# ECG Arrhythmia Classification using High Order Spectrum and 2D Graph Fourier Transform
## 4 Experiments and Analysis
### Spectral Feature
#### 4.4.2 Feature Extraction  
On the basis of the bispectrum and 2D-GFT, more distinguishing features can be obtained. The spectral flatness, spectral brightness and spectral roll off are calculated. Results are present in Figures 9 and 10.  
Figure 8: Accuracy curve at different parameters. (**a**) boundary \(F\); (**b**) coefficient \(\beta\).  
Figure 9 is the combination of three spectral features of bispectrum of Class N, Class S, Class V, and Class F. The central line indicates the median value, and top and bottom edges indicate the maximum and minimum value respectively. Symbol '+' are outliers. Figure 9a shows the spectral flatness values mainly range from 0 to 0.18, and the median value of Class N and Class S is lower than Class V and Class F. In Figure 9b, most values are close to 1. There is an obvious distinction between the spectral brightness of Class F and other three classes. Class F signals can be discriminated based on spectral brightness. Because the measure of the right skewness of the signal is the roll-off of the spectrum, most of the energy contained in the spectral coefficients is concentrated to the right of the average. It can be seen from the Figure 9c that the median value of the spectral roll-off of class F is the largest, about 30.6, while the median value of class N is the smallest, about 28.5. Spectral roll-off is the key factor to raise recognition rate.  
Figure 9: Adjusted Boxplot of spectral features of N, S, V & F beats after bispectrum. (**a**) Spectral Flatness; (**b**) Spectral Brightness; (**c**) Spectral Roll-off.  
Data listed in Table 3 are confidence interval (CI = 95%) of three kinds of features. For instance, the probability of a selected sample's spectral flatness falling in interval [0.0101, 0.0106] is 95%. Compared with other classes, class N has the closest upper and lower bounds, which means little fluctuation.  
Figure 10 contains the spectral feature after 2D-GFT. In Figure 10a, median spectral flatness values are between 0.35 to 0.36 for Class N, 0.36 to 0.37 for Class S, 0.34 to 0.35 for Class V and 0.31 to 0.32 for Class F. Compared with Figure 9a, the value in Figure 10a is more distinguishable. In Figure 10b, median spectral brightness values of three classes are near 0.53, only value of class V is above it. The  
Figure 10: Adjusted boxplot of spectral features of N, S, V, and F beats after bispectrum and 2D-GFT. (**a**) Spectral Flatness; (**b**) Spectral Brightness; (**c**) Spectral Roll-off.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **Spectral Flatness** & **Spectral Brightness** & **Spectral Roll-off** \\ \hline N & 0.0101 to 0.0106 & 0.9928 to 0.9931 & 28.510 to 28.532 \\ \hline S & 0.0159 to 0.0204 & 0.9868 to 0.9896 & 28.921 to 28.972 \\ \hline V & 0.0438 to 0.0470 & 0.9619 to 0.9639 & 29.343 to 29.436 \\ \hline F & 0.0587 to 0.0598 & 0.9421 to 0.9428 & 30.634 to 30.6910. \\ \hline \hline \end{tabular}
\end{table}
Table 3: CI (95%) of spectral features of N, S, V & F beats after bispectrum.  
boxplot of Figure 10c is more concentrated than that of Figure 9c, the median spectral roll-off values of three classes are 25, 24, 25 and 26 with less outliers (+) outside the top and bottom edges.  
Table 4 contains the confidence intervals of four classes after bispectrum and 2D-GFT. Similarly to those in Table 3, the indexes of class N are the most stable.