A New Feature Extraction Method for EMG Signals

2.1 Database

In this section, the used sEMG database (CapgMyo) is described, which includes sEMG data of 23 intact subjects [26, 27]. The database was recorded using 8 acquisition modules, and each module has 16 differential electrodes. Each gesture was repeated 10 times and held between 3s and 10s. There are three acquisition procedures for CapgMyo database, and as a result of these procedures, the database consists of three sub-databases (DB-a, DB-b, and DB-c). While DB-a database has 8 hand gestures of 18 subjects which can be seen in Table 1, DB-b has 8 hand gestures of 10 subjects. DB-c has 12 hand gestures of 10 subjects and was held for 3s. As a pre-processing process, 45-55Hz bandstop filter was applied to eliminate power line interference.

2.2 Feature extraction methods

The feature extraction process was carried out on segmented data. A sliding window method was used for the segmentation. After trying different window lengths and increments, it is found that 250ms window length and 64ms increment gave the best classification results. AR, ST methods, which are frequently used in the literature and have high score values, and the new feature extraction method were employed to extract features from each segment of the data. The detailed explanations of the feature extraction methods are presented in the sub-sections below.

2.2.1 AR Features

The AR features are most popular EMG features [3], and uses a linear combination of the previous samples $X_{i-p}$  and a white noise error term $w_i$ to describe each sample of the EMG signal as follows

$X_i=\frac{1}{N} \sum_{m=1}^p a_m X_{i-m}+w_i$        (1)

where, p is the order of the AR model, and classifiers use $a_{\mathrm{m}}$ coefficients as features.

2.2.2 ST Features

ST is the extension of WT using Morlet wavelet as basic wavelet. ST has a superior property that moving function changes with time. Moving and scalable localizing window (Gaussian window) gives time localization property for signals [28]. ST method transforms x(t) signal into time-frequency domain as follows

 $s(t, f)=\int_{-\infty}^{\infty} x(t) w(t-\tau, f) e^{-2 \pi i f \tau} d \tau$              (2)

where, $w(t-\tau, f)$ is called as window function and can be expanded to form ST as follows

$s(t, f)=\int_{-\infty}^{\infty} x(t) \frac{1}{\sigma(f) \sqrt{2 \pi}} e^{\left((t-\tau)^2\right) /\left(2 \sigma f^2\right)} e^{-2 \pi i f \tau} d \tau$              (3)

where, τ controls the position of the window over time, $\sigma(f)$ is the standard deviation of the moving window and calculated as follows

$\sigma(f)=\frac{1}{|f|}$             (4)

The performance of ST can be improved when the standard deviation of the moving window is changed as follows

$\sigma(f)=\frac{1}{a+b / \sqrt{f}}$         (5)

Table 1. Gestures in DB-a and DB-b

1.	Tumb up	t1.jpg	5.	Abduction of all fingers	t2.jpg
2.	Extension of index and middle, flexion of the others	t3.jpg	6.	Fingers flexed together in fist	t4.jpg
3.	Flexion of ring and little finger, extension of the others	t5.jpg	7.	Pointing index	t6.jpg
4.	Thumb opposing base of little finger	t7.jpg	8.	Adduction of extended fingers	t8.jpg

where, the values of a and b are varying between 0 and 1. Using the new $\sigma(f)$, the Gaussian window can be written as

$w(t, f)=\frac{a+b \sqrt{f}}{k \sqrt{2 \pi}} e^{\left((a+b \sqrt{f})^2 t^2\right) /\left(2 k^2\right)}$                (6)

where, $k<\sqrt{a^2+b^2}$. ST can now be formulated as follows

$s(t, f)=\int_{-\infty}^{\infty} x(\alpha+f) e^{\left(-2 \pi^2 \alpha^2 k^2\right) /(a+b \sqrt{|f|})^2} e^{2 \pi i \alpha \tau} d \alpha$           (7)

Mean value, standard deviation, energy, entropy, and kurtosis values of the ST signals are used as features. These values are calculated as follows

Mean $=\frac{1}{n+j} \sum a b s(s(j, n))$                 (8)

where, abs is the absolute value of the complex signal, and s(j,n) is the transformed signal.

St. Dev. $=\sqrt{\frac{1}{n+j} \sum(\operatorname{abs}(s(j, n))-\operatorname{Mean}(s))^2}$          (9)

Energy $=\sum(\operatorname{abs}(s(j, n)))^2$               (10)

Entropy $=\sum-P(s(j, n)) \log (P(s(j, n)))$              (11)

P(s(j,n)) is the probability distribution of s(j,n).

Kurtosis $=\frac{\frac{1}{n+j} \sum(a b s(s(j, n))-\operatorname{Mean}(s))^4}{\left(\frac{1}{n+j} \sum(a b s(s(j, n))-\operatorname{Mean}(s))^2\right)^\quad\quad2}$                (12)

2.2.3 AR coefficients of positive and negative regions

Although most of the time domain features are based on the statistical properties of the data, their classification accuracies are generally low except AR coefficients. Therefore, a new feature extraction method, which is based on AR coefficients of the sum of the samples in the positive and negative regions, is proposed for EMG signal classification. The first step of the new method is to sum the samples in positive and negative regions as follows

$A_{\mathrm{n}}=\sum_{i=1}^{N_n} x_i$              (13)

where, n is the index number of the region, $N_n$ is the number of samples of the positive or negative regions. The graphical representation of this process can also be seen in Figure 1.

f1.png

Figure 1. Summation of the positive and negative regions

The AR coefficients of the sum of samples in the regions can be expressed mathematically as follows

$A_i=\frac{1}{N} \sum_{m=1}^p a_m A_{i-m}+w_i$                 (14)

To evaluate the accuracy of the new feature and multiple classifier method, the CapgMyo database with three sub-databases (DB-a, DB-b, and DB-c) was processed with software written in MATLAB. 10-fold cross-validation methods were run. 10-fold cross-validation calculates the average performance of the tests and in each iteration uses one tenth of the data. As a first evaluation, individual performances of the new feature and all high scored features were investigated and the classification accuracy results can be seen in Table 2. As can be seen from Table 2, the LDA algorithm has poorly performed in EMG signals classification for all individual features. The single and multiple classifier results of the new feature have high classification accuracy with the DB-a and SVM algorithm. Nevertheless, KNN algorithm with the new feature seems not suitable for multi classifier method due to its low accuracy. The reason for this is to decrease the number of features in the feature space causes the classification results to have higher rates of error.

Considering the average performance of the new feature for the SVM algorithm, it can be observed from the results in Table 2 that when a single classifier is used, it gives better results than all features. However, when a multiple classifier is used, the result of the ST feature is better. It can also be seen that the multiple classifier results increase the classification accuracy.

In the second study, AR and ST features which have the best classification results were used with the new feature to increase the classification performance. The classification results of the algorithms for these combined features are shown in Table 3. The SVM algorithm seems to give the best results when the three features are used together. It is seen from Table 3 that single and multiple classifier results for the SVM are very close to each other. In fact, the results of the KNN algorithm for three features were quite high except for the DB-a database. However, the low classification result in the DB-a database reduced the average single classifier result of the KNN algorithm. It can be seen from these results that the classification results of the features are different for each database and the combination of the features will increase the classification results. When the results are evaluated in terms of the number of classifiers, the single classifier results of the SVM algorithm are quite good. The use of multiple classifiers in the LDA algorithm increases the classification accuracy but decreases in the KNN algorithm. The problem of the KNN algorithm consists of the new feature. If this study is compared with the study of Du [27], Du achieved 99.1% classification accuracy in DB-a, DB-b, and DB-c by using ConvNet and the majority voting method. In this study, an average of 99.57%. success has been achieved by using the SVM algorithm with the new feature and two high scored features, which can be seem in Table 3. It is known that the computation load of SVM algorithm is lower than ConvNet.

Table 2. Individual feature results of the methods for single and multiple classifier

Table 3. Results of three features for single and multiple classifier