# A Multivariate Evaluation Model of Physical Education Teaching Quality with Random Matrix Optimization Neural Network

Authors: Wang Zhang; Yu Wen
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The status of physical education courses in education is increasing, there are many problems in teaching traditional physical education courses, and information technology and information-based education are developing continuously, providing enough space for the research of the topic. The online teaching of public physical education courses in colleges and universities is very complex, and its quality evaluation faces many difficulties. Considering the problem that most traditional PE teaching quality evaluation methods are affected by the accuracy of the established model in the process of positioning, a PE teaching quality evaluation model based on random matrix theory is established by using the advantage that random matrix theory does not rely on the simplification and assumptions of the system model and can extract effective information from a large amount of data. Firstly, the influencing factor data and physical education state data are constructed as a state augmentation matrix. Then, the average spectral radius of the characteristic statistic is used to construct indicators to analyze the size of the correlation between each influencing factor and physical education state to achieve the fundamental positioning of physical education quality. The main influencing factors of online teaching of public physical education classes in colleges and universities mainly include teacher quality, teaching process, course resources, and course effect, and the construction of an evaluation index system should be implemented based on adhering to the scientificity, accessibility, independence, and generality from these four aspects to construct the evaluation index system and evaluation criteria of online teaching quality of public physical education class in colleges and universities, which provides the final realization of the goal of physical education class in colleges and universities.


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## Body

## 1. Introduction

As an important symbol of modern society, physical education is a compulsory subject for the overall development of talents in schools. However, in the process of quality education, the value of physical education is irreplaceable by other courses, the status of physical education is getting higher and higher, the role of physical education is getting more and more attention, and people pay more and more attention to it. The continuous development of information technology has provided new ideas for the reform of public physical education in colleges and universities. Through the integration of information technology, it can continuously promote the reform of teaching contents, teaching methods, and teaching approaches of public physical education classes in colleges and universities, and provide important help to cultivate students' innovative consciousness [1]. In recent years, the continuous development of information technology has provided more possibilities for the reform of public physical education classes in colleges and universities, there is a deeper understanding of the importance of continuously improving the level of information technology, the related investment has been increasing, and the continuous improvement of the level of information technology in college sports services has provided important support for the online teaching of public physical education classes in colleges and universities.Most classical statistical methods are obtained by a large number of research calculations under the premise that the dimensionality of the matrix is determined. In recent years, intelligent monitoring devices have been used in physical education with the development of intelligent teaching, and the amount of data collected has been growing exponentially, making the dimensionality of the matrices constantly converge to the infinite. Therefore, how to analyze these large dimensional data and obtain the statistical properties of the data within the large dimensional data has posed new challenges to research scholars within various subject areas [2]. Data-driven methods do not rely on conventional models, can make up for the shortcomings of conventional models in the analysis process, and are favored in various fields. Scholars of big data research generally believe that there is a certain correlation between various data of the same event, and the data influence each other. Big data technology can obtain certain event occurrence rules by mining and analyzing data, to explain the complex relationships of some systems. Among them, data-driven approaches based on data do not rely on conventional models, can compensate for the shortcomings of conventional models during the analysis process, and are highly preferred within various fields. Big data research scholars generally agree that there are certain correlations determined between various data of the same event and that the data influence each other. Big data technology can explain some systemic complex relationships by mining and analyzing the data to obtain certain patterns of event occurrence [3]. However, the classical statistical theorems are no longer applicable for mining and statistical analysis of massive big data, while the new limit theory can replace the classical statistical theory for mining and analysis of large dimensional data in specific situations. According to the random matrix theory, the system data obtained at this time will exhibit certain statistical randomness; when there is a signal source excitation in the system, the internal and operational mechanisms of the system will change under the action of the signal source and the statistical properties will be destroyed. In the framework of random matrix theory, both the single-loop law and the M-P law are important scientific achievements under this theoretical system [4].According to the essential characteristics of the physical education curriculum, based on the research results of many scholars, this thesis analyzes the abnormal state of the system through M-P law based on the random matrix theory and determines the physical education teaching method by using the average educational distribution as the state index. Then, an evaluation model of physical education based on data correlation analysis is constructed by using the augmentation matrix method to determine the quality of physical education through correlation analysis. A compulsory public course to improve physical fitness, health, and physical literacy through scientific and reasonable physical exercise is an important part of the school curriculum and is an indispensable link to achieving comprehensive development of quality education.


## 2. Related Work

Literature [5] pointed out that physical education is an important part of quality education and the foundation of quality education, and provides the driving force for the development of quality education, which can enhance students’ physical fitness, promote their intellectual development, regulate their psychological and physiological balance, cultivate their tenacious quality of will, and enhance their patriotic feelings. Liu [6] suggested that physical education is an integral part of quality education, a carrier of quality education, and the driving force of quality education, which helps to improve student's physical fitness, develop their intelligence, foster their competitive consciousness, and develop their innovative ability. The first application of random matrix theory to the study of detecting power system anomalies was presented in the literature [7], in which a new and generalizable analysis method based on random matrix theory was proposed. In [8], the random matrix theory is applied for the first time to the analysis of pulse signals and a classification of the pulse characteristics of human beings in different states, such as before and after staying up late, and the pulse characteristics of cardiovascular patients are also analyzed using the pulse processing model. Li et al. [9] divide the optimization problem into three steps, which are also the three main elements of the optimization problem study: convergence, convergence speed, and global quality of optimization. Convergence refers to the algorithm’s ability to converge to a reasonably smooth point from the beginning of its operation; convergence speed is to allow the algorithm to converge faster; optimization global quality is to guarantee that the algorithm can converge to a smaller value, such as a global minimum. Dai et al. [10] analyze the expressive performance of convolutional neural networks and their loss planes. In a realistic deep convolutional neural network using shared weights and maximum pooling layers, some linearly independent features arise in wider layers (meaning that the number of neurons in the layer is much larger than the number of training data samples). In the literature [11], a spherical spin-glass model was used to explore the nonconvex loss function of a simple model of a fully connected feedforward neural network, and it was found that the minimum critical value of the stochastic loss function lies within a narrow band definition and is bounded by a global minimum. In the literature [12], the distribution of eigenvalues of the Hessian matrix at the critical point is studied using random matrices and an attempt is made to characterize the variation of the lost plane in this way. The article invokes the free probability theory analytical framework and some analytical tools from random matrix theory and utilizes some simplifying assumptions in an attempt to calculate the approximate distribution of the eigenvalues of the Hessian matrix, which in neural networks depends heavily on the ratio of the energy and measurement parameters to the data values withholding the larger value indicating less relative data. Jiang et al. [13] performed extensive training and data processing and found that the Hessian matrix is degenerate at any moment and deduced that the loss plane features are determined by both the network structure and the input dataset. During the study of the spectrum of the Hessian matrix, it was found that increasing the number of network parameter scales most of the spectrum if the input data are fixed while fixing the network dimensions and changing the input data affects larger values of the spectrum. Suto [14] tried to explore the nonlinear problem in neural networks by studying the GMM stochastic matrix model in neural networks and finding its presolution formula. The authors work on data feature extraction in high-dimensional space using random projections from the perspective of random feature extraction. Using a nonlinear function acting on the weight matrix and the input data can be used to observe the extraction of stochastic features This approach helps to understand the characteristics of neural networks before and at the beginning of training.The continuous development of information technology has provided new ideas for the reform of public physical education in colleges and universities. Through the integration of information technology, it can continuously promote the reform of teaching content, teaching means, and teaching methods of public physical education courses in colleges and universities, and provide important help to cultivate students' sense of innovation.


## 3. Construction of a Multivariate Evaluation Model of Physical Education Teaching Quality Based on a Random Matrix Optimization Network

### 3.1. Random Matrix Optimization Network Algorithm Construction

Random matrix theory originated from quantum physics. In recent decades, the use of random matrix theory in mathematical statistics of large dimensional data and the remarkable statistical results have made random matrix theory widely and deeply studied by the community. Random matrix theory can reflect the fluctuation characteristics of data by analyzing the correlation between random data and mapping the state of complex systems by data characteristics. However, in practical engineering problems, the dimensions of the data are not all large dimensional data, and there may be cases such as too little data. When the data dimension is in tens or hundreds, some properties of the random matrix still converge with considerable accuracy, which provides the possibility of using the random matrix theory for practical engineering problems.When the elements of the matrixM are random and the dimension n tends to infinity, the study of its empirical spectral distribution is the most basic research content in the theory of random matrices and the most important research part [15]. When n tends to infinity, the distribution function at this time we call the limiting spectral distribution, in the study the limiting spectral distribution function is not found to be random, but there are laws to investigate. The study of random matrix theory consists of two main parts: asymptotic study and nonasymptotic study. The standard condition number can reflect the stability of the system very well, and it can show the influence on the function change when the input has a small change and fluctuation. The standard condition number can be used to characterize whether a matrix is “well formed” or “ill-conditioned.” Generally, the larger the standard condition number of the matrix, the closer the matrix is to a singular matrix, that is, an irreversible matrix. Such a matrix is often “sick.” In this state, the calculation error will become larger and the accuracy of the system will decrease. Asymptotic and nonasymptotic dimensional bounds are studied, where the study of nonasymptotic can be called finite-dimensional random matrix theory, mainly to study the problem of nonasymptotic distribution in some high-dimensional but fixed-dimensional scenarios, and it is also very meaningful to give the precise spectral distribution of the matrix for a specific dimension. The study of asymptotics is mainly focused on infinite-dimensional random matrix theory, which is also the main research point of this paper. In such a scenario where the dimensionality of the random matrix tends to infinity, there will exist asymptotic distributions similar to the large number theorem in classical statistics.In the scenario of physical education quality evaluation, we should not only care about the distribution of extreme eigenvalues but also the research on the distribution of very large and very small eigenvalues is very important. The research on eigenvalue extrema mainly focuses on the distribution of the very large, very small eigenvalues and eigenvalue extrema [15]. For the Wishart matrix, when the fourth-order moments of the elements are finite and satisfy 0 < t < l, its very large and very small eigenvalues satisfy.(1)κt−n=1+ηκt+Δκijt,κt+n=1−ηκt+Δκijt.It can be seen that the Tracy–Widom distributions of both the Gaussian orthogonal matrix and the Gaussian matrix are calculated based on the Gaussian–You matrix. The Tracy–Widom distribution is shown in Figure1, where the yellow histogram is the distribution of 500,000 limiting eigenvalues and the blue line is the Tracy–Widom distribution. It can be seen that the Tracy–Widom distribution can well describe the distribution of the extreme values of the eigenvalues of the Wishart matrix.Figure 1
Matrix limit eigenvalue distribution and T-W distribution.A standard condition number is a powerful tool for studying the distribution of eigenvalues of a random matrix. The standard condition number is a good indicator of the stability of the system and can indicate the effect on the change of the function when there are small fluctuations in the input. Before the educational innovation of the system, the characteristic roots corresponding to the system state data matrix are distributed between the outer ring and the inner ring, which is consistent with the single ring theorem. Some points are distributed outside the ring, which should be caused by bad data, but for a single ring. The result of the ring theorem has no effect. In general, the larger the standard condition number of a matrix, the closer the matrix is to a singular matrix, i.e., an integrable matrix, which is often “pathological” [16]. In such a state, it leads to larger computational errors and lower accuracy of the system. The standard condition number is a property of the matrix itself. Let an n∗n-dimensional matrix A and the condition number of the matrix A be defined as(2)Ait+1=f∑j=1mAjtwij.The use of random matrix theory to analyze deep neural networks is mainly based on the following.(1)
The loss plane of a deep neural network has the characteristic of high-dimensional nonconvex, and the dimension of the Hessian matrix of the network is very large; for example, in the simple handwritten character set recognition network, the dimension is already tens of thousands, the high-dimensional case will produce many counter-intuitive phenomena, and it is difficult to analyze such a network by using traditional matrix operation.(2)
The parameters in the network are random variables. For the training of deep neural networks, the results are not the same every time because many parameters are random variables in the training process, and the theory of random matrices can reveal their essential laws of them. Using the asymptotic spectrum theory of large dimensional random matrices, we can reveal the inherent statistical characteristics of neural networks and help us understand and analyze the optimization of networks.The physical meaning of the eigenvalues of a matrix is to indicate the degree of skewness of the loss function along the direction of the eigenvector corresponding to that eigenvalue, so the eigenvalues of the Hessian matrix are very important for studying the geometric properties of the lost plane. When analyzing the geometric properties of the lost plane, the eigenvalue extrema of the matrix is also very important. The maximum and minimum eigenvalues of the matrix determine the steepness of the lost plane, which directly affects the performance of the network convergence. The distribution of the eigenvalue extrema can be calculated using the Tracy–Widom distribution, the eigenvalues of the Hessian matrixλ1<λ2<λ3<…<λn, where the eigenvalues of the extrema are defined as(3)λEN=λN−kδ.For the ratio of the very large eigenvalues to the very small eigenvalues, which is the standard condition number, the effect on the loss plane is also very significant, which can fully reflect the stability of the network and has an important impact on the convergence of the network. The distribution of the standard condition number obeys the T-W-C standard distribution.In the analysis of the eigenvalue distribution, it was found that larger eigenvalues are more likely to affect the optimization performance of the network [17]. Larger eigenvalues have the following characteristics: they are far from the high-frequency center of the distribution (the high-frequency center of this distribution is concentrated near zero), they also satisfy a distance difference from the high-frequency center greater than three times the standard deviation, and the frequency of occurrence of larger eigenvalues is very small, based on which such larger eigenvalues are called outliers. Based on this, such larger eigenvalues are called outliers. In the study of larger eigenvalues, we focus on the study of the largest eigenvalues, that is, their extreme eigenvalues.In terms of distance metrics, the geometric structure of data maintains relationships reflecting certain data category relationships, geometric structure consideration is also divided into local and global, and the prerequisite assumption of data structure distribution is that in high-dimensional space, data are distributed in geometric flow structure, so the local geometric flow structure and global geometric structure of data become the direction to focus on in distance metrics for unsupervised feature selection. The classic statistical theorem is no longer suitable for mining and statistics of massive big data, and the new limit theory can replace the classical statistical theory to mine and analyze large dimensional data under certain circumstances. According to the random matrix theory, the system data obtained at this time will show certain statistical randomness; when there is a signal source excitation in the system, the internal mechanism and operation mechanism of the system will change under the action of the signal source, and the statistical characteristics will be destroyed. For example, SPFS selects features that can maintain similar relationships between pairs of data in high-dimensional feature space as much as possible, which is to maintain similar information in the global structure. Global and local structure-keeping feature selection considers global similarity along with local streamwise structure, which makes the model results closer to the class of actual sample data.


### 3.2. Construction of a Multivariate Evaluation Model of Physical Education Teaching Quality Based on Random Matrix Optimization Neural Network

In recent years, with the improvement of computer software and hardware resources, neural networks and deep learning methods have become popular tools in data processing and analysis. Currently, such methods have yielded many optimal solutions for many problems in the fields of image recognition, speech recognition, and natural language processing, and have produced many successful applications in the evaluation of physical education quality.The current teaching quality evaluation system of university teachers still uses the traditional evaluation habits. In the form of evaluation, it mainly includes peer evaluation, leadership evaluation, and students' teaching evaluation. In the content of evaluation, it mainly includes teachers' teaching ideas, teaching knowledge, teaching attitude,andteaching skills. The evaluation method mainly adopts quantitative analysis. According to the evaluation criteria, the evaluation results are divided into excellent, good, qualified, and unqualified [18]. This evaluation system mainly focuses on teachers’ performance in teaching activities as the basis of evaluation content, and teachers will make choices of content, methods, and means that are not suitable for actual teaching to pursue conformity with the evaluation standards, and cannot objectively work to evaluate teachers’ teaching quality.Since the quality evaluation of physical education collected in the actual physical education process is different from the data in the ideal state. So, some processing of the actual collected data is needed before the random matrix processing of the quality evaluation data. To solve the above problems, a multi-scale fusion reconstruction network is proposed in this paper. The advantages of this network are reflected in the following: (1) the network structure is designed as a parallel learning model with multi-scale features, and cross-fusion connections are designed between each parallel pathway, which in turn makes the different scale features of each pathway enhance each other, and thus helps to improve the reconstruction quality. (2) The pseudo-3D convolutional residual module is further designed in the parallel learning network model and deployed in each parallel pathway, which can effectively learn the spatio-temporal correlation features in the physical education case. (3) In the testing phase, the reconstructed video is obtained by forwarding pass only, which shortens the time required to reconstruct the video. The structure of the multi-scale fusion reconstruction network (MSF-Net) is shown in Figure 2. The MSF-Net has six layers, which correspond to features of the same scale horizontally and decreasing feature scale vertically. The feature scales of the highest layer correspond to the number of feature channels, the number of video frames, and the spatial resolution size, respectively.Figure 2
Augmentation matrix correlation analysis flow.For correlation analysis of the obtained physical education state data, it is necessary to build a voltage transient fault source location model for correlation analysis of system state data by applying the incremental matrix to the data source matrix establishment based on random matrix theory. Firstly, the system operation state is judged by the random matrix single-loop theorem and M-P law, and the moment of voltage transient event is determined with the average spectral radius as the state index [19]. Then, the state data matrix and the influencing factor matrix are used to establish the augmentation matrix, the difference between the mean spectral radius of the state augmentation matrix and the integral of the difference between the mean spectral radii is obtained and used as the locating indicator to determine the superiority or inferiority of the PE through correlation analysis, and the process is shown in Figure 2.The RMT analysis of the incremental matrix was used to explore the intrinsic connection between the influencing factors and the physical education status of each monitoring point by using the characteristics of the incremental matrix. The correlation between the influencing factor data and the operation state data is used to determine the influence of the physical education state on each monitoring point, and the result is used to determine which monitoring point is closer to the real state of physical education, to judge the quality of physical education [20]. In terms of distance metrics, the geometric structure of data maintains relationships reflecting certain data category relationships, and geometric structure consideration is also divided into local and global. The prerequisite assumption of data structure distribution is that in high-dimensional space, data are distributed in geometric flow structure, so the local geometric flow structure and global geometric structure of data become the direction of unsupervised feature selection focus consideration in distance metrics. By using the state data matrix and the random noise matrix to construct the reference state augmentation matrix, the correlation between the data in the state data matrix can eliminate the interference of the final result by comparing it with the state augmentation matrix. The reference state broadening matrix is shown in(4)gnx=lima⟶01an∑gx−aknk−1k,where x is the element value within the state data matrix gnx and k is the element value within the random noise matrix N. After establishing the state augmentation matrix using the grid state data and the influencing factor data, the MSR in the linear statistics is used as the correlation analysis index between the matrix data to perform the correlation analysis between the data. The statistical learning-based approach, on the other hand, uses some methods of statistics to select features. Since statistics deals mostly with discrete data, the data are discretized before using statistical learning methods. Statistical selection of features is often based on statistical measures such as variance and chi-square test [21]. The obvious drawback of these methods is that the statistical selection of features tends to ignore the diversity of the features and tends to select features with high redundancy. Defining the difference of the mean spectral radius of the augmentation matrix as an indicator can exclude the interference caused by duplicate data in the state data and the influencing factor data. On the real-time sliding window time scale, the integral of the difference of the mean spectral radii is defined as(5)rhi=Nhi1·Nhi1+Nhi−1−1,where Nhi1 and Nhi−1 are the sampling start and end times of the real-time sliding window, respectively. rhi can be used to characterize the magnitude of the correlation between different influences at that sampling time.For all situations, pay attention to the individual differences of students, and develop programs to improve the physical fitness level of high school students from the perspective of sustainable development; enhancing physical fitness is the true meaning of sports and is also the starting point destination of school sports. The indicators of physical fitness of our youth are usually the traditional physical fitness indicators such as morphology, function, and basic quality, while the indicators of health fitness such as reaction time, MBI index, body composition, and scoliosis are less involved, which leads to insufficient measurement and analysis of new problems in students’ health status. Sports participation is a manifestation of students’ attitudes and behaviors to actively participate in sports, both in and out of class, and includes physical and psychological inputs at the cognitive and affective levels. Through active sports participation, students can deepen their knowledge of physical education, master sports techniques, and physical exercise, and promote health; they can also deepen interpersonal interactions and promote social adaptation [22].Sparse learning-based methods, on the other hand, are commonly used for embedded unsupervised feature selection, which is usually done by exploring the internal structure of the data through spectral analysis techniques and guiding feature selection through sparse learning while maintaining the data structure. The multi-cluster feature selection (MCFS) method is a classical sparse learning feature selection method, which first uses spectral clustering to analyze the clustering of sample data, then uses parametric sparse regression on the model after obtaining the class situation of the data, then evaluates the importance of the features and ranks them, and finally selects the specified number of features with the highest importance [23]. Non-negative discriminative feature selection assumes that the classification results after performing spectral clustering are the classification labels of the data, and uses the pseudo-labels of the classification results as information to guide feature selection.Only if the evaluation system of physical education teachers’ educational ability is constructed more scientifically and objectively, can the collected evaluation information of physical education teachers be guaranteed to be more credible and effective. Only in this way can the evaluation results of physical education teachers’ teaching ability be more scientific and reasonable, which is the fundamental guarantee factor to determine the reasonableness of the evaluation results and the success of the final evaluation goal [24]. The multiple evaluation systems of physical education teaching quality based on matrix optimization neural network can also regulate the teaching behavior of physical education teachers through the improvement of the evaluation mode of physical education teachers’ teaching ability, can strengthen the professional ethics of physical education teachers, and can improve the teaching quality of the whole physical education teaching field. It can truly achieve the comprehensive, coordinated, and orderly development of physical education teachers’ education work.


## 3.1. Random Matrix Optimization Network Algorithm Construction

Random matrix theory originated from quantum physics. In recent decades, the use of random matrix theory in mathematical statistics of large dimensional data and the remarkable statistical results have made random matrix theory widely and deeply studied by the community. Random matrix theory can reflect the fluctuation characteristics of data by analyzing the correlation between random data and mapping the state of complex systems by data characteristics. However, in practical engineering problems, the dimensions of the data are not all large dimensional data, and there may be cases such as too little data. When the data dimension is in tens or hundreds, some properties of the random matrix still converge with considerable accuracy, which provides the possibility of using the random matrix theory for practical engineering problems.When the elements of the matrixM are random and the dimension n tends to infinity, the study of its empirical spectral distribution is the most basic research content in the theory of random matrices and the most important research part [15]. When n tends to infinity, the distribution function at this time we call the limiting spectral distribution, in the study the limiting spectral distribution function is not found to be random, but there are laws to investigate. The study of random matrix theory consists of two main parts: asymptotic study and nonasymptotic study. The standard condition number can reflect the stability of the system very well, and it can show the influence on the function change when the input has a small change and fluctuation. The standard condition number can be used to characterize whether a matrix is “well formed” or “ill-conditioned.” Generally, the larger the standard condition number of the matrix, the closer the matrix is to a singular matrix, that is, an irreversible matrix. Such a matrix is often “sick.” In this state, the calculation error will become larger and the accuracy of the system will decrease. Asymptotic and nonasymptotic dimensional bounds are studied, where the study of nonasymptotic can be called finite-dimensional random matrix theory, mainly to study the problem of nonasymptotic distribution in some high-dimensional but fixed-dimensional scenarios, and it is also very meaningful to give the precise spectral distribution of the matrix for a specific dimension. The study of asymptotics is mainly focused on infinite-dimensional random matrix theory, which is also the main research point of this paper. In such a scenario where the dimensionality of the random matrix tends to infinity, there will exist asymptotic distributions similar to the large number theorem in classical statistics.In the scenario of physical education quality evaluation, we should not only care about the distribution of extreme eigenvalues but also the research on the distribution of very large and very small eigenvalues is very important. The research on eigenvalue extrema mainly focuses on the distribution of the very large, very small eigenvalues and eigenvalue extrema [15]. For the Wishart matrix, when the fourth-order moments of the elements are finite and satisfy 0 < t < l, its very large and very small eigenvalues satisfy.(1)κt−n=1+ηκt+Δκijt,κt+n=1−ηκt+Δκijt.It can be seen that the Tracy–Widom distributions of both the Gaussian orthogonal matrix and the Gaussian matrix are calculated based on the Gaussian–You matrix. The Tracy–Widom distribution is shown in Figure1, where the yellow histogram is the distribution of 500,000 limiting eigenvalues and the blue line is the Tracy–Widom distribution. It can be seen that the Tracy–Widom distribution can well describe the distribution of the extreme values of the eigenvalues of the Wishart matrix.Figure 1
Matrix limit eigenvalue distribution and T-W distribution.A standard condition number is a powerful tool for studying the distribution of eigenvalues of a random matrix. The standard condition number is a good indicator of the stability of the system and can indicate the effect on the change of the function when there are small fluctuations in the input. Before the educational innovation of the system, the characteristic roots corresponding to the system state data matrix are distributed between the outer ring and the inner ring, which is consistent with the single ring theorem. Some points are distributed outside the ring, which should be caused by bad data, but for a single ring. The result of the ring theorem has no effect. In general, the larger the standard condition number of a matrix, the closer the matrix is to a singular matrix, i.e., an integrable matrix, which is often “pathological” [16]. In such a state, it leads to larger computational errors and lower accuracy of the system. The standard condition number is a property of the matrix itself. Let an n∗n-dimensional matrix A and the condition number of the matrix A be defined as(2)Ait+1=f∑j=1mAjtwij.The use of random matrix theory to analyze deep neural networks is mainly based on the following.(1)
The loss plane of a deep neural network has the characteristic of high-dimensional nonconvex, and the dimension of the Hessian matrix of the network is very large; for example, in the simple handwritten character set recognition network, the dimension is already tens of thousands, the high-dimensional case will produce many counter-intuitive phenomena, and it is difficult to analyze such a network by using traditional matrix operation.(2)
The parameters in the network are random variables. For the training of deep neural networks, the results are not the same every time because many parameters are random variables in the training process, and the theory of random matrices can reveal their essential laws of them. Using the asymptotic spectrum theory of large dimensional random matrices, we can reveal the inherent statistical characteristics of neural networks and help us understand and analyze the optimization of networks.The physical meaning of the eigenvalues of a matrix is to indicate the degree of skewness of the loss function along the direction of the eigenvector corresponding to that eigenvalue, so the eigenvalues of the Hessian matrix are very important for studying the geometric properties of the lost plane. When analyzing the geometric properties of the lost plane, the eigenvalue extrema of the matrix is also very important. The maximum and minimum eigenvalues of the matrix determine the steepness of the lost plane, which directly affects the performance of the network convergence. The distribution of the eigenvalue extrema can be calculated using the Tracy–Widom distribution, the eigenvalues of the Hessian matrixλ1<λ2<λ3<…<λn, where the eigenvalues of the extrema are defined as(3)λEN=λN−kδ.For the ratio of the very large eigenvalues to the very small eigenvalues, which is the standard condition number, the effect on the loss plane is also very significant, which can fully reflect the stability of the network and has an important impact on the convergence of the network. The distribution of the standard condition number obeys the T-W-C standard distribution.In the analysis of the eigenvalue distribution, it was found that larger eigenvalues are more likely to affect the optimization performance of the network [17]. Larger eigenvalues have the following characteristics: they are far from the high-frequency center of the distribution (the high-frequency center of this distribution is concentrated near zero), they also satisfy a distance difference from the high-frequency center greater than three times the standard deviation, and the frequency of occurrence of larger eigenvalues is very small, based on which such larger eigenvalues are called outliers. Based on this, such larger eigenvalues are called outliers. In the study of larger eigenvalues, we focus on the study of the largest eigenvalues, that is, their extreme eigenvalues.In terms of distance metrics, the geometric structure of data maintains relationships reflecting certain data category relationships, geometric structure consideration is also divided into local and global, and the prerequisite assumption of data structure distribution is that in high-dimensional space, data are distributed in geometric flow structure, so the local geometric flow structure and global geometric structure of data become the direction to focus on in distance metrics for unsupervised feature selection. The classic statistical theorem is no longer suitable for mining and statistics of massive big data, and the new limit theory can replace the classical statistical theory to mine and analyze large dimensional data under certain circumstances. According to the random matrix theory, the system data obtained at this time will show certain statistical randomness; when there is a signal source excitation in the system, the internal mechanism and operation mechanism of the system will change under the action of the signal source, and the statistical characteristics will be destroyed. For example, SPFS selects features that can maintain similar relationships between pairs of data in high-dimensional feature space as much as possible, which is to maintain similar information in the global structure. Global and local structure-keeping feature selection considers global similarity along with local streamwise structure, which makes the model results closer to the class of actual sample data.


## 3.2. Construction of a Multivariate Evaluation Model of Physical Education Teaching Quality Based on Random Matrix Optimization Neural Network

In recent years, with the improvement of computer software and hardware resources, neural networks and deep learning methods have become popular tools in data processing and analysis. Currently, such methods have yielded many optimal solutions for many problems in the fields of image recognition, speech recognition, and natural language processing, and have produced many successful applications in the evaluation of physical education quality.The current teaching quality evaluation system of university teachers still uses the traditional evaluation habits. In the form of evaluation, it mainly includes peer evaluation, leadership evaluation, and students' teaching evaluation. In the content of evaluation, it mainly includes teachers' teaching ideas, teaching knowledge, teaching attitude,andteaching skills. The evaluation method mainly adopts quantitative analysis. According to the evaluation criteria, the evaluation results are divided into excellent, good, qualified, and unqualified [18]. This evaluation system mainly focuses on teachers’ performance in teaching activities as the basis of evaluation content, and teachers will make choices of content, methods, and means that are not suitable for actual teaching to pursue conformity with the evaluation standards, and cannot objectively work to evaluate teachers’ teaching quality.Since the quality evaluation of physical education collected in the actual physical education process is different from the data in the ideal state. So, some processing of the actual collected data is needed before the random matrix processing of the quality evaluation data. To solve the above problems, a multi-scale fusion reconstruction network is proposed in this paper. The advantages of this network are reflected in the following: (1) the network structure is designed as a parallel learning model with multi-scale features, and cross-fusion connections are designed between each parallel pathway, which in turn makes the different scale features of each pathway enhance each other, and thus helps to improve the reconstruction quality. (2) The pseudo-3D convolutional residual module is further designed in the parallel learning network model and deployed in each parallel pathway, which can effectively learn the spatio-temporal correlation features in the physical education case. (3) In the testing phase, the reconstructed video is obtained by forwarding pass only, which shortens the time required to reconstruct the video. The structure of the multi-scale fusion reconstruction network (MSF-Net) is shown in Figure 2. The MSF-Net has six layers, which correspond to features of the same scale horizontally and decreasing feature scale vertically. The feature scales of the highest layer correspond to the number of feature channels, the number of video frames, and the spatial resolution size, respectively.Figure 2
Augmentation matrix correlation analysis flow.For correlation analysis of the obtained physical education state data, it is necessary to build a voltage transient fault source location model for correlation analysis of system state data by applying the incremental matrix to the data source matrix establishment based on random matrix theory. Firstly, the system operation state is judged by the random matrix single-loop theorem and M-P law, and the moment of voltage transient event is determined with the average spectral radius as the state index [19]. Then, the state data matrix and the influencing factor matrix are used to establish the augmentation matrix, the difference between the mean spectral radius of the state augmentation matrix and the integral of the difference between the mean spectral radii is obtained and used as the locating indicator to determine the superiority or inferiority of the PE through correlation analysis, and the process is shown in Figure 2.The RMT analysis of the incremental matrix was used to explore the intrinsic connection between the influencing factors and the physical education status of each monitoring point by using the characteristics of the incremental matrix. The correlation between the influencing factor data and the operation state data is used to determine the influence of the physical education state on each monitoring point, and the result is used to determine which monitoring point is closer to the real state of physical education, to judge the quality of physical education [20]. In terms of distance metrics, the geometric structure of data maintains relationships reflecting certain data category relationships, and geometric structure consideration is also divided into local and global. The prerequisite assumption of data structure distribution is that in high-dimensional space, data are distributed in geometric flow structure, so the local geometric flow structure and global geometric structure of data become the direction of unsupervised feature selection focus consideration in distance metrics. By using the state data matrix and the random noise matrix to construct the reference state augmentation matrix, the correlation between the data in the state data matrix can eliminate the interference of the final result by comparing it with the state augmentation matrix. The reference state broadening matrix is shown in(4)gnx=lima⟶01an∑gx−aknk−1k,where x is the element value within the state data matrix gnx and k is the element value within the random noise matrix N. After establishing the state augmentation matrix using the grid state data and the influencing factor data, the MSR in the linear statistics is used as the correlation analysis index between the matrix data to perform the correlation analysis between the data. The statistical learning-based approach, on the other hand, uses some methods of statistics to select features. Since statistics deals mostly with discrete data, the data are discretized before using statistical learning methods. Statistical selection of features is often based on statistical measures such as variance and chi-square test [21]. The obvious drawback of these methods is that the statistical selection of features tends to ignore the diversity of the features and tends to select features with high redundancy. Defining the difference of the mean spectral radius of the augmentation matrix as an indicator can exclude the interference caused by duplicate data in the state data and the influencing factor data. On the real-time sliding window time scale, the integral of the difference of the mean spectral radii is defined as(5)rhi=Nhi1·Nhi1+Nhi−1−1,where Nhi1 and Nhi−1 are the sampling start and end times of the real-time sliding window, respectively. rhi can be used to characterize the magnitude of the correlation between different influences at that sampling time.For all situations, pay attention to the individual differences of students, and develop programs to improve the physical fitness level of high school students from the perspective of sustainable development; enhancing physical fitness is the true meaning of sports and is also the starting point destination of school sports. The indicators of physical fitness of our youth are usually the traditional physical fitness indicators such as morphology, function, and basic quality, while the indicators of health fitness such as reaction time, MBI index, body composition, and scoliosis are less involved, which leads to insufficient measurement and analysis of new problems in students’ health status. Sports participation is a manifestation of students’ attitudes and behaviors to actively participate in sports, both in and out of class, and includes physical and psychological inputs at the cognitive and affective levels. Through active sports participation, students can deepen their knowledge of physical education, master sports techniques, and physical exercise, and promote health; they can also deepen interpersonal interactions and promote social adaptation [22].Sparse learning-based methods, on the other hand, are commonly used for embedded unsupervised feature selection, which is usually done by exploring the internal structure of the data through spectral analysis techniques and guiding feature selection through sparse learning while maintaining the data structure. The multi-cluster feature selection (MCFS) method is a classical sparse learning feature selection method, which first uses spectral clustering to analyze the clustering of sample data, then uses parametric sparse regression on the model after obtaining the class situation of the data, then evaluates the importance of the features and ranks them, and finally selects the specified number of features with the highest importance [23]. Non-negative discriminative feature selection assumes that the classification results after performing spectral clustering are the classification labels of the data, and uses the pseudo-labels of the classification results as information to guide feature selection.Only if the evaluation system of physical education teachers’ educational ability is constructed more scientifically and objectively, can the collected evaluation information of physical education teachers be guaranteed to be more credible and effective. Only in this way can the evaluation results of physical education teachers’ teaching ability be more scientific and reasonable, which is the fundamental guarantee factor to determine the reasonableness of the evaluation results and the success of the final evaluation goal [24]. The multiple evaluation systems of physical education teaching quality based on matrix optimization neural network can also regulate the teaching behavior of physical education teachers through the improvement of the evaluation mode of physical education teachers’ teaching ability, can strengthen the professional ethics of physical education teachers, and can improve the teaching quality of the whole physical education teaching field. It can truly achieve the comprehensive, coordinated, and orderly development of physical education teachers’ education work.


## 4. Experimental Verification and Conclusion

### 4.1. Validation of the RMT-Based Physical Education Teaching Quality Evaluation Model

Noise will be generated in some digital signal acquisition instruments, and the more common ones are baseline drift, low-frequency noise, etc. These will lead to inaccurate measured physical education data and affect the subsequent signal analysis, so these disturbances need to be dealt with by some means. The single-loop theorem and the change of M-P law of the system state before and after physical education in normal teaching mode are obtained by analysis, as shown in Figure3.Figure 3
The effect of the single-loop theorem of physical education teaching quality evaluation system.The reason for not filtering high-frequency noise in this experiment is that high-frequency information can be used to process the physical education data under the processing method of the random matrix to extract some variable values, and the extracted peaks and valleys in the next section are because of the presence of high-frequency information to take a relatively large number of peak and valley variable data in a short period. Of course, with the improvement of the instrument, the built-in filtering of high-frequency noise may lead to the fact that we may not be able to extract so many values of the peak-wave-valley variables in 2 minutes, in which case the acquisition time can be extended appropriately, or other more variables can be selected for processing and analysis. In Figure3, as the system fails, the abnormal state develops continuously and the characteristic root gradually approaches from the outer ring to the inner ring, and the state at this time can be treated as a developmental state of the fault.From Figure4, it can be concluded that before the physical education reform satisfies the M-P law, the histogram of the spectral distribution is uniformly distributed, and the distribution of the roots is regular between two limit values. When the data are directly cut into matrices according to the timeline and then processed by the random matrix single-loop theorem, the spectral distribution obtained after processing will be concentrated in the center of the circle, which leads to a poor differentiation of the spectral distribution obtained after processing each pulse data and has a relatively large impact on the analysis of the results, which is not conducive to our classification and identification. Therefore, the accuracy of the original physical education data needs to be selected so that there is a certain repetition rate between the data points in periodic pulse data.Figure 4
M-P law of the system state after physical education reform.As can be seen in Figure5, the average PSNR value of each frame in the reconstructed video by the GAP-TV algorithm is only 26.58 dB, the SSIM is 0.848, and the reconstruction quality is significantly lower than that of other algorithms, which indicates that the prior knowledge based on the total variance is not sufficient to effectively represent the video features. Both GMM-TP and MMLE-GMM use Gaussian mixture models as the statistical prior for the physical education assessment system to be reconstructed. Statistical before the system is reconstructed. The difference between the two is that GMM-TP learns a fixed set of parametric models from training data, while MMLE-GMM adaptively learns model parameters from a given compressed measurement. Therefore, MMLE-GMM performs slightly better than GMM-TP on the test dataset. MMLE-MFA is a variant of MMLE-GMM, which reduces the reconstruction time, but the performance of the reconstruction is degraded. PnP-FFDNet uses FFDNet as a deep image denoiser and embeds it in an iterative optimization framework, and the reconstruction quality of this algorithm is slightly better than that of the traditional iterative algorithm. Among all the methods, the algorithm proposed in this chapter has the best performance on two datasets, AERIAL and CRASH, and the other metrics are slightly inferior to DCI. This is because the DeSCI algorithm uses a low-rank constraint as the reconstruction before physical education, while the algorithm proposed in this paper adopts a data-driven strategy and uses a deep network as the prior representation of video sequences. The generic test set CRASH, AERIAL, and P.E. instruction data are rich in detail variations, while the remaining P.E. instruction data are mostly smooth structured. The low-rank constraint of DeSCI has better representation capability for smooth structure-rich videos, while the deep network prior model of the algorithm in this chapter has good representation capability for texture details.Figure 5
Quality comparison of different algorithms.


### 4.2. Construction of Multiple Evaluation Systems for the Quality of Authentic Physical Education

In addition to evaluating the reconstruction quality, this thesis also evaluates the reconstruction time between RE2-Net and the comparison algorithms. In this case, the NVIDIA GeForce RTX 2070 was used to run RE2-Net and E2E-CNN, and the rest of the algorithms were run on an Intel Core i70550U CPU. Figure6 shows the time complexity (in seconds) required for each algorithm to reconstruct the six sports instructions in the generic dataset. The minimum time complexity value and the maximum frame rate in these algorithms are marked in bold. It is easy to see that, except for the algorithms proposed in this chapter and E2E-CNN, all the algorithms are based on iterative optimization, and the running time of such algorithms is directly related to the complexity of each iteration. Since each iteration needs to search for nonlocal similar patch blocks and ensure the minimization of the weighted kernel function, DeSCI requires 1 hour to reconstruct 8 types of physical education data from a single 256∗256 compressed measurement. In contrast, the algorithm proposed in this chapter only needs to input the compressed measurement frames into the overall network, and the reconstruction results can be obtained through the feedforward calculation of the neural network. As shown in the data in the figure, the algorithm in this chapter can achieve the reconstruction task of video compression perception in only 3 seconds, and the frame rate of reconstruction can reach 11.27, which realizes the near real-time reconstruction.Figure 6
Time complexity test by each algorithm.Verification of the effect of the number of iterations: The effect of the number of iterations on the reconstruction accuracy of NLR-CSNet was first tested. The PSNR value of the reconstruction metric was plotted against the number of iterations (on a logarithmic scale) for the Lena image (256256) with a measurement rate of 0.1. To simulate the noise, three different intensities of random Gaussian noise were added to the original compressed measurements. As shown in Figure7, the first curve corresponds to the reconstructed results with the original measurements without noise interference, and the remaining three curves correspond to the reconstructed plots with Gaussian noise with noise standard deviations of 0.01, 0.05, and 0.1 added to the measurements, respectively. By using the state data matrix and the random noise matrix to construct the reference state augmentation matrix, the correlation between the data in the state data matrix can eliminate the interference of the final results by comparing it with the state augmentation matrix. With the maximum number of iterations set to 10000, it can be seen from the four plots that the reconstruction quality improves rapidly up to 1000 iterations, then rises slowly to about 2000 iterations, and saturates at 3000 iterations. Even if the intensity of Gaussian noise added to the measurements increases, the PSNR curves do not decrease with the increase in the number of iterations. This shows that NLR-CSNet is robust to the effect of the number of iterations and has good noise perception.Figure 7
Relationship graphs for different intensities of Gaussian noise.As Figure8 shows the confusion of different signal-to-noise ratios, the PR-VNE algorithm uses a reinforcement learning agent in the training phase to explore how the model should perform the virtual network mapping. The input of the reinforcement learning agent is the consensus matrix representation of the physical network before each virtual network mapping, and the output is the probability of selecting each node. When a virtual request arrives, the reinforcement learning agent randomly selects the physical nodes that meet the requirements and provides feedback to the reinforcement learning model based on the evaluation metrics of the results of the selected mapping scheme. The reinforcement learning agent needs to strike a balance between the exploration of new models and the utilization of trained models. The reinforcement learning agent is rewarded more when the nodes selected by the model bring better gains; when the nodes selected by the model bring less or negative gains, the reinforcement learning agent is rewarded less. In a multi-classification problem, the inter-class classification accuracy of different classes is also an important criterion for network performance. A confusion matrix is an important tool for measuring inter-class classification accuracy, which categorizes the number of correct and incorrect classes of a multi-classification model and then represents them in the form of a visual matrix. This is a very basic and intuitive method, and the calculation is a very simple matrix.Figure 8
Confusion of different signal-to-noise ratios.In the confusion matrix, the horizontal coordinate indicates the experimentally predicted modulation mode, the vertical coordinate indicates the true modulation mode, and the darker the color of each square in the matrix indicates the higher probability that the corresponding true modulation mode is judged to be the corresponding predicted modulation mode. For this network, the confusion matrix is a diagonal array when the prediction performance of the network is optimal. In this experiment, it can be observed that as the signal-to-noise ratio increases, the prediction performance of the network gets better. However, in general, the network does not classify well for both modulation types, QAM16 and QAM64, and always misclassifies between them. This is because both modulation types belong to QAM modulation, but they adopt different binary methods. The network designed in this paper cannot identify their specific types well, but it can identify them that both belong to QAM modulation more accurately.


## 4.1. Validation of the RMT-Based Physical Education Teaching Quality Evaluation Model

Noise will be generated in some digital signal acquisition instruments, and the more common ones are baseline drift, low-frequency noise, etc. These will lead to inaccurate measured physical education data and affect the subsequent signal analysis, so these disturbances need to be dealt with by some means. The single-loop theorem and the change of M-P law of the system state before and after physical education in normal teaching mode are obtained by analysis, as shown in Figure3.Figure 3
The effect of the single-loop theorem of physical education teaching quality evaluation system.The reason for not filtering high-frequency noise in this experiment is that high-frequency information can be used to process the physical education data under the processing method of the random matrix to extract some variable values, and the extracted peaks and valleys in the next section are because of the presence of high-frequency information to take a relatively large number of peak and valley variable data in a short period. Of course, with the improvement of the instrument, the built-in filtering of high-frequency noise may lead to the fact that we may not be able to extract so many values of the peak-wave-valley variables in 2 minutes, in which case the acquisition time can be extended appropriately, or other more variables can be selected for processing and analysis. In Figure3, as the system fails, the abnormal state develops continuously and the characteristic root gradually approaches from the outer ring to the inner ring, and the state at this time can be treated as a developmental state of the fault.From Figure4, it can be concluded that before the physical education reform satisfies the M-P law, the histogram of the spectral distribution is uniformly distributed, and the distribution of the roots is regular between two limit values. When the data are directly cut into matrices according to the timeline and then processed by the random matrix single-loop theorem, the spectral distribution obtained after processing will be concentrated in the center of the circle, which leads to a poor differentiation of the spectral distribution obtained after processing each pulse data and has a relatively large impact on the analysis of the results, which is not conducive to our classification and identification. Therefore, the accuracy of the original physical education data needs to be selected so that there is a certain repetition rate between the data points in periodic pulse data.Figure 4
M-P law of the system state after physical education reform.As can be seen in Figure5, the average PSNR value of each frame in the reconstructed video by the GAP-TV algorithm is only 26.58 dB, the SSIM is 0.848, and the reconstruction quality is significantly lower than that of other algorithms, which indicates that the prior knowledge based on the total variance is not sufficient to effectively represent the video features. Both GMM-TP and MMLE-GMM use Gaussian mixture models as the statistical prior for the physical education assessment system to be reconstructed. Statistical before the system is reconstructed. The difference between the two is that GMM-TP learns a fixed set of parametric models from training data, while MMLE-GMM adaptively learns model parameters from a given compressed measurement. Therefore, MMLE-GMM performs slightly better than GMM-TP on the test dataset. MMLE-MFA is a variant of MMLE-GMM, which reduces the reconstruction time, but the performance of the reconstruction is degraded. PnP-FFDNet uses FFDNet as a deep image denoiser and embeds it in an iterative optimization framework, and the reconstruction quality of this algorithm is slightly better than that of the traditional iterative algorithm. Among all the methods, the algorithm proposed in this chapter has the best performance on two datasets, AERIAL and CRASH, and the other metrics are slightly inferior to DCI. This is because the DeSCI algorithm uses a low-rank constraint as the reconstruction before physical education, while the algorithm proposed in this paper adopts a data-driven strategy and uses a deep network as the prior representation of video sequences. The generic test set CRASH, AERIAL, and P.E. instruction data are rich in detail variations, while the remaining P.E. instruction data are mostly smooth structured. The low-rank constraint of DeSCI has better representation capability for smooth structure-rich videos, while the deep network prior model of the algorithm in this chapter has good representation capability for texture details.Figure 5
Quality comparison of different algorithms.


## 4.2. Construction of Multiple Evaluation Systems for the Quality of Authentic Physical Education

In addition to evaluating the reconstruction quality, this thesis also evaluates the reconstruction time between RE2-Net and the comparison algorithms. In this case, the NVIDIA GeForce RTX 2070 was used to run RE2-Net and E2E-CNN, and the rest of the algorithms were run on an Intel Core i70550U CPU. Figure6 shows the time complexity (in seconds) required for each algorithm to reconstruct the six sports instructions in the generic dataset. The minimum time complexity value and the maximum frame rate in these algorithms are marked in bold. It is easy to see that, except for the algorithms proposed in this chapter and E2E-CNN, all the algorithms are based on iterative optimization, and the running time of such algorithms is directly related to the complexity of each iteration. Since each iteration needs to search for nonlocal similar patch blocks and ensure the minimization of the weighted kernel function, DeSCI requires 1 hour to reconstruct 8 types of physical education data from a single 256∗256 compressed measurement. In contrast, the algorithm proposed in this chapter only needs to input the compressed measurement frames into the overall network, and the reconstruction results can be obtained through the feedforward calculation of the neural network. As shown in the data in the figure, the algorithm in this chapter can achieve the reconstruction task of video compression perception in only 3 seconds, and the frame rate of reconstruction can reach 11.27, which realizes the near real-time reconstruction.Figure 6
Time complexity test by each algorithm.Verification of the effect of the number of iterations: The effect of the number of iterations on the reconstruction accuracy of NLR-CSNet was first tested. The PSNR value of the reconstruction metric was plotted against the number of iterations (on a logarithmic scale) for the Lena image (256256) with a measurement rate of 0.1. To simulate the noise, three different intensities of random Gaussian noise were added to the original compressed measurements. As shown in Figure7, the first curve corresponds to the reconstructed results with the original measurements without noise interference, and the remaining three curves correspond to the reconstructed plots with Gaussian noise with noise standard deviations of 0.01, 0.05, and 0.1 added to the measurements, respectively. By using the state data matrix and the random noise matrix to construct the reference state augmentation matrix, the correlation between the data in the state data matrix can eliminate the interference of the final results by comparing it with the state augmentation matrix. With the maximum number of iterations set to 10000, it can be seen from the four plots that the reconstruction quality improves rapidly up to 1000 iterations, then rises slowly to about 2000 iterations, and saturates at 3000 iterations. Even if the intensity of Gaussian noise added to the measurements increases, the PSNR curves do not decrease with the increase in the number of iterations. This shows that NLR-CSNet is robust to the effect of the number of iterations and has good noise perception.Figure 7
Relationship graphs for different intensities of Gaussian noise.As Figure8 shows the confusion of different signal-to-noise ratios, the PR-VNE algorithm uses a reinforcement learning agent in the training phase to explore how the model should perform the virtual network mapping. The input of the reinforcement learning agent is the consensus matrix representation of the physical network before each virtual network mapping, and the output is the probability of selecting each node. When a virtual request arrives, the reinforcement learning agent randomly selects the physical nodes that meet the requirements and provides feedback to the reinforcement learning model based on the evaluation metrics of the results of the selected mapping scheme. The reinforcement learning agent needs to strike a balance between the exploration of new models and the utilization of trained models. The reinforcement learning agent is rewarded more when the nodes selected by the model bring better gains; when the nodes selected by the model bring less or negative gains, the reinforcement learning agent is rewarded less. In a multi-classification problem, the inter-class classification accuracy of different classes is also an important criterion for network performance. A confusion matrix is an important tool for measuring inter-class classification accuracy, which categorizes the number of correct and incorrect classes of a multi-classification model and then represents them in the form of a visual matrix. This is a very basic and intuitive method, and the calculation is a very simple matrix.Figure 8
Confusion of different signal-to-noise ratios.In the confusion matrix, the horizontal coordinate indicates the experimentally predicted modulation mode, the vertical coordinate indicates the true modulation mode, and the darker the color of each square in the matrix indicates the higher probability that the corresponding true modulation mode is judged to be the corresponding predicted modulation mode. For this network, the confusion matrix is a diagonal array when the prediction performance of the network is optimal. In this experiment, it can be observed that as the signal-to-noise ratio increases, the prediction performance of the network gets better. However, in general, the network does not classify well for both modulation types, QAM16 and QAM64, and always misclassifies between them. This is because both modulation types belong to QAM modulation, but they adopt different binary methods. The network designed in this paper cannot identify their specific types well, but it can identify them that both belong to QAM modulation more accurately.


## 5. Conclusions

This study constructs a multivariate evaluation model of physical education teaching quality through a random matrix optimization neural network to study the improvement of the evaluation system of high school physical education teachers’ teaching ability. In the future, the evaluation activities need to be improved and changed according to the corresponding background of the times, so that the evaluation can be more objective and effective. In this paper, the application of random matrix theory in the study of physical education quality is studied in depth. Firstly, according to the random matrix theory and the augmented matrix method, a multivariate evaluation model of physical education quality is established. Secondly, for complex physical education events, a physical education strategy method combining random matrix theory and perturbation power and perturbation energy method is proposed. Then, for the complex power grid system, the community structure theory is used to partition the complex power grid, and the random matrix theory-based voltage transient fault source location model is used to analyze each sub-network to solve the problems of too much data and too long analysis time. Finally, to address the problems of too many partitions or too small dimension of state data matrix due to grid partitioning, an RMT-CNN-based physical education quality evaluation method is proposed, which can use CNN training to obtain optimized feature statistics, improve the universality of statistics, and make the random matrix theory more applicable to various structures. Since random matrix theory is a big data analysis method based on mathematical statistics, it can extract the correlation between data from massive data. Based on this advantage of random matrix theory, a physical education teaching quality model based on random matrix theory is constructed. The classification effect of the network for the two modulation types of QAM16 and QAM64 is not good, and there will always be misjudgments between the two. Although the network designed in this paper cannot identify its specific type well, it can be identified more accurately that all belong to QAM modulation. The evaluation index system should be constructed based on adhering to the scientificity, accessibility, independence, and generality, and the implementation of these four aspects to build out the online teaching quality evaluation index system and evaluation criteria for public physical education classes in colleges and universities, which provides a certain realistic basis for the ultimate realization of the objectives of physical education classes in colleges and universities.



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*Source: 6553012-2022-07-30.xml*