# Diagnosing Various Severity Levels of Congestive Heart Failure Based on Long-Term HRV Signal
## 3 Methods
### Feature Extraction
#### 3.1.2 Non-Linear HRV Features  
In this paper, non-linear indicators were obtained by local Hurst exponent analysis based on the wavelet theory, detrended fluctuation analysis (DFA), entropy analysis, and Poincare plot analysis.  
Biomedical signals are generated by complex self-regulating systems that process inputs with a wide range of characteristics [10; 11]. Previous studies have shown that HRV signals with healthy people are a multi-fractal signal. However, the HRV signal with CHF patients is approximately a single fractal signal [10; 11]. The fractal properties are characterized by \(\Delta h\) (\(\Delta h=h_{\max}-h_{\min}\), \(h\) is the Hurst exponent) [11]. In 1999, [PERSON] et al. [11] evaluated the local Hurst exponent \(h\) through the modulus of the maxima values of the wavelet transform at each point in the time series and scales \(a=2\times 1.15^{i}\), \(i=10\),... 41. They have found the Hurst exponent has a great ability to distinguish CHF patients from normal people [11]. We analyzed the fractal characteristics of the subjects based on long-term HRV signals. The scales in our research were consistent with other papers, i.e., \(a=2\times 1.15^{i}\), \(i=10\),...41.  
DFA is often used to quantify HRV signals. This technique is a modification of root-mean-square analysis of random walks applied to non-stationary signals [12; 13]. In this paper, we extracted two features using the DFA algorithm: \(\alpha_{1}\) was obtained by least square fitting of \(F(n)\) and small scale \(n\) (\(4\leq n\leq 16\)); \(\alpha_{2}\) was obtained by least square fitting of \(F(n)\) and larger scale \(n\) than 16.  
Sample entropy (SampEn) and fuzzy measure entropy (FuzzyMEn) are often used as measures for the analysis of the complexity of HRV signals [14; 15; 16; 17]. Usually, SampEn and FuzzyMEn are influenced  
\begin{table}
\begin{tabular}{c c c} \hline
**Variable** & **Unit** & **Description** \\ \hline PNN10 & \% & Percentage of differences between adjacent NN intervals that are longer than 10 ms. \\ PNN20 & \% & Percentage of differences between adjacent NN intervals that are longer than 20 ms. \\ PNN30 & \% & Percentage of differences between adjacent NN intervals that are longer than 30 ms. \\ PNN50 & \% & Percentage of differences between adjacent NN intervals that are longer than 50 ms. \\ Mean & ms & Mean of all NN intervals. \\ SDNN & ms & Standard deviation of all NN intervals. \\ RMSSD & ms & Square root of the mean of the sum of the square of differences between adjacent NN intervals. \\ Triangular Index & & The number of all NN divided by the height of histogram of all NN Intervals. The interval of the histogram is set to 1/218 ms. \\ TOTPWR & ms\({}^{2}\) & The power between 0 and 0.4 Hz. \\ PVLF & ms\({}^{2}\) & The power between 0 and 0.04 Hz, reflecting the activity of sympathetic. \\ PLF & ms\({}^{2}\) & The power between 0.04 and 0.15 Hz, reflecting dual regulation of sympathetic and \\  & & parasympathetic nerves. \\ PHF & ms\({}^{2}\) & The power between 0.15 and 0.4 Hz, reflecting the activity of parasympathetic. \\ RATIO1 & & PLF/PHF, reflecting the balance between sympathetic and parasympathetic nerves. \\ RATIO2 & & PHF/PLF, reflecting the balance between sympathetic and parasympathetic nerves. \\ NPLF & & Normalized power of LF, PLF/ (PLF + PHF). \\ NPHF & & Normalized power of HF, PHF/ (PLF + PHF). \\ \hline \end{tabular}
\end{table}
Table 3: Heart rate variability (HRV) measures in the time-domain and frequency-domain.  
by the parameters of embedding dimension \(m\) and tolerance threshold \(r\)[16; 17]. In this paper, the best combination of \(m\) and \(r\) for SampEn and FuzzyMEn were obtained by statistical significance analysis.  
The Poincare plot can reflect the nonlinear characteristics of the nature of the HRV signal. It is a graph of each RR (or NN) interval against the next interval [18; 19]. In this article, we extracted three features based on the Poincare diagram analysis, i.e., SD1 (the width of the Poincare plot), SD2 (the length of the Poincare plot), and SD1/SD2 [20].