# Plant Electrical Signal Classification Based on Waveform Similarity
## 2 Related Works
### Time Series Waveform Recognition and Classification
#### 2.2.3 Features Extraction and Classification  
Next, we can list these common time series features--i.e., time-domain features, statistical features, frequency-domain features, and nonlinear features, etc. Time domain features include waveform length, peak amplitude, area, and slope, etc. Statistical features include average value, variance, coefficient of variation (CV), skewness, kurtosis, Hjorth's parameters (activity, mobility, and complexity) [47]. Frequency domain features include frequency spectrum, power spectrum, energy, etc. Nonlinear features include permutation entropy [62], sample entropy [63], correlation dimension [64], largest Lyapunov exponents (LLE) [65; 66; 67], and Hurst exponents [68], etc. Skewness features can represent distribution asymmetry of time series. When the value of skewness is positive, the waveform is skewed to the right. If the value of skewness is negative, the waveform is skewed to the left. The absolute value of skewness shows the deviation degree of waveform distribution. The larger value means the larger deviation, and vice versa. The expression of skewness is \(skewness=\frac{\sum\limits_{i=1}^{N}{(x_{i}-\mu_{x})^{4}}}{N\sigma_{x}^{2}}\), where \(x_{i}(i\in[1,N])\) is the time series, \(\mu_{x}\) is the average value, and \(\sigma_{x}\) is the standard deviation. Kurtosis is the fourth standardized moment. Positive kurtosis indicates a \"heavy-tailed\" distribution and negative kurtosis indicates a \"light-tailed\" distribution. The expression of Kurtosis is \(kur=\frac{\sum\limits_{i=1}^{N}{(x_{i}-\mu_{x})^{4}}}{N\sigma_{x}^{4}}\), where \(x_{i}(i\in[1,N])\) is the time series, \(\mu_{x}\) is the average value, and \(\sigma_{x}\) is the standard deviation. Hjorth parameters [47] include activity, mobility, and complexity. The activity parameter represents the variance of a time series. The mobility parameter represents the mean frequency, or the proportion of standard deviation of the power spectrum. The complexity parameter represents the change in frequency. It also indicates the deviation of the slope. Assume that \(dx_{i}=x_{i+1}-x_{i}\), \((i=1,...,n-1)\), \(dx=d_{i+1}-d_{i}\), \((i=1,...,n-2)\), then calculate the variances includes \(\sigma_{1}=\frac{1}{n}\sum\limits_{i=1}^{n}{x_{i}^{2}}\), \(\sigma_{2}=\frac{1}{n-1}\sum\limits_{i=1}^{n-1}{dx_{i}^{2}}\), and \(\sigma_{3}=\frac{1}{n-2}\sum\limits_{i=1}^{n-2}{dx_{i}^{2}}\). The expressions of Hjorth parameters are \(activity=\sigma_{1}\), \(mobility=\sigma_{2}/\sigma_{1}\), and \(complexity=\sqrt{\sigma_{3}/\sigma_{2}-mobility}\). The energy of time series can be expressed as \(E_{x}=\sum\limits_{n=-\infty}^{\infty}{\left|{x_{n}}\right|^{2}}\), and average power expression is \(P_{x}=\lim\limits_{N\rightarrow\infty}\frac{1}{2N+1}\sum\limits_{n=-N}^{N}{ \left|{x_{n}}\right|^{2}}\). Permutation entropy (PE) [62] describes the complexity and regularity of non-stationary and nonlinear chaotic time series. The smaller value of permutation entropy means more regularity, and the bigger value means it is more stochastic. Compared with approximate entropy, it is insensitive to noise and steady. The computation cost is low with few parameters. It is used to distinguish the random and regular changes of EEG signals to trace the transient variation of EEG, predict the epilepsy seizure, and classify sleep state and waking state. The parameters of permutation entropy are the embedding dimension n and delay time [62]. Sample entropy (SampEn) is a modification of approximate entropy for analyzing deterministic chaotic and stochastic processes. It can be used to describe the complexity of time series such as ECG or EEG. SampEn does not count a self-match or depend on data length. It is sensitive to input parameters: m (length of embedding dimension), r (similarity criterion), and N (length of time series). \(r\) is usually selected as a factor of the standard deviation (SD), and m = 2 (or greater) reveals more of the dynamics of the data. SampEn value is zero or positive.