3.1. 3D Pose Data Acquisition Based on Inertial Sensors and Pose Motion Capture

Cheerleading is a comprehensive sports activity that combines dance, gymnastics, and music, emphasizing the smoothness and coordination of movements. Due to the complexity and diversity of cheerleading movements, there are non physical dependencies between body joints, which increases the difficulty of action recognition ^[14]. In order to accurately extract and analyze these joint relationships, the human skeleton diagram is introduced in the study. By constructing a human skeleton diagram, the connection and interaction relationships of each joint in cheerleading exercise can be intuitively represented. The skeleton relationship diagram of the cheerleading action drawn is shown in Fig. 1.

Fig. 1. Skeleton of cheerleading athletes.

Fig. 1 shows the original movement and simplified skeleton of a cheerleader. From Fig. 1, multiple human skeleton vertices represent joint points, while connecting lines represent edges of the skeleton graph. Once fully connected, it can represent the attribute relationships between joints. Cheerleading exercises involve highly coordinated multi-joint movements (such as synchronized arm swings and leg jumps) that have non physical dependencies between joints. Traditional action recognition methods, such as CNN, are difficult to model such complex spatial relationships due to their inability to directly process non-Euclidean data. Therefore, this study chose GCN as the basic framework. GCN excels in processing graph structured data (such as human skeletal maps) and achieves feature propagation by encoding joint connections through adjacency matrices. This network structure can extend CNN from regular grids to unordered graphs of arbitrary structures, using skeleton information images as input to analyze the motion patterns of target objects ^{[15, 16]}. The main structure of GCN is shown in Fig. 2.

Fig. 2. GCN structure diagram.

The GCN structure in Fig. 2 is similar to the CNN structure, consisting of an input layer, a graph convolutional layer, and an output layer. GCN typically utilizes the feature information of nodes and their neighboring nodes in the graph to obtain feature vectors through weighted averaging, thereby increasing the weight of nodes with lower degrees. Then, these feature vectors are trained and learned through neural networks to effectively utilize the structural information of the graph ^[17]. GCN calculates the new feature representation of the current node by weighted averaging the features of neighboring nodes, which can be achieved through matrix multiplication. The propagation mode between GCN layers is shown in Eq. (1) ^[18].

In Eq. (1), $A$ represents the adjacency matrix. $\tilde{A}$ represents adding an identity matrix based on the adjacency matrix. $H^{(l)}$ represents the features of layer $l$. $\sigma$ signifies the nonlinear activation function. $W^{(l)}$ represents the current trainable parameter matrix. $\tilde{D}$ represents the degree matrix of $\tilde{A}$. $\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}}$ represents matrix normalization processing. The propagation mode $z$ of the entire GCN layer is shown in Eq. (2).

In Eq. (2), $W^{(0)}$ signifies the observable parameters of the input layer. $X$ represents a multidimensional eigenvector matrix. However, traditional GCN has two major limitations in cheerleading action recognition: firstly, the pre-defined adjacency matrix of GCN can only represent binary joint relationships (such as “hand elbow”), and cannot model high-order interactions (such as the collaborative relationship between “hand waist foot” in lifting actions); Secondly, cheerleading movements have spatiotemporal characteristics and require joint analysis of multiple frame motion sequences. To address these issues, the study upgraded GCN to Hypergraph Convolutional Network (HGCN). Unlike GCN, HGCN uses hyperedges to group multiple joints (such as simultaneously connecting hands, waist, and feet during lifting actions), thus modeling complex multi-joint dependencies ^{[19, 20]}. For example, a hyperedge in HGCN can simultaneously represent the collaborative relationship of three joints, which is crucial for capturing cheerleading specific movements.

3.2. Design of Action Recognition Algorithm for Cheerleaders Based on ISTHC

Although traditional HGCN has significant advantages in extracting high-order feature information using hyperedges, it can effectively simulate the relationships among multiple joints. However, the HGCN has shortcomings in handling coordinated movements of distant joints such as hands and feet, especially in recognizing cheerleading movements involving synchronized movements of the upper and lower body ^[21]. Therefore, in order to accurately identify the technical movements of cheerleading, an improved hypergraph convolutional network (IHGCN) is proposed. The framework structure of IHGCN is shown in Fig. 3.

Fig. 3. IHGCN structure diagram.

In Fig. 3, IHGCN mainly consists of two parts: SAM module and topology module. To further optimize, the study introduced SAM, which dynamically assigns weights based on the importance of joints in specific actions. Although HGCN provides a hypergraph structure, its edge weights are still static. SAM can adaptively strengthen key joints (such as arms in swinging movements) and weaken secondary joints (such as head fine-tuning), thereby improving feature discrimination.

In the IHGCN model, a triplet in the hypergraph contains a set of hyperedges $E$, a set of vertices $V$, and a weight matrix $W$ for each edge. $v$, $e$ and $w$ respectively represent the weight matrices of a vertex, a connecting edge, and an edge. The convolution operation in IHGCN is shown in Eq. (3) ^[22].

In Eq. (3), $\sigma$ represents the nonlinear activation function. $H$ and $H^T$ respectively represent hypergraphs and their transposes. $w^l$ signifies the weight matrix of the 3D action sequence. $x^l$ represents the parameter matrix of the 3D action sequence. $W$ signifies the weight matrix of the hyperedge. $W^l$ signifies the parameter matrix of the hyperedge. $D_v$ represents the diagonal matrix of vertex degrees. $D_e$ represents the diagonal matrix of hyperedges. $H_m$ represents the adjacency matrix transformed from $H$. Through SAM, it is easy to obtain the representation of the initial correlation matrix of bone joints in both temporal and spatial dimensions. The temporal channel module refers to the ability to allocate attention weight values for each frame of the video action sequence in a reasonable manner, so that important dynamic joints can be identified and unimportant dynamic joints can be eliminated. The output layer of the self-attention layer after temporal channel optimization is shown in Eq. (4).

In Eq. (4), $\alpha$ represents the attention matrix. After obtaining the output of the attention layer, the function $\tau$ is used to refine each frame of the hypergraph, as shown in Eq. (5).

In Eq. (5), $H_m$ represents the adjacency matrix derived from the hypergraph transformation. $H_t$ represents Time Sparse Hypergraph (TTH). The channel module is similar to a general CNN, which has independent spatial kernels to capture different spatial information. The channel module proposed in this study can dynamically recommend a unique hypergraph convolution kernel for each channel, allowing joint connections under different motion forms to be split and refined. After the convolution operation is completed, it is re-aggregated to obtain the final Channel Sparse Hypergraph (CTH). The process of generating CTH is shown in Eq. (6).

In Eq. (6), $\Omega$ represents an increasing function. $M$ represents the aggregation function. $C$ represents the push function. $W_\alpha$ and $W_\beta$ both belong to the weight matrix. The construction mode of dynamic recommendation is shown in Eq. (7).

In Eq. (7), all algebraic meanings remain the same as before. By reducing the dimensionality of input data, the difficulty of dynamic push can be reduced, making it easier to obtain the joint relationship matrix for each sample. The adjacency matrix of feature channels for different actions is shown in Eq. (8).

In Eq. (8), $W_\gamma$ represents the weight matrix. Due to the complexity of general action temporal series and channel sequences, in order to improve the spatiotemporal relationship of the fused hypergraph joints, the study introduces Spatio-Temporal Hypergraph Convolution (STHC) to establish a spatiotemporal relationship window for multiple joints ^[23]. Each action sequence is window decomposed and finally combined, as shown in Eq. (9).

In Eq. (9), $H^\zeta$ represents the combined spatiotemporal hypergraph. $\zeta$ represents a hyperedge frame. $R^{N \times T \times E}$ is the spatio-temporal feature matrix obtained by window update, and its dimension is $N \times T \times E$, where $N$ represents the number of joints, $T$ represents the time step, and $E$ represents the number of feature channels. By continuously updating the window, feature $X^*$ can be obtained, as shown in Eq. (10).

Finally, to reduce timing and channel redundancy, the study integrated TTH and CTH. TTH prunes redundant frames in the temporal sequence (such as transition poses between jumping actions), while CTH optimizes the channel dimension feature map to focus on task related joints. These modules together form the Improved Spatiotemporal Hypergraph Convolution (ISTHC) framework, which achieves unified modeling of spatial, temporal, and channel dimensions. The ISTHC framework is shown in Fig. 4.

Fig. 4. ISTHC structure diagram.

In Fig. 4, the entire model adds the STHC module based on the IHGCN framework. Firstly, HGCN performs hypernode feature extraction on the technical action data of the original cheerleader. Secondly, TTH is performed in SAM, and CTH is performed in the topology module. Afterwards, STHC is used to perform window segmentation and recombination on the fused hypergraph of refined and channel hypergraphs, in order to extract more diverse motion joints of cheerleaders.

4.1. The Ablation Test Results of ISTHC Model

A high-level experimental platform is constructed for comparative testing. The hardware configuration of the experimental platform includes Intel® Core™ i9-10900K CPU @ 3.70GHz$\times$32, and NVIDIA GeForce RTX 3080 GPU. All data are run on the PyTorch framework with weight decay set to 0.002. Two publicly available bone datasets are selected for the experiment, PoseTrack and DanceTrack. PoseTrack is a video sequence dataset containing over 150000 human motion poses, suitable for various motion scenarios. DanceTrack is a large dataset focused on various dance movements, containing 50 different types of dance movements, with a total of approximately 70000 samples. During the experiment, a total of 20000 preprocessed valid data are collected from two datasets and divided into training and testing sets in an 8:2 ratio. The final ISTHC model is composed of multiple components, including HGCN, SAM, TTH, CTH, and STHC. It is necessary to first use ablation experiments to test the impact of different modules on the entire ISTHC algorithm model. HGCN-SAM, HGCN-SAM-TTR, HGCN-SAM-CTH, and ISTHC are compared. The action recognition accuracy is shown in Fig. 5.

Figs. 5(a) and 5(b) show the recognition accuracy of four ablation combinations, respectively. From Fig. 5(a), compared with the other three combinations, the recognition performance of HGCN combined with SAM was poor, and the highest recognition accuracy of this combination in the training set was only 94.1%. On the basis of HGCN-SAM, two modules, TTR and CTH were added separately to obtain HGCN-SAM-TTR and HGCN-SAM-CTH. It was found that the highest recognition accuracy of these two combinations in the training set was 95.8% and 96.2%, respectively. After adding TTR module and CTH module to HGCN-SAM, the overall performance of the algorithm was significantly improved. As shown in Fig. 5(b), ISTHC had the best recognition performance compared with the other three ablation combinations, with a recognition accuracy of 97.9% in the testing set. The recognition time of four ablation combinations on different datasets during the testing process is compared, as shown in Fig. 6.

Fig. 5. Recognition accuracy of different combinations.

Fig. 6. Recognition time of different combinations.

Fig. 6 shows the recognition time variation values of four ablation combinations during the testing process. As shown in Fig. 6, with the increase of sample size, the recognition time of the four ablation combinations fluctuated to varying degrees, and the fluctuation range of ISTHC was the smallest. Overall, the average recognition time of HGCN-SAM, HGCN-SAM-TTR, HGCN-SAM-CTH, and ISTHC during the testing of 1000 samples was 0.19s, 0.16s, 0.15s, and 0.07s, respectively. The average recognition time of ISTHC is lower compared with the other three ablation combinations, indicating that this combination has a faster recognition speed and higher efficiency.

4.2. Performance Comparison Testing of Different Algorithms

In addition to conducting ablation tests on ISTHC, the study further introduces other models from relevant fields for comparison to verify the good performance of ISTHC. Traditional HGCN, reference ^[24], and improved GCN from reference ^[25]are selected as comparison models, with loss values as reference indicators. The changes in loss curves of the four models in the training and testing sets are shown in Fig. 7.

Figs. 7(a) and 7(b) show the changes in loss curves of HGCN, reference ^[24], reference ^[25], and ISTHC in the training and testing sets, respectively. From Fig. 7, the loss values of ISTHC reached a stable state quickly in both datasets, while the other three models required longer iterations to reach stability. According to Fig. 7(a), HGCN, reference ^[24], reference ^[25], and ISTHC reached a stable state after 118, 82, 86, and 37 iterations, respectively. Similarly, in Fig. 7(b), HGCN, reference ^[24], reference ^[25], and ISTHC reached a stable state after 112, 85, 89, and 56 iterations, respectively. Overall, ISTHC has the best iterative performance and good stability, which can quickly adapt to the action recognition work of cheerleaders. In order to more accurately quantify the performance comparison results of various models, the study tests the above models using precision, recall, F1, Mean Squared Error (MSE), and Mean Absolute Error (MAE) as reference indicators, as displayed in Table 1.

Fig. 7. Loss curves of the four comparison models.

According to Table 1, ISTHC had better benchmark performance compared with HGCN, reference ^[24], and reference ^[25], with precision, recall, and F1 values as high as 0.96, 0.98, and 0.97, respectively. Traditional HGCN had the worst benchmark performance, with precision, recall, and F1 values as low as 0.75, 0.82, and 0.78, respectively. In addition, ISTHC also performed the best in terms of error, with MSE values of 0.43, 0.25, 0.26, and 0.12 for HGCN, reference ^[24], reference ^[25], and ISTHC, and MAE values of 0.58, 0.35, 0.32, and 0.25, respectively. In summary, the benchmark performance of the new algorithm proposed in the study is the best, with more stable and superior recognition ability compared with similar recognition algorithms.

4.3. Analysis of Model Application Effectiveness

To verify the recognition performance of the ISTHC in practical applications, the study first collects and preprocesses the 3D pose data of cheerleaders based on inertial sensors. Secondly, the posture dataset is divided into four categories: basic actions, formation transformation actions, strength actions, and difficulty actions, each containing different specific actions. The processed pose dataset is used to test the performance of four models in practical applications. The accuracy of different models in recognizing various actions is displayed in Table 2.

According to Table 2, the accuracy of ISTHC in identifying 9 different cheerleading movements was above 95%, with the highest accuracy of 99.2% for identifying swinging arm action. The accuracy of identifying global transformation was relatively low, only at 96.3%. The accuracy of the model in reference ^[25] in identifying various cheerleading movements reached as high as 92.1% and as low as 89.5%. The accuracy of the model in reference ^[24] in identifying various cheerleading movements reached as high as 89.4% and as low as 86.3%. The actual performance of the HGCN is the worst, with the highest accuracy of identifying various cheerleading movements being only 85.5% and the lowest being 81.9%. The human bone matching points of cheerleading movements identified by four models are compared, as shown in Fig. 8.

The four subgraphs in Fig. 8 respectively show the bone point matching of HGCN, reference ^[24], reference ^[25], and ISTHC models for identifying a cheerleading action. Based on Fig. 8, ISTHC performs the best in matching bone points in practical recognition problems, which can accurately identify various key bone points in cheerleading movements.

Fig. 8. Bone point anastomosing performance of cheerleading movement recognized by different models.

Table 3 provides a detailed comparison of the performance of five different algorithms (OpenPose, 3D CNN, ST-GCN, Transformer, and ISTHC) in human pose estimation tasks from three key dimensions of accuracy, real-time performance, and computational efficiency. In terms of accuracy, ISTHC performs best in conventional, occlused-out and low-light scenes, with accuracy rates of 97.60%, 94.50% and 93.80%, respectively, while the accuracy of other algorithms such as Transformer, ST-GCN, 3D CNN and OpenPose decreases in turn. In terms of real-time performance, ISTHC has the lowest processing delay (0.1 ms/frame) and the highest maximum frame rate (1000fps), far exceeding other algorithms, while algorithms such as OpenPose and Transformer lag behind in terms of processing delay and frame rate. In terms of computational efficiency, ISTHC has the smallest number of parameters (1.2M) and the shortest training time (4.9 hours), compared with 3D CNN and OpenPose, which have higher number of parameters and training time. Overall, ISTHC performs best in the task of human pose estimation, especially in the accuracy and real-time performance, while other algorithms have shortcomings in some aspects.