# Sign Language Sentence Recognition Using Hybrid Graph Embedding and Adaptive Convolutional Networks
## 3 Proposed Hybrid Graph Embedding and Adaptive Convolution Networks
### Feature Extraction
Fusion and optimization techniques are employed to refine the extracted features, integrate multimodal features, and reduce redundancy through dimensionality reduction methods like PCA or LDA. The final step, output feature vectors, represents the optimized dataset, ready for classification models. This structured approach eliminates redundancy and enhances clarity in feature extraction. \[\text{L}_{\text{total}}=\Big{\{}\text{L}_{\text{glove}},\text{L}_{\text{pose}} \Big{\}}, \tag{3}\]  
In Equation (3), the following can be noted: \(\text{L}_{\text{glove}}\): Hand glove landmarks record delicate finger and hand movements, and \(\text{L}_{\text{pose}}\): position landmarks describe the body's posture and movements. Dimensions: \(\Big{\{}\text{L}_{\text{glove}},\text{L}_{\text{pose}}\Big{\}}\in\mathbb{R}^{ N\times 3}\), where \(N\) is the number of keypoints with 3D spatial coordinates. The landmark set captures every key component of human communication for downstream processing. The Landmark Feature Vector representation for each landmark \(i\) in a frame is a high-dimensional feature vector:  
\[\text{X}_{\text{i}}=\left[\text{p}_{\text{x}}\,,\text{p}_{\text{y}},\text{p}_{ \text{z}},\text{v}_{\text{x}},\text{v}_{\text{y}},\text{v}_{\text{z}},\text{c }\right] \tag{4}\]  
In Equation (4), \(\text{p}_{\text{x}}\,\text{p}_{\text{y}}\), and \(\text{p}_{\text{z}}\) represent 3D spatial coordinates for the precise location of the landmark. \(\text{v}_{\text{x}},\text{v}_{\text{y}},\text{ and }\text{v}_{\text{z}}\) represent velocity components for encoding the motion dynamics of the landmark over time. \(\text{c}\) represents the confidence score, indicating the reliability of the detected landmark as determined by MediaPipe. Position components: \(\text{p}_{\text{x}}\), \(\text{p}_{\text{y}}\), and \(\text{p}_{\text{z}}\) in meters (\(\mathbb{R}^{3}\)). Velocity components: \(\text{v}_{\text{x}},\text{v}_{\text{y}}\), and \(\text{v}_{\text{z}}\) in meters per second (\(\mathbb{R}^{3}\)). Dimension: \(X_{i}\in\mathbb{R}^{7}\) for each keypoint. Velocity components measure landmark position changes throughout time. Use finite differences as calculated in Equation (5) as follows:  
\[ \begin{array}{l}\text{v}_{\text{x}}=\frac{\text{v}_{\text{x}+1}-\text{x}_{ \text{y}}}{\Delta_{\text{t}}},\\ \text{v}_{\text{y}}=\frac{\text{v}_{\text{y}+1}-\text{y}_{\text{z}}}{\Delta_{ \text{t}}},\\ \text{v}_{\text{z}}=\frac{\text{v}_{\text{z}+1}-\text{z}_{\text{z}}}{\Delta_{ \text{t}}}\end{array}  \tag{5}\]  
In Equation (5), Dimension: \(\text{v}_{\text{x}},\text{v}_{\text{y}},\text{and }\text{v}_{\text{z}}\in\mathbb{R}\) measured in meters per second (m/s). Gesture identification requires time information because movement sequences have semantic significance. To gather information from users, the system makes use of wearable gadgets. The wearable gadgets have sensors built in so they can record your hand motions and gestures. A variety of sensors, including magnetometers, accelerometers, and gyroscopes, are built into the wearable gadgets to record hand motions and orientation from various angles. Figure 2b shows the configuration used during this operation, which uses the WULALA data glove hardware space. Figure 2b shows the WULALA data glove specifications, not the processing environment. Figure 2c shows the captured sign language gesture using a sample glove sensor. In Figure 2c, the accuracy of sign language identification is enhanced through the fusion of multiple sensor data streams, including motion, curvature, and inertial sensor readings. This fusion process reduces inconsistencies in gesture recognition by integrating complementary information from different modalities. Before fusion, individual sensor data may contain noise or missing values, leading to potential misclassification. After fusion, the combined dataset provides a more comprehensive motion trajectory, improving recognition reliability.