the same. For example, a total of 46 records were used by [PERSON] et al. [38], except recordings No.102 and No.104 which have no lead II information. [PERSON] et al. [43] used 14 recordings for classification, and for each type of the ECG signal, a segment of 10 seconds were selected. According to [PERSON] et al. [38], the combination of Parameter and Visual Pattern of ECG signals reached 97.70% of accuracy. [PERSON] et al. divided 100,467 heartbeats into 5 categories with an accuracy rate of 89.0% [39]. [PERSON] [40] used the best evolutionary neural system based on SVM classifier to classify the data of 17 categories, then obtained an average accuracy of 90.20%. The methods proposed by [PERSON] et al. [41] and [PERSON] et al. [42] in previous years were Multi-lead fused method and ECG Morphology, respectively, achieving an accuracy of 86%. [PERSON] et al. proposed a combination of STFT-Based Spectrogram and Convolutional Neural Network to achieve an accuracy of 99.0% [43]. [PERSON] et al. [44], got an accuracy of 98.1% when combined the automated system of CNN and LSTM to analyze ECG signals. In this paper, we propose a method of combining 2D-GFT with bispectrum, which achieves 96.2% accuracy. In our results, the average accuracy of merely bispectrum is only 87.8%, lower than most of methods listed in this Table 10. But when combined with 2D-GFT, the proposed method yields a higher average accuracy of this experiment to 96.2%, which suggests the method is a promising one in cross-validation. Table 12 contains the detailed values of the proposed method in this section. After 2D-GFT, all metrics are improved. Especially, _Sen_ is improved by more than 30%. By our designed method, the _Sen_, _Spe_ and _Ppr_ of the S beats are 71.5%,99.3% and 82.6%, those of the V beats are 76.7%, 99.2% and 86.9%, those of the F beats are 46.2%, 99.9% and 91.0%, respectively.