# Toward Improving the Reliability of Discrete Movement Recognition of sEMG Signals
## 4 Proposed Methods
### GMM-kNN Fusion with a Reject Option  
As a nonparametric method, kNN is one of the most widely adopted classification algorithms. Though it is simple to implement, it is shown that kNN can produce classifiers with performance close to the optimal Bayes classifier [42; 43; 44]. KNN does not make any assumptions about the data, and it can be used on many occasions. The limitation of kNN is that it compares the test sample with the training data each time a decision on the test sample is demanded, so it requires a lot of memory and is computationally expensive [45]. We have conducted a study on recognizing the 12 hand movements of 10 repetitions with sEMG signals collected from 27 subjects using GMM and kNN classifiers. When the first five repetitions are used as training samples, and the rest five are used as test samples, the result is shown in Figure 1. It can be observed from Figure 1 that the classification accuracy of kNN is superior to GMM in both its higher accuracy and lower standard deviation. However, the computational cost of kNN is much higher than GMM. The analysis shows that the average computational time for recognizing the sEMG signals for one movement by kNN is nearly 260 ms, almost 80 times more than GMM. Considering the characteristics of kNN and GMM, we propose a two-layer classification scheme, which may take advantage of the two classifiers to improve the classification performance efficiently. The classifier is named GMM-kNN fusion with a reject option (GK-R). The proposed model consists of two layers, as shown in Figure 2. The first layer is a GMM-R classifier. The test sample will be sent to the GMM-R classifier for decision at first. If the maximum percentage is larger than the predefined threshold, the class label corresponding to the maximum percentage will be assigned to the test samples. Otherwise, the decision on the test sample is up to the second layer, which is a kNN with a reject option (kNN-R) classifier. The kNN-R classifier conducts a similar post-processing method on the  
Figure 1: Comparison of k-nearest neighbor (kNN) and Gaussian mixture model (GMM) for movement recognizing. (**a**) Comparison of classification accuracy. The \(K\) in kNN is six, and the number of Gaussian components in GMM is three; (**b**) Comparison of average time cost for recognizing one movement. class labels of each observation to what GMM does. Suppose the percentage of each class label obtained by kNN is \(\text{K}_{1},\ldots,\text{K}_{C}\); the predicted class label can be determined as follows. \[\hat{k}=\underset{c\in\text{1C}}{\text{argmax}}\ K_{c} \tag{12}\]  
Suppose \(\delta_{k}\) is a predefined threshold used to evaluate the validity of the prediction by the second-layer classifier. Then the decision on the test sample **X** will be determined by two factors: the maximum percentage obtained by kNN and the predicted class label by the GMM-R and kNN-R classifier. When the two classifiers make the same prediction, or the maximum percentage obtained by kNN is higher than the predefined threshold, the predicted class label will be assigned to the test sample. Otherwise, the test sample will be labeled as \"no motion\". The final decision can be expressed as follows. \[f(\textbf{X})=\left\{ \begin{array}{l}\hat{k},\text{ if }\text{K}_{\hat{k}} \geq\delta_{k}\text{ }\text{or }\hat{g}=\hat{k}\\ \hat{\text{C}},\text{ otherwise}\end{array} \right. \tag{13}\]  
where \(\hat{\text{C}}\) represents the prediction is rejected, and the movement will be labeled as \"no motion\". The corresponding class label is 0. The following classifiers are applied to prove the effectiveness of the proposed classification scheme. * LDA-R(LDA with majority voting and a reject option). LDA-R is an extension to LDA. For each observation in test samples, the conventional LDA will assign a class label to it. Unlike the study in [24], a majority voting is performed to the series of class labels. The percentages of observations that fall into each class are obtained. Thresholding is performed on the maximum percentages.