3.1 Overall Design of Student Motion System and Data Preprocessing Optimization Algorithm

The method of association rules is an essential part of data mining, meaning there is a certain relationship between one or several groups of data in the database. PSO is a widely used algorithm derived from bird predation. Combining the two, using the ability of GSA-PSO to converge to optimize the Apriori algorithm, a data mining algorithm for association rules based on PSO was formed, and the optimal association rules were obtained ^[16,17]. The main purpose of the aerobics exercise data analysis system is to achieve rapid convergence and data mining analysis of student exercise data. Fig. 1 shows the overall architecture.

The system in Fig. 1 comprises four parts: data collection, data conversion, hybrid gravity particle swarm algorithm operation module, and the visual interface of the university teaching system, which together constitute the construction of a sports database system. In the overall process, GSA is used to optimize the PSO. The two were combined into a hybrid GSA-PSO algorithm for rule extraction. First, the algorithm assumes that there are a total number of particles in a gravitational system $N$, and the position of particle $i$ is expressed as formula (1).

where ${x}_{i}^{n}$ represents the location of particles in the third dimension space $i$ within the scope of the region. Owing to the influence of gravitation, the particle force $i$ on the particle $d$ in the dimension $t$ can be expressed as formula (2).

Fig. 1. Overall architecture of the system.

where ${F}_{ij}^{d}\left(t\right)$ indicates the force of particles; $M_{i},M_{j}$ represent the gravitational mass of different particles; $\varepsilon $ is a small constant; $G\left(t\right)$ expresses the gravitational constant at a specific time $t$, as the universe time is increased; $G\left(t\right)$ is the gravitational constant at time $t$. The older the universe, the smaller the value of $G\left(t\right)$; $t$ is different specific times; $R_{ij\left(t\right)}$ is the Euclidean distance between different particles at different specific times. The specific expression is shown in the formula (3).

where $G_{0}$ means the initial gravitational constant of the universe, which is generally assigned a value of 1 or 100; $\alpha $ is a constant and is generally assigned a value of 20 or 23; $T$ is the maximum number of iterations. In the actual operation, for the characteristics of randomness integrated into GSA, a random number $d$ is generally assumed in the dimensional space $rand$. The acceleration expression of the particle at any time in space and the basic definition of the gravitational mass can be obtained based on the law of motion. The details are in the following formula (4).

where $a_{i}\left(t\right)$ indicates the acceleration; $m_{i}\left(t\right)$ represents the gravitational mass equal to the value of the inertial mass $F_{i}\left(t\right)$; $f_{i}\left(t\right)$ means the particle fitness function value at a specific time $t$; $f_{worst}\left(t\right)$ indicates the worst fitness function value of the group at a specific time $t$. The expression of mass is expressed as formula (5).

The positions and velocities of different particles can be calculated by combining the above formulae, as expressed as formula (6).

where $v_{id}\left(t+1\right)$ indicates the velocity of the particle at the next time; $randv_{id}\left(t\right)$ refers to the current velocity of the particle; $a_{id}\left(t\right)$ denotes the velocity change or acceleration; $x_{id}\left(t+1\right)$ expresses the position, which is the same as the speed. GSA and PSO are combined to form a hybrid GSA-PSO algorithm to have global search ability and particle information sharing ability simultaneously. formula (7) is the specific expression.

where $c_{1},c_{2}$ represent the learning factor; $r_{1},r_{2},r_{3}$ are any number in the interval $\left[0,1\right]$; $a_{id}\left(t\right)$ denotes the acceleration in the GSA algorithm. The gravitational force of the particle and the ability to exchange global information can reach a state of balance during the optimization by adjusting the value of the learning factor. From the above formula, the acceleration of particles is related to the gravitational algorithm, and the update of the particle speed is related to the local optimal and global optimal positions. All particles within the range have mutual attraction and can perceive and approach the global optimal position ^[18]. The GSA-PSO algorithm is used to optimize and solve the discrete data problem. Fig. 2 presents the method diagram.

Fig. 2. GSA-PSO algorithm optimization diagram for discrete data.

Fig. 2 shows four original data: T1, T2, T3, and T4. These original data are converted to B1, B2, B3, and B4 under the optimization of the GSA-PSO algorithm. That is, assuming that there are four products, for transaction B1, only the first and third products need to be purchased.

3.2 Optimization Method of Student Movement Data Mining based on the GSA-PSO Algorithm

Owing to the large amount of data on college students’ aerobics exercises, and the Apriori algorithm is relatively inefficient for data mining in large-scale databases, the calculation occupies a large amount of computer memory space. The research combines the improved the GSA-PSO algorithm with the Apriori algorithm again. It uses the ability of the improved GSA-PSO to converge quickly to make up for the deficiency of the Apriori algorithm to realize the extraction of optimal association rules ^[19,20]. The new algorithm can be used to extract rules to reduce the computing time and generate redundant rules. Fig. 3 shows the data mining model combined with the algorithm.

Fig. 3. Association rule data mining model under the GSA-PSO algorithm.

The fitness of the individual was evaluated using the PSO objective function as the guidance function to carry out the particle search in the region. In addition, the quantitative evaluation of each individual was set with the fitness function as the evaluation function, which has an impact on the execution efficiency of the algorithm and the quality of the data mining results. The Apriori algorithm was the first association rule mining algorithm and the most classic one. Association rules consume relatively high time and space complexity. Its primary data mining process is divided into two stages: find all high-frequency items from the data collection and find the association rules from these items with higher frequency. Confidence and support are the two most basic and important criteria when mining association rules ^[21]. The expression of the support degree is expressed as formula (8).

where $S\left(A\rightarrow B\right)$ indicates the support degree; $A,B$ are the transactions; $P\left(A\cup B\right)$ is the proportion of the number of transactions in the entire database. The expression of the degree of confidence is shown in the following formula (9).

where $C\left(A\rightarrow B\right)$ represents the confidence, and its internal meaning is the proportion of all events that contain transactions simultaneously. $B$constructs the fitness function using confidence and support. It combines the two and multiplies the corresponding impact factors, sums the results, and uses the obtained sum as the fitness value. Assuming there are particles $x$, the fitness function is expressed as formula (10).

where $C\left(x\right)$ stands for the degree of confidence; $S\left(x\right)$ is the degree of support; $a,b$ are the relevant parameters of the support and confidence in the fitness function, all of which meet the range of the region $\left[0,1\right]$, and the sum of the two parameters is equal to 1. When the support parameter is 0, the association rule contains confidence, and the algorithm, in this case, may fall into rules with high confidence and low support. Similarly, the association rules only contain support when the confidence parameter is 0. In this case, the association rules may miss the vortex of rules with low support and high confidence, and these rules generally have a higher value for the actual situation. In the PSO algorithm, different particles have different velocities, positions, and fitness values at different times ^[22,23]. Assuming there are particles $M$, the speed and position of the particles are updated, as shown in the following formula (11).

where the velocity of a particle at a specific time $t$ is expressed as $v_{id}$; the position is marked as $pbest$; the individual optimal position is labeled as $pbest_{id}$; the group optimal position is denoted as $gbest_{id}$. PSO operation is performed, and the following formula (12) is details.

The above formula performs the particle swarm binary update, as shown in Eq. (13).

where $i$ means the size of the population, and the value range is $\left[1,N\right]$; $sig\left(x\right)$ is the function, and the value range is $\left(0,1\right)$; $d$ expresses the particle space dimension $1,2,\cdots ,D$, and the parameter is $r$; this is because the value range of $sig\left(x\right)$ function on the interval is $\left(0,1\right)$. The speed range of the particle is then satisfied when there is an independent variable $x$, $\left[-10,10\right]$; that is, the maximum speed of the particle is always less than 10. The particle speed in iterative movement increased as the solution approached the local optimal solution. Fig. 4 shows the flow chart of association rule data mining under the GSA-PSO algorithm.

Fig. 4. Flow chart of the association rule data mining under the GSA-PSO algorithm.

4.1 Comparative Analysis of Performance Tests of Different Algorithms

This study first compared the performance of GSA-PSO and PSO algorithms to test the performance of the new hybrid algorithm after combining the GSA and PSO algorithms using the Python language to start the program. The system processor was the Intel (R) Core (TM) i7-8700K CPU@3.70GHz. The system running memory was 16.0GB, and the operating system used Windows 10. The population size was set to 50, and the maximum number of iterations was set to 1000. The experiment selected the Physionet motor imagery data set as the experimental data set, removed 100 error messages in the data set after processing, and used the remaining data as the experimental data set. The data set could be divided into multimodal functions and unimodal functions. The features were evaluated to identify their impact on the predictive outcomes, a critical step in machine learning. In this experiment, no features or all features were used when initially testing the performance of the model. The performance index features were added gradually in the future, and the changes in the performance of the model were observed simultaneously. At the same time, Python tools and datasets were used to visualize the importance of features to evaluate the model. Each obtained basic function was run 20 times, and the average value and variance of each function were calculated, as shown in Fig. 5.

Observing the loss curve of the above algorithm, the loss function of the GSA-PSO algorithm decreased the fastest. After 80K training steps, the loss function could decrease gradually to less than 60, which has remained within the range of 40\textendash{}60. The loss function of the traditional PSO algorithm has been decreasing slowly. After 150K training steps, the loss value decreased to less than 90, and the function fluctuated between 60 and 90. Based on the above results, the loss curve of the proposed GSA-PSO algorithm fluctuated less, and the stability and accuracy were better. The algorithm was then used to compare the fitness of several different algorithms for different kurtosis functions. The population size, number of dimensions, and maximum number of iterations were assumed to be 50, 30, and 1000, respectively. Fig. 6 shows the results of specific conditions.

The proposed GSA-PSO algorithm was more stable in accuracy and had a faster convergence speed than other algorithms, as shown in Fig. 6. In the unimodal function comparison, the GSA-PSO algorithm test was unstable. The PSO algorithm was relatively stable in the unimodal function test, but the fitness function curve was sharp in the multimodal function test. In addition, the IPSODE algorithm was very significant in the multimodal function test but very gentle in the unimodal function test. In the GSA-PSO algorithm, the fitness stabilized when the number of iterations reached 200 in the unimodal function. The fitness began to level off when the number of iterations reached 100 in the multimodal function. By comparison, the feasibility of the GSA-PSO algorithm was the highest. The decision-making performance of the characteristics of college students’ sports was compared using the GSA-PSO-A algorithm, as shown in Fig. 7.

The GSA-PSO-A algorithm, the improved PSO algorithm, the traditional mining algorithm, and the PSO algorithm were compared and analyzed in the change chart of the decision-making performance (Fig. 7). The autocorrelation characteristics of the data information of the student movement evaluation and decision-making system were extracted. The accuracy of the four algorithms for motion decision-making began to increase as the number of adaptive-related features increased. The accuracy growth rate of the proposed algorithm was fastest when the feature was 2, and the growth slope was as high as 97.6%. As the number of features changed, the accuracy of the proposed algorithm was always the best. The accuracy was almost 100% when the number of adaptive feature values was 20. Although the other three algorithms had the fastest increase in accuracy before the number of adaptive eigenvalues reached 5, the accuracy of the final algorithm was lower than that of the proposed algorithm. That is, the GSA-PSO-A algorithm had higher decision-making accuracy for expressive training of college students’ sports aerobics and better data fusion, which can improve the evaluation and decision-making ability of the students’ sports expressiveness.

Fig. 5. Comparison loss function curve of the GSA-PSO algorithm.

Fig. 6. Comparison of the unimodal function and multimodal function under different algorithms.

Fig. 7. Comparison of the decision-making perfor-mance of college students’ sports and aerobics.

4.2 Performance Test of College Students Training Prediction Model under GSA-PSO-A Algorithm

The above comparison of the performance of different algorithms showed that the model of the proposed algorithm had the best effect. Therefore, 200 college students were selected randomly from a university and divided randomly into two groups. Their performance was recorded during the whole experiment, and their performance ability in real sports aerobics was used in the data comparison experiment. Fig. 8 shows the performance analysis and test of the sports model under the GSA-PSO-A algorithm for the accuracy of the sports performance training prediction model for college students.

The real training results of the sports performance of the two groups of college students were almost consistent with the predicted training results (Fig. 8), which showed that the model predicted that the sports performance of the students was higher. In addition, through calculation, the prediction accuracy of the models for the two teams was as high as 97.6%, which was significantly higher than the traditional Apriori algorithm model. The above results showed that the prediction system designed by the research could have higher accuracy and better performance. The college students’ expressiveness training model system was applied to 180 first-year students. Fig. 9 shows the relative error graph of the students’ expressiveness in sports and aerobics.

The relative error 1 meant that only the relative error of the prediction model of the student’s sports performance was considered in the experiment (Fig. 9). Relative error 2 considered the prediction model of the student’s usual sports performance, physical health, and training attitude relative error. In the figure, the overall error trend of relative error 1 was higher than that of relative error 2. Among the student groups, only a few students had a higher error 1 in their performance than error 2, suggesting that the overall relative error of error 2 in student performance was less than error 1. Among them, the minimum and maximum errors of error 2 were 0.033 and 0.061, respectively. In this experiment, the average relative error reached 0.039, which was an algorithm with a small error that was lower than the traditional Apriori algorithm model. The above results showed that taking the students’ physical health and training attitude into consideration in the sports performance training model of college students constructed by the research algorithm could significantly improve the accuracy of the sports performance model of students. The study applied the sports performance training model system to two groups of students for confirmation. One group only took the students’ performance training results as reference factors, and the other group took the students’ usual sports performance, physical fitness, and training attitude as reference factors. The performance training scores of the students before and after the experiment were obtained, and the impact of using the model constructed by the research institute on the performance of the students’ sports performance training was tested further, as shown in Fig. 10.

Fig. 10 shows various factors on the students’ training performance, under the influence of the students’ physical health, sense of belief, training attitude, the difficulty of the course, and the length of the exercise. The students’ sports performance and the training effect scores all increased. Among them, the performance improvement of the students ranking in the top 50% of the performance training results was more prominent. The physical health and exercise time had the greatest impact on improving the students’ performance. The training performance of the students increased by 7 and 8%, respectively, under the influence of these two factors. The students whose performance ranked in the bottom 50% had obvious refreshing effects. The training effect of students could be increased by 8 and 10%, respectively, under the influence of physical health and training attitude factors, and the improvement was the most obvious. Therefore, the GSA-PSO-A algorithm proposed by the research institute to model the training effect of students can improve the training of students, which is conducive to the teaching quality of physical education courses. The training effect is most obviously affected by the students’ physical health, training attitude, and course exercise time. Table 1 lists the accuracy of different models in predicting the sports performance of college students.

The GSA-PSO-A algorithm has the highest prediction accuracy for college students' sports performance, with a value as high as 95.25% (Table 1). When iterating 74 times, the time consumption of the research method was only 2.17s. Among the remaining five algorithms, IPSO, SAPSO, and DKPSO performed better in actual applications. Taking the IPSO algorithm as an example, the prediction accuracy of the model under this algorithm is 94.28% when the number of iterations was 87, and the running time reached 4.56s. The GSA-PSO-A algorithm has the strongest prediction and data mining ability for college aerobics performance and can achieve better results in practical applications.

Fig. 8. Comparison between the prediction training and the actual training results of the sports performance of the two groups of college students.

Fig. 9. Comparison chart of the relative error of 180 students’ sports performance.

Fig. 10. Results of the students’ training results before and after the experiment.