# ECG Arrhythmia Classification using High Order Spectrum and 2D Graph Fourier Transform
## 4 Experiments and Analysis
### Classification Results
#### 4.5.1 Cross-validation Test  
The whole amount of the heartbeats used for cross-validation is 75,604. Numbers of different types of heartbeat are shown in Table 5.  
Table 6 is the average confusion matrix of classification results after merely bispectrum. Take N beats in Table 6 as an example, 89.95% beats are correctly classified on average, 10.05% beats are misclassified into Class S, Class V and Class F.  
Table 7 shows the metrics values measuring the classification performance associated to each class, including average value and standard deviation (SD). The method gives a high value of correct rate in executing arrhythmia classification, which is above 89.3%. Among all classes, standard deviation keeps below 0.245. Take F beats in Table 7 as an example, the _Acc_ is 96.9%, the _Err_ is 3.1%, and the SD is 0.002. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Ground Truth**} & \multicolumn{4}{c}{**Classification Results (\%)**} \\ \cline{2-5}  & **N** & **S** & **V** & **F** \\ \hline
**N** & 89.95 & 7.69 & 2.22 & 0.14 \\ \hline
**S** & 9.65 & 74.22 & 16.06 & 0.07 \\ \hline
**V** & 7.57 & 15.09 & 77.22 & 0.12 \\ \hline
**F** & 0.74 & 6.11 & 38.43 & 54.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average Confusion matrix of ECG heartbeat classification results after bispectrum in cross-validation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **Spectral Flatness** & **Spectral Brightness** & **Spectral Roll-off** \\ \hline N & 0.3557 to 0.3563 & 0.5288 to 0.5289 & 24.667 to 24.680 \\ \hline S & 0.3658 to 0.3674 & 0.5315 to 0.5321 & 24.296 to 24.352 \\ \hline V & 0.3492 to 0.3511 & 0.5275 to 0.5287 & 24.866 to 24.899 \\ \hline F & 0.3116 to 0.3122 & 0.5281 to 0.5282 & 25.8 Table 8 is the average confusion matrix of classification results after bispectrum and 2D-GFT. Also take N beats as an example, 96.28% beats are correctly classified on average, 3.72% beats are misclassified into Class S, Class V and Class F. Compared with the corresponding ones in Table 6, data in Table 8 get a remarkable improvement, about 5% for each class. Table 9 shows the metrics values after bispectrum+2D GFT. Also take F beats as an example, the \(Acc\) is 98.8%, the \(Err\) is 1.2%, and the SD is 0.1%. Compared with Table 7, the indicators in Table 9 are better. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Class N** & **Class S** & **Class V** & **Class F** \\ \hline \multirow{4}{*}{**Average Classification Results**} & _Acc_ & Mean & 0.893 & 0.951 & 0.939 & 0.969 \\ \cline{2-6}  & _Err_ & Mean & 0.107 & 0.049 & 0.061 & 0.031 \\ \cline{2-6}  & _Acc / Err_ & SD & 0.020 & 0.003 & 0.007 & 0.002 \\ \cline{2-6}  & _Sen_ & Mean & 0.982 & 0.41 & 0.498 & 0.19 \\ \cline{2-6}  & _SD_ & 0.002 & 0.026 & 0.032 & 0.057 \\ \cline{2-6}  & _Spe_ & Mean & 0.456 & 0.990 & 0.985 & 0.995 \\ \cline{2-6}  & _SD_ & 0.041 & 0.001 & 0.004 & 0.003 \\ \hline \multirow{2}{*}{\(Ppr\)} & Mean & 0.900 & 0.743 & 0.772 & 0.546 \\ \cline{2-6}  & _SD_ & 0.328 & 0.511 & 0.511 & 0.508 \\ \cline{2-6}  & _Mean_ & 0.622 & 0.579 & 0.661 & 0.316 \\ \cline{2-6}  & _SD_ & 0.037 & 0.026 & 0.029 & 0.082 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average Metrics of ECG heartbeat classification results after bispectrum in cross-validation.