# Sensor-Based Hand Gesture Detection and Recognition by Key Intervals
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Training Set** & **180** & **320** & **450** & **590** & **750** \\
**Size \(M_{\text{TR}}\)** & & & & & \\ \hline \(r=0.1\) & 0.857 & 0.892 & 0.910 & 0.921 & 0.926 \\ \(r=0.2\) & 0.915 & 0.917 & 0.923 & 0.935 & 0.938 \\ \(r=0.3\) & 0.920 & 0.938 & 0.940 & 0.941 & 0.954 \\ \(r=0.4\) & 0.939 & 0.940 & 0.943 & 0.944 & 0.953 \\ \(r=0.5\) & 0.941 & 0.952 & 0.955 & 0.955 & 0.957 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The AUROC performance of the proposed algorithm with various training set sizes \(M_{\text{TR}}\) and various values of ITR ratio \(r\). The AUROC measurements were based on the same testing set. We next considered the classification performance for the correctly detected foreground gestures. Table 4 shows the corresponding confusion matrix of the proposed algorithm with \(r=0.3\). The corresponding neural network was trained by a set with size \(M_{\text{\tiny IR}}=750\). Each cell in the confusion matrix represents the percentage of the gesture in the corresponding row classified as the gesture in the corresponding column. Let \(Q_{i}\) be the classification accuracy of gesture class \(i\), which is defined as the number of gestures in class \(i\) that are correctly classified divided by the total number of gestures in class \(i\). Therefore, \(Q_{i}\) is the value of the cell in the \(i\)th column and \(i\)th row of the confusion matrix. As revealed in Table 4, the proposed algorithm attains a high classification accuracy \(Q_{i}\) for all the gesture classes. The proposed algorithm is also able to operate in conjunction with other classification algorithms. In these cases, the proposed algorithm serves only as the gesture detector. Existing gesture classification techniques such as support vector machine (SVM) [6], LSTM [7], bidirectional LSTM (Bi-LSTM) [17], CNN [18], and Residual PairNet [19] can then be adopted to classify the detected gestures. Table 5 shows the classification accuracies of these classification algorithms. For comparison purpose, the proposed algorithm for both detection and classification was also considered in Table 5. We can see from the table that the proposed algorithm outperforms the other algorithms for classification. This is because the joint training of both detection and classification in the proposed algorithm is beneficial for simultaneous detection and classification. That is, when PKI and SKI are matched, the corresponding class is the gesture class of the detected gesture. No other additional efforts are needed for the classification. In addition to the separate evaluation of detection and classification, the combined evaluation was also considered in this study. To carry out the evaluation, we considered a sequence of gestures as a string of characters, where each character corresponds to a gesture. The alphabet of the characters was the set of all the foreground gesture classes. The evaluation of the classification results of a gesture sequence was then based on the edit distance [35] between two strings, where one string corresponds to the ground truth of the sequence, and the other is the classification results of the sequence. In the edit distance between two strings, the displacements, deletions, and insertions of characters from one string to the other are taken into consideration [35]. A displacement \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Gest. 1** & **Gest. 2** & **Gest 3** & **Gest. 4** & **Gest. 5** \\ \hline Gest. 1 & 100.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ Gest. 2 & 0.50 & 99.25 & 0.00 & 0.25 & 0.00 \\ Gest. 3 & 0.00 & 0.00 & 100.00 & 0.00 & 0.00 \\ Gest. 4 & 0.00 & 0.00 & 0.45 & 99.55 & 0.00 \\ Gest. 5 & 0.00 & 0.53 & 0.00 & 0.00 & 99.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The confusion matrix on the correctly detected foreground gestures for the proposed algorithm with \(M_{\text{\tiny IR}}=750\) and \(r=0.3\).