# Support Vector Machine-Based EMG Signal Classification Techniques: A Review
## Appendix A Common Features
### Time Domain
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* Root Mean Square Value (RSM)  RMS is modeled as a Gaussian random process with modulated amplitude, which is related to a constant force and contraction without fatigue; it is very similar to the calculation of the standard deviation since it is given by \[\text{RMS}=\sqrt{\frac{1}{N}\sum_{k=1}^{N}x_{k}^{2}}.\] (14)
* Integrated EMG (IEMG)  Some features such as the IEMG also allow signal recognition without a pattern. This is used as an initial detection rate and it is related to the trigger point of the EMG signal sequence. It is defined as the sum of the absolute values of each EMG sample, and it can be expressed as [83]: \[\text{IEMG}=\sum_{k=1}^{N}|x_{k}|.\] (15)
* Auto-Regressive Coefficients (AR)
The AR form a prediction model that describes each EMG signal sample \(x_{k}\) as a linear combination of the \(P-1\) previous samples \(x_{k-1}\),..., \(x_{k-P}\) plus a white noise error term \(w_{k}\); this model is expressed as \[x_{k}=\sum_{p=1}^{P}a_{p}x_{k-p}+w_{k},\] (114) where \(P\) is the order of the AR model. The most common \(P\) used is 6 [10; 22; 23; 28]; nevertheless, some authors [12] used orders 1, 2 and 3, while [PERSON] et al. [26] used \(P=5\). * Standard Deviation (STD) STD is defined as the square root of the variance, that is, \[\text{STD}=\sqrt{\frac{1}{N}\sum_{k=1}^{N}\left(x_{k}-\bar{x}\right)^{2}},\] (115) where \(\bar{x}\) is the AAV. * Difference of Absolute Standard Deviation (DASDV) DASDV is similar to RMS since it is the standard deviation from wavelength [84]; it is defined by \[\text{DASDV}=\sqrt{\frac{1}{N-1}\sum_{k=1}^{N-1}\left(x_{k+1}-x_{k}\right)^{2}}.\] (116)
* Log-Detector (LOG) This feature provides an estimate of the strength of muscle contraction [85]. However, its definition is changed to be based on logarithm feature and record detector [82]. LOG can be calculated as: \[\text{LOG}=\exp\left(\frac{1}{N}\sum_{k=1}^{N}\log\lvert x_{k}\rvert\right).\] (117)
* Myopulse Percentage rate (MYOP) MYOP is a myopulse output averaged value, which is defined as \"1\" when the EMG signal absolute value exceeds a determined lower bound \(L\)[81]. Mathematically, it is calculated by: \[\text{MYOP}=\frac{1}{N}\sum_{k=1}^{N}\phi(x_{k}),\] (118) where \[\phi(x)= \begin{cases}1,&\text{if }x>L,\\ 0,&\text{otherwise}.\end{cases} \]
* Absolute Value of the Third, Fourth and Fifth Temporal Moments (TM3, TM4 and TM5) Temporal moment is a statistical analysis proposed by [PERSON] and [PERSON] [86]. The first and the second temporal moments are the absolute values of AAV and VAR, and the next three are defined as \[\text{TM3}=\left\lvert\frac{1}{N}\sum_{k=1}^{N}x_{k}^{3}\right\rvert,\] (119)\[\text{TM4} =\left|\frac{1}{N}\sum_{k=1}^{N}x_{k}^{4}\right|, \tag{20}\] \[\text{TM5} =\left|\frac{1}{N}\sum_{k=1}^{N}x_{k}^{5}\right|. \tag{21}\]
* Histogram (HIST) This feature parts elements in EMG signal into M segments, which have to be equally spaced. Finally, HIST returns a number of signal elements for each segment [82]. A suggested number for M is 9. * _v_-Order (V) V is a non-linear detector that computes implicitly the strength of a muscular contraction. It is defined from a functional mathematical model of EMG signal generation, given by the expression \[s_{k}=(\gamma m_{k}^{\alpha})n_{i},\] where \(\gamma\) and \(\alpha\) are constants and \(n_{i}\) is a class of the ergodic Gaussian processes; \(\alpha\) is theoretically 0.5, but a rate between 1 and 1.75 was obtained experimentally [87]. An optimal value for V has been reported as 2 [85], which leads to the same definition of RMS. The mathematical definition of V is \[\text{V}=\left(\frac{1}{N}\sum_{k=1}^{N}x_{k}^{v}\right)^{1/v}.\] (22)
* Mean Absolute Value Slope (MAVSLP) MAVSLP is a by-product of MAV; it computes differences between adjacent MAV segments [88]. Its equation is given by \[\text{MAVSLP}_{i}=\text{MAV}_{i+1}-\text{MAV}_{i},\] (23) where \(i=1\),..., \(I\) is the number of segments covering the EMG signal. However, with a higher number of segments, its definition approaches that of a traditional MAV feature.