# A Gaussian High-Dimensional Random Matrix-Based Method for Detecting Abnormal Student Behaviour in Chinese Language Classrooms

Authors: Xuyun Zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In this paper, a Gaussian high-dimensional random matrix approach is used to conduct an in-depth study and analysis of the detection of abnormal student behaviour in Chinese language classrooms, and a corresponding model is designed for practical application. The Gaussian high-dimensional random matrix technique and recurrent neural network technique are applied to build a basic technical framework for intelligent proctoring. An innovative method of human posture estimation is used to complete the proctoring task, and the structure of the Gaussian high-dimensional random matrix method is simplified and the model is compressed to achieve real-time and parallelism of the method. A PolSAR sparse representation classification (OGRM_SRC) algorithm based on orthogonal Gaussian random matrices (OGRM) is proposed to construct an observation dictionary based on polarisation features and OGRM to select typical ground target samples in polarized feature images. The system not only functions as a psychometric assessment of students but also is capable of detecting and analysing abnormal student behaviour based on the improved forest algorithm. The residuals of the pixel to be classified are calculated relative to each atom in the observation dictionary, and the minimum reconstruction residual is used as the classification criterion. The OGRM_SRC algorithm is applied to classify the pixel, and the final classification results are obtained and evaluated for accuracy. We propose a fine-grained action recognition optimisation method for recurrent neural networks, fusing temporal attention information and spatial attention information to improve the action recognition method and improve the model’s ability to recognise fine-grained abnormal behaviours such as looking left, looking right, and copying with head down. Based on this, we conducted some comparative experiments to validate the effectiveness of our work and verified that the system achieved a recognition efficiency of 76.8 FPS and a recognition accuracy of 98.5% in a graphical computing processor.


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## Body

## 1. Introduction

With the rapid development of society, the pace of people’s lives is also increasing, and the high pace of life can easily lead to a series of physical or psychological problems. Compared to adults who have some work experience and life experience, university students who have just left the protection of their friends and family are more likely to have problems and even irreversible behaviour such as dropping out of school or even committing suicide. Although there is a large amount of video surveillance data, the level of campus security management is not optimistic due to the funding and security awareness of all levels of university security construction, which generally remains in the way of recording and monitoring data for the supervision of abnormal student behaviour [1]. Most colleges and universities lack analysis of abnormal behaviour of individual students, making it difficult to visualise and display abnormal behaviour of individual students, and it is difficult to identify abnormal students through psychological counselling and manual monitoring alone. At the same time, key institutions are more sophisticated than ordinary universities due to the speed with which equipment and intelligent monitoring systems are updated. However, the monitoring equipment in ordinary universities is old, the campus security construction is lax, and the limited security management coverage is small. The hardware problems of the monitoring equipment make it difficult for most of the intelligent monitoring systems to cover the whole campus in ordinary universities where the hardware conditions are mixed and far from meeting the level of modern campus security construction [2]. Therefore, this paper designs a widely applicable system for the detection and analysis of abnormal student behaviour on campus, which analyses and detects the video stored in the surveillance equipment without the need to update old surveillance equipment, promoting the development of intelligent surveillance and intelligent management in the campus environment.Moreover, traditional video surveillance manually uses the human eye, and as the attention of security personnel cannot be guaranteed to be always highly focused, important information in the video may be missed due to fatigue or distraction of security personnel; more importantly, relying on human eye inspection is extremely inefficient, and it is difficult to achieve immediate feedback for dozens of surveillance images across the campus. In addition, the campus scene is so complex that it is easy to make mistakes with just the naked eye [3]. As a result, it is difficult for the traditional monitoring system to meet the current requirements of a “smart campus.” As an important means of security protection, the value of the monitoring system cannot be fully utilised if it is not real time and efficient. Commonly used data processing methods mainly include data cleaning, data merging, data splitting, data calculation, and data transformation. (1) As mentioned before, there will be some duplication of data and missing data in the obtained data table. At this time, data cleaning is required. The common data cleaning methods in daily life mainly include duplicate data processing, missing data processing, and spaces.In the process of students’ self-learning, teachers often supervise and regulate students’ learning behaviour to ensure the effectiveness of learning, improve the efficiency and quality of students’ learning, and complete their learning tasks. The external supervision from the teacher can facilitate the development of students’ self-control. However, unlike in traditional classrooms, our students tend to study on their own without the supervision of the teacher, so there are often abnormal behaviours in the self-study classroom that do not allow students to study properly, thus, the discipline of the self-study class is not guaranteed, which not only affects their learning effect but also affects the surrounding students. Therefore, self-study classes do not fulfill their purpose. This paper proposes the use of video supervision to compensate for the inability of teachers to provide timely and real-time supervision in study sessions. This method allows students to develop independent learning skills and allows the teacher to keep track of student learning. The use of video monitoring of students’ unusual behaviour in study sessions can greatly improve student discipline in study halls and increase the efficiency of student learning in study classes. In addition to this, the study concludes with some suggestions on how to use video supervision properly.


## 2. Related Work

In the field of video anomaly detection and video analysis, trajectory-based detection methods have been popular [4]. By training the trajectory error of the target object in the video, the error range is determined, and then the error of the trajectory in the video is compared with the error of the trajectory in the training set in the test set, and if the error is out of range, it is determined to be anomalous. However, the trajectory-based analysis method relies heavily on tracking techniques, which will aggravate the task of video anomaly detection if there are more objects in the video, and the training effect is not very good, which is not conducive to anomaly detection in crowded or complex scenes [5]. The classical central limit theorem is one of the widely used limit theories in multivariate statistical analysis, and the classical central limit theorem holds under the assumption that the dimensionality of the random variable is fixed, i.e., not too large compared to the sample size. However, according to the results of validation, the limiting behaviour of the statistic no longer applies when the dimensionality becomes larger [6]. Specifically, it gives a general method for testing the overall information with sample information in a high-dimensional framework. The constructed linear spectral statistic is not only effective in solving the testing problems that do not apply to the statistics based on classical limit theorems but also has a high testing accuracy and high generalization in a high-dimensional framework or under classical models.Qi et al. proposed a PolSAR image classification method based on an improved polarisation scattering matrix and an H/α-Wishart classifier [7]. The method uses the Quegan algorithm to solve the polarisation distortion parameter matrix and improve the polarisation scattering matrix, using the matrix to construct a more accurate H/α two-dimensional plane and classifies PolSAR images by the H/α-Wishart classifier [8]. Alzahab et al. used a Markov model to automatically classify SAR sea ice images by first dividing the sea ice images into irregular regions and then using Markov random fields to develop annotations of joint information to classify each piece of information at the pixel level [9]. This method can effectively classify sea ice regions, but they only analyse sea ice data provided by the Canadian Ice Service, which is only applicable to sea ice image processing in specific situations and has a smaller application [10]. Chen et al. proposed a kernel singular vector decomposition (KSVD) algorithm, which is based on a learning decomposition method to generate adaptive bases and extends the KSVD algorithm in nonlinear feature space [11]. An algorithm is an iterative approach that alternates between the sparse encoding of the kernel feature space based on a nonlinear dictionary and an update process for each atom in the dictionary, ending with a linear support vector machine classifier to obtain the classification accuracy [12]. Flex Net creatively simplifies image preprocessing operations by allowing images to be spontaneously selected throughout the network’s prediction process for image features that contribute more to the task. The image processing process is completely free from tedious manual features, allowing the network to fully automate the image processing task, and these features have made it widely used in the field of computer vision. The characteristics of close-range monitoring are high stability: the whole machine has high stability, adopts a military-grade laser, and is fully sealed with nitrogen to effectively ensure its service life. GoPro’s unique laser homogenization technology makes the laser spot very uniform, without horizontal lines and speckles, and the image quality at night is as delicate as that in the daytime.Behavioural states are the regular behaviour of students over a certain period, i.e., individual behaviour within a group pattern [13]. There are two approaches to the study of human behavioural states: one is based on the direct classification of student behaviour by target classification; the other is the detection of student behaviour using human gesture recognition. The former simply finds the target box containing the student’s area and then directly classifies it. The latter method identifies the key points on the student’s body posture, then distinguishes the student’s behaviour by the distribution and arrangement of the key points, and finally obtains the student’s state by the student’s behavioural actions over some time. Both methods aim to identify the state information of an individual, and research scholars have developed some feasible ideas in the field of individual behavioural states, which provide a solid theoretical basis for the identification of student behavioural states in the campus environment. The Basement algorithm is first used to identify dangerous areas within the surveillance screen. Then, based on the FL-RFCN algorithm, small target human bodies within the surveillance screen are detected, individuals entering the danger zone are alerted, and students are identified based on the Multi-angle ID algorithm. Finally, the student’s psychological stress level is queried from the psychological stress database identified in Chapter 3 based on the student’s identity information and a graded warning is given to students in the danger zone based on their psychological stress level.


## 3. A Gaussian High-Dimensional Random Matrix Design for Student Behaviour in Chinese Language Classrooms

As technology advances, time-series data whose dimensionality increases with sample size or whose dimensionality is large relative to the sample size is becoming more common. Examples include time-varying spatial data, functional magnetic resonance imaging (fMRI) datasets, and spectral imaging datasets. Some basic knowledge about the limiting distribution of the extreme eigenroots of high-dimensional random matrices and the origin of the TW distribution, the extreme eigenroots of Wigner matrices and the limiting behaviour of the extreme eigenroots of sample covariance matrices in statistics are briefly introduced in the Basics section [14]. Under certain conditions and after a series of transformations, the maximum eigenroots of the Wigner matrix obey the TW distribution and, coincidentally, the maximum eigenroots of the sample covariance matrix also obey the TW distribution.(1)El=EVlvl−EHlhlEr=EVrvr−EHrhr.In summary, there are two main characteristics of sparse representations, namely, overcompleteness and sparsity. Sparsity refers to the fact that when a sparse representation of the original image is performed, the coefficients are sparse, i.e., the image is represented linearly using only a small number of dictionary atoms.A randomness matrix is better for image reconstruction containing less information, but due to the random generation of the matrix, the signal fluctuation, robustness is not strong, and the random matrix structure is complex, the running time is long, especially for processing satellite images with a large amount of information, it needs great space to store the measurement matrix, so the image classification is less effective in practical applications. Deterministic matrices are characterised by the fact that if the construction parameters of the matrix are certain, the constituent elements of the matrix are determined and cannot be changed. However, these matrices cannot be set to an arbitrary measurement matrix size based on the image, which is a great limitation for measuring satellite images of different sizes.(2)x'′=argmaxx'′s.t.yce+Dx'′≥σx'′=argmaxyce+Dx'′s.t.x'′≥sl.Targets can be identified using the average polarized scattering anglea, but cannot be distinguished if the primary scattering mechanism of ground targets is the same. To solve this problem, Cloud proposes a parameter that characterises the scattering randomness of a target, the polarized scattering entropy H. The polarized scattering entropy H is a parameter that measures the scattering randomness of a target and can distinguish between ground targets with the same primary scattering mechanism but different scattering randomness, and is expressed as follows.(3)H=−∑m=1npmlnpm.The mutual orthogonality of the electric and magnetic fields forms an electromagnetic wave. If the electromagnetic wave propagates in the direction of thez-axis in Cartesian coordinates, the electric field intensity of the electromagnetic wave can be projected onto the x-axis and y-axis, respectively, and the x- and y-components can be obtained by decomposing the electric field vector at a point in space in the two orthogonal directions.(4)Ez,t=Ex02+Ey021/2sinwt+kz.The polarisation scattering matrix of a ground target is obtained by probing the magnitude information and phase information within the ground cell. Ground targets are divided into deterministic ground targets and distributed ground targets, with different polarisation scattering matrices available for deterministic ground targets and distributed ground targets. The electromagnetic scattering characteristics of deterministic ground targets can be fully characterised using the scattering matrix [15]. However, in practical measurements, there are more distributed ground targets and the scattering characteristics of the targets are more random, the scattering matrix cannot fully represent all the scattering information and a statistical approach needs to be applied to describe their electromagnetic scattering characteristics. Therefore, to characterize the polarisation of the ground targets, new parameters need to be introduced to enable them to reflect the differences in phase and amplitude of the scattered waves in each polarisation channel, as shown in Figure 1.Figure 1
Intelligent video surveillance system architecture.Intelligent video surveillance systems involve more disciplines, such as information technology and neural networks, and the content system is very large. The specific video information captured in the actual monitoring can be divided into two categories: one is the close-view monitoring, human body information in this monitoring range will be a more specific presentation on the video screen; the second is the distant view monitoring, that is, monitoring due to the human body is far from the monitoring probe, resulting in the human body information which cannot be fully captured, and becomes more blurred. According to the above classification, for the distant view surveillance, the human movement trajectory is mainly detected from an overall perspective; for the close view surveillance, the abnormal behaviour occurring in the human body that can be identified as the human body limb behaviour is fully captured.(5)T∗∗+ET∗|S2=w1trS1∑1S22+EtrS1∑1S22.From the above algorithm description, the curve classification method can discriminate between closed and spiral curves more effectively. However, in the specific implementation of the algorithm, different algorithms are adopted for different types of curves, and the calculation of both algorithms needs to be carried out at the same time, and the higher calculation volume will put a relatively large pressure on the hardware equipment [16]. In addition, the trajectory of the human body is not limited to the above two types in the process of realistic movement, if it is an S-shaped curve, it will to a certain extent interfere with the discrimination of spiral-shaped curves, i.e., the curves are not closed, and the centre points, as well as the trajectory points, are equally distributed in four areas, which will generate false alarms when the threshold value is exceeded.(6)S=1n∑j=knxk−x¯xk−x¯∗∗.However, the practical application of this algorithm involves first learning the specific trajectory, by learning the distribution patterns of the sub-trajectories in the training trajectory before the feature information of the whole trajectory can be extracted. This requires many samples for the training process, which contains a huge amount of temporal and spatial information. This algorithm is not suitable for the needs of university campus video surveillance, as it requires sample training for trajectory identification and is only suitable for more specific sites, such as road traffic monitoring of vehicles at intersections. For the campus irregular intersections and places, the human movement appears complex trajectory, plus the trajectory contains the time information, the calculation is too large, and is not suitable for the campus alone personal travel trajectory detection.When the human body moves, the posture of the human body can locate a set of movement states; this set of quantified movement states is the human body’s behavioural characteristics. The extraction of human behavioural features is the key problem to be solved for human behavioural recognition, if the human behavioural features are not well solved, behavioural recognition will not be possible. The specific human behaviour extraction process is to express the movement state with a set of suitable feature data for the specific movement sequence of the human body. The motion sequence refers to the time-series motion signal data when the human body moves or the object moves. Motion sequences have applications in many fields, such as the sports world. According to the motion sequences of athletes during training and competitions, they can analyse the deficiencies of athletes and improve their skills; in animation generation, motion capture technology is used to detect and record the performers’ limbs in real time. The motion trajectory in the three-dimensional space captures the performer’s movement and transforms it into digital “abstract motion” to drive the virtual human model, making the animation production process more intuitive and the effect more vivid.The behavioural gesture presented in each frame of the video sequence is regarded as an independent behavioural state, and each independent state is combined using probability so that in the state space method, the different motion sequences can be regarded as a continuous behaviour consisting of a sequence of independent states [17]. The probabilistic likelihood of each state is compared, with the standard sequence of behaviours, and after the complete behaviours have been compared, the overall likelihood value of the whole behaviour is calculated and the standard behaviour with the highest overall likelihood value, as shown in Figure 2.Figure 2
Alpha pose structure.AlphaPose is a representative method of the top-down approach and its structure is shown in Figure2. As the output of the network has only one body pose information, only the coordinates and confidential information of the body key points in the graph need to be output. With the number of human key points prespecified, the output of the network is a vector with a fixed dimension, and therefore the fully connected layer can be used directly as the output of the network. In contrast, the speed bottleneck for this type of method is the number of bodies in the image, and the time overhead of the algorithm is proportional to the number of bodies in the image. Therefore, these methods are often used in scenarios where the number of bodies is small and can demonstrate excellent recognition accuracy in the applicable scenarios.


## 4. Analysis of Students’ Abnormal Behaviour Detection

In this summary, we use the method of knowledge distillation for compression and supervised training of feature extraction networks. In machine learning, it is assumed that there is a potential functional relationship between the input to the output which is unknown. This task is more feasible if the new model is allowed to approximate the original model since the function of the original model is known, a task that is equivalent to the process of machine learning to approximate a known data distribution, while the original model can provide continuous information that is not available in the known data distribution, i.e., the probability value distribution of softmax, adding a priori information to the training process of the new model.Although knowledge distillation methods allow simple network models to fit the distribution of functions of complex networks and thus have the representational power of complex models, this fitting is not unlimited, i.e., the degree of fit is related to the structure of the small model. The ability to fit a small model is also related to the structure of the model itself. An overly simple network structure will not allow the small model to have sufficient representational power to successfully fit the function distribution of a complex network despite the a priori information of the complex network, while an overly complex network structure will result in unnecessary computational overhead [18]. Therefore, it is also important to design the structure of simple models. Commonly used data analysis methods include event analysis, funnel analysis, user path analysis, retention analysis, session analysis, thermal analysis, attribution analysis, interval analysis, distribution analysis, LTV analysis, user behaviour sequence analysis, user attribute analysis, and user grouping analysis. The current monitoring system is generally more “monitoring” and less “controlling,” and the number of monitoring points is much larger than the number of control points. According to dialectical thinking, the two functions of the monitoring system should be complementary and indispensable, and there should be as many monitoring quantities as there are control quantities.The resolution of the face image in this paper is 112∗ 92, which is a fixed value. Therefore, if the number of LBP blocks in the image is larger, the area of LBP is smaller, while if the number of LBP blocks is smaller, the area of LBP is larger. However, as the number of blocks increases, the dimensionality of the LBP histogram features increases dramatically and the segmentation of the face image becomes too small. Too large a dimensionality not only leads to a reduction in classification speed but also increases interference caused by high-frequency noise. At the same time, too small a partition can result in a histogram that is too sparse and loses statistical significance, while excessive dimensionality reduction can also affect the accuracy. Although reducing the feature dimension of LBP by PCA can improve the differences between categories, excessive reduction of the feature dimension of LBP will lead to a reduction in the classification effect. Therefore, the dimensionality of the facial LBP features after PCA should be kept within a reasonable range. Therefore, this paper conducts a comparison experiment on the errors in the ORL database with a different number of LBP image blocks and different PCA dimensions. The best LBP feature block size and PCA dimension are selected in Figure 3.Figure 3
Error comparison experiment.The goal of top-down human pose recognition is to obtain reliable high-resolution heat maps for the detection of skeletal joints, so pose recognition is performed with minimal loss of spatial structure relationships. Most existing methods for pose feature extraction first reduce the resolution of the original image and then use the low-resolution features to recover the high-resolution features. To always maintain a high-resolution feature representation, this chapter uses a high-resolution network to extract the skeletal joint point features.In the process of student-led learning, the main aim is to complete the learning task. To complete the learning task, students can divide their learning task into several appropriate learning objectives. One is to simplify a complex and tedious learning task, and the other is to be able to judge whether they have achieved the learning task through different learning objectives [19]. Learning objectives need to be set according to the student’s actual ability. If targets are set too high, students will not be able to complete them on time, which will affect their self-confidence in self-learning and hence the effectiveness of independent learning. If the target is set too low, students may find the task too easy to achieve in a short period and may find it difficult to arouse interest in learning.The U-Net model is a basic left-right symmetric U-shaped structure, like that of a self-encoder, which performs four downsamples during the convolution process and four upsamples during the deconvolution process, restoring the original resolution of the input image through the high-level semantic features obtained during the convolution process. The U-Net model combines the low- and high-level information of the network. The high-level features can be used to extract complex features of the image, while the low-level features improve the accuracy of the extracted image, as shown in Figure4.Figure 4
Structure of multiple face recognition based on LBP-PAC-ABASNet and H-softmax.Both the gradient disappearance and the gradient explosion problems arise because the partial derivatives of the activation function and the weights are multiplied together in a chain when the deeper network is performing the optimisation of the weights [20]. When the partial derivative of the activation function and the initialised weights are multiplied by less than 1, the gradient descent is a cumulative multiplication of many numbers less than 1, and the closer the result is to 0, the more likely the gradient disappears. The gradient explosion is the opposite, when the initialisation weights and the partial derivatives of the activation function are multiplied together to produce a number greater than 1, it is easy to cause the gradient explosion problem.In deep networks, downsampling (pooling) is always performed to increase the perceptual field of the network and reduce the computational effort. This increases the perceptual field but reduces the spatial resolution of the feature map. To maintain the spatial resolution of the feature map while expanding the perceptual field, deep networks can use a null convolution method. This method is very effective in tasks such as target detection and semantic segmentation. On the one hand, it increases the perceptual field, allowing the detection and segmentation of larger targets in the image, and on the other hand, it maintains the original high resolution of the image, allowing a certain amount of detailed information to be retained and more accurate target localisation. At the same time, by designing different expansion rate parameters, the cavity convolution can provide different perceptual fields, i.e., allowing the network to obtain multi-scale information in the image.


## 5. Experimental Design

Data preprocessing is a very important part of the data mining process, but it is very time and effort consuming. Experience has shown that good data preprocessing saves effort when building models. It is important to preprocess data because there is a lot of noisy data, redundant data, or incomplete data in the dataset that affects the prediction results.In the RNN + ST method, only the input human skeletal motion information is spatially featured, and the temporal features are not spatially processed after the temporal feature enhancement. The method retains the temporal disparity information at the original input scale, allowing the temporal disparity information not to scale with the weight information of the key points; the RNN + TS method spatially features both the input information and the temporal disparity information, allowing the temporal disparity information to scale with the spatial weight assignment, i.e., making the displacement information of the more important key points larger and the displacement information of the less important key points smaller. Abnormal behaviour detection based on video images is mainly divided into image processing methods and deep learning methods. The implementation of image processing technology is mainly divided into single-frame image detection and multi-frame image detection. Single-frame image detection uses grayscale processing on a single-frame image to segment the detected person through a grayscale threshold or target image edge detection and then matches anomalous models to detect anomalous behaviours. The multi-frame image detection realizes the segmentation of the detection target according to the change of the mixed Gaussian background model of the continuous multi-frame sequence images.To provide a more accurate indication of the robustness of the proposed algorithms, 10 sets of tests were performed under the ORL database [21]. The parameters in the 10 tests are identical for each algorithm; LBP-PCA-BPNN is an algorithm that has not been optimised by the ABAS algorithm, while LBP-PCA-ABASNet is an algorithm that has been optimised by the ABAS algorithm. The other parameters were the same for both algorithms. In the different experimental groups, LBP-PCA-BPNN was found to be highly volatile, while LBP-PCA-ABASNet was less volatile and had a better robust performance. Figure 5 shows the robustness verification experiments for the proposed face recognition algorithm.Figure 5
Ablation experiment with reduced training time.Face recognition results in campus environments can be affected by factors such as lighting, resolution and angle, so the accuracy of the dataset and the recognition results in real-world scenarios may vary. This paper, therefore, conducts the tests in classroom sites to verify the effectiveness of the algorithm and to ensure that the same object gets a fixed and unique digital identification in the video. Multi-target tracking is usually limited to scenes with known target categories, such as visual tracking of multiple pedestrians and vehicles. Therefore, multi-object tracking algorithms highly rely on off-the-shelf object detectors. The quality of object detection is directly related to the subsequent multi-target trajectory association. Differently, single-target tracking algorithms require to deal with the arbitrary classes of objects, i.e., do not know any prior information about the target. Although the preconditions are slightly different, as the name suggests, single-target tracking and multi-target tracking are closely related to object recognition and tracking in video, so they have close technical details such as appearance modeling, motion analysis, and trajectory association. .The name above each person is the corresponding facial image category. Face detection is performed using the YOLOv5 algorithm, followed by face recognition using the ABASNet algorithm. The training time and the number of iterations is greatly reduced using transfer learning here, converging after 50 iterations; the training and recognition times for ABASNet are 21 seconds and 0.06 seconds, respectively, after 50 iterations. The accuracy of face recognition in this algorithm is consistent with that of deep learning algorithms when the number of people is less than 10,000. The algorithm can be used on lightweight embedded devices or mobile terminals because of its real-time recognition and simple network structure, and it has the advantages of fast recognition, fast training, a small number of face samples required, high accuracy, and low hardware level. The algorithm in this paper is, therefore, extremely effective in promoting the use of multiple face recognition in campus applications.


## 6. Analysis of Results

### 6.1. Performance of Gaussian High-Dimensional Random Matrix Algorithms

As the number of dimensions increases, the empirical value of the efficacy of all tests becomes 1, which demonstrates the consistency of the three tests. This is to be expected, as more information is available as the dimensionality increases, making it easier to test. In contrast, LE and LN are more effective than BS in all cases. This is because the maximum characteristic root of the matrix is more sensitive to outliers relative to the trace. The LN performs slightly worse than the LE due to errors in parameter estimation, as shown in Figure6.Figure 6
Empirical type I error rates for BS, LE, and LN under discrete random variables.Separately, the autoregressive component is more sensitive to differences than the sliding mean component. The alternative hypothesis is that small differences in the autoregressive component, say only 0.1, still test well even in the smaller sample Case (30, 150), with an efficacy above 0.9. For the sliding average component, the test is slightly less effective in the smaller sample case, but increases as the sample dimension increases and the efficacy tend to 1. Safety monitoring requires continuous detection and tracking of pedestrians and objects in a specific area, to detect abnormal behaviours of pedestrians or potential safety hazards in the scene in time. Security monitoring is widely used in every corner of daily life, such as schools, banks, supermarkets, railway stations, parking lots, office buildings, and street intersections. Intelligent monitoring automatically analyses and warns people through the identification, tracking, and higher-level semantic understanding of suspicious pedestrians, which improves efficiency and greatly reduces the people’s workload.Overall, even though the differences between the original and alternative hypotheses are small, the test efficacy still performs well and is close to 1 even when a particularly large sample size is not required, which again demonstrates the validity of the proposed approach. It is also worth noting that this chapter presents the limiting behaviour of the extreme eigenroots of the self-sampled covariance matrix for a special case of the VARMA model, while the corresponding results for a more generalised VARMA model are still a challenging task and may require methodological innovations for such high-dimensional random matrices where there is no independence between the ranks, which is an issue to be investigated next.The mean and variance parameters of the empirical distribution of the linear spectral statistic and the mean and variance parameters of its asymptotic distribution have systematic deviations, as shown in Figure7.Figure 7
Gaussian distribution test results.Both methods can maintain high test efficacy under the general alternative hypothesis. The theoretical properties of these three tests are extensively investigated under the original hypothesis and three alternative hypotheses, thus clarifying the advantages and disadvantages of combining multiple statistics with different methods. Numerous numerical simulations show that the efficacy of the new tests will be equal to or better than that of the existing methods. Numerical simulations show that the new tests have high empirical efficacy under most of the alternative hypotheses, suggesting that the new tests are more widely applicable and perform more consistently.The experimental results show that this angle-based trajectory detection method provides real-time detection of various trajectory curves in a generic way that can more accurately reflect the human motion trajectories that may occur in real-world situations on campus. Although SCED’s algorithm has a stronger generality in terms of trajectory types, the advantages of the algorithm proposed in this chapter, which does not require sample training and a more targeted curve type discrimination, allow this algorithm to work better with the same hardware configuration.


### 6.2. Results of Classroom Aberrant Behaviour Detection

After validation with publicly available datasets, we found that EM and MV metrics can be used as evaluation criteria for anomaly detection algorithms in unsupervised cases. We use the EM and MV metrics to compare unsupervised anomaly detection algorithms on student behaviour data. Since the algorithms work similarly on data of different sizes, this experiment uses behavioural data of 2000 students for anomaly detection for better presentation. As the EM and MV metrics of the algorithms differed significantly, the EM metrics of the original OCSVM algorithm were expanded by a factor of 10,000, and the MV metrics of the original LOF and OCSVM algorithms were reduced by a factor of 1,000 and 10,000, respectively, for the sake of visualisation of the plots, and the experimental results are shown in Figure8.Figure 8
EM score curve.In Figure8, the EM metrics for the improved iForest algorithm (Bt-iForest), iForest, OCSVM, and LOF algorithms are 7.995E − 4, 7.965E − 4, 3.987E − 8, and 3.971E − 4, respectively. The legend of the improved iForest algorithm shows that the grey star-shaped line is always above the other curves, indicating that this algorithm has the best detection effect. As the number of RNN layers increases, the accuracy of the model tends to increase and then decrease. This is because when the number of RNN layers is shallow, the representational power of the model has difficulty fitting the distribution of the training data; while when the number of RNN layers increases, the representational power of the model increases whenever the complexity of the model structure increases; when the number of RNN layers is too deep, the training of the RNN suffers from gradient disappearance and gradient explosion due to the constant multiplication of the cyclic weight matrix. Therefore, too deep RNN models are difficult to converge in training, resulting in a sharp drop inaccuracy.Comparing the relative positions of the curves in Figure9 shows that the metrics of the BASE method improved when combined with the temporal attention mechanism and the spatial attention mechanism alone, respectively, and the metrics improved more when combined with the spatial attention mechanism alone. This is because, in the RNN + ST approach, we only assign weights to candidates’ spatial motion patterns without corresponding weight scaling to information about candidates’ motion differences in the temporal dimension, which leads to many false detections or missed detections when the algorithm inputs inconsistent and contradictory information about candidates in the process of identifying certain abnormal behaviours.Figure 9
Classroom state analysis.As can be seen in Figure9, a greater proportion of students with poorer mental health status played on their mobile phones and dozed off, with the sum of the two behaviours exceeding 85%, along with correspondingly poorer academic performance, while a greater proportion of students with less mental stress listened to and read books, with correspondingly better academic performance. Although both hand-raising and standing were less frequent among all students, students who engaged in classroom behaviour of raising their hands and standing for teacher–student interaction were in a better mental state whenever this occurred.As students who are prone to risky behaviour on campus are often students who are psychologically stressed, and psychologically stressed students are more likely and at risk of abnormal behaviour. Therefore, student classroom behaviour from the Campus Health video was used to identify students who were playing on their mobile phones and sleeping in the classroom behaviour. Students who played with their mobile phones and slept for more than 75% of the 120 lessons were marked as students with high psychological stress and poor heart health and recorded in the Campus Smart Health system and given higher-level warnings in subsequent chapters for abnormal behaviours and risky actions of students with poor heart health.Two hundred face categories with a total of 18,000 images were then divided into a training set and a test set according to 8 : 2 and fed into the ABASNet network for training. The models were tested in the test set at different iteration counts. The network tends to fit when the number of iterations reaches 382, and the highest accuracy of face recognition is achieved when the number of iterations is around 463. Therefore, the face recognition model at iteration number 463 was chosen for student identification in hazardous areas.


## 6.1. Performance of Gaussian High-Dimensional Random Matrix Algorithms

As the number of dimensions increases, the empirical value of the efficacy of all tests becomes 1, which demonstrates the consistency of the three tests. This is to be expected, as more information is available as the dimensionality increases, making it easier to test. In contrast, LE and LN are more effective than BS in all cases. This is because the maximum characteristic root of the matrix is more sensitive to outliers relative to the trace. The LN performs slightly worse than the LE due to errors in parameter estimation, as shown in Figure6.Figure 6
Empirical type I error rates for BS, LE, and LN under discrete random variables.Separately, the autoregressive component is more sensitive to differences than the sliding mean component. The alternative hypothesis is that small differences in the autoregressive component, say only 0.1, still test well even in the smaller sample Case (30, 150), with an efficacy above 0.9. For the sliding average component, the test is slightly less effective in the smaller sample case, but increases as the sample dimension increases and the efficacy tend to 1. Safety monitoring requires continuous detection and tracking of pedestrians and objects in a specific area, to detect abnormal behaviours of pedestrians or potential safety hazards in the scene in time. Security monitoring is widely used in every corner of daily life, such as schools, banks, supermarkets, railway stations, parking lots, office buildings, and street intersections. Intelligent monitoring automatically analyses and warns people through the identification, tracking, and higher-level semantic understanding of suspicious pedestrians, which improves efficiency and greatly reduces the people’s workload.Overall, even though the differences between the original and alternative hypotheses are small, the test efficacy still performs well and is close to 1 even when a particularly large sample size is not required, which again demonstrates the validity of the proposed approach. It is also worth noting that this chapter presents the limiting behaviour of the extreme eigenroots of the self-sampled covariance matrix for a special case of the VARMA model, while the corresponding results for a more generalised VARMA model are still a challenging task and may require methodological innovations for such high-dimensional random matrices where there is no independence between the ranks, which is an issue to be investigated next.The mean and variance parameters of the empirical distribution of the linear spectral statistic and the mean and variance parameters of its asymptotic distribution have systematic deviations, as shown in Figure7.Figure 7
Gaussian distribution test results.Both methods can maintain high test efficacy under the general alternative hypothesis. The theoretical properties of these three tests are extensively investigated under the original hypothesis and three alternative hypotheses, thus clarifying the advantages and disadvantages of combining multiple statistics with different methods. Numerous numerical simulations show that the efficacy of the new tests will be equal to or better than that of the existing methods. Numerical simulations show that the new tests have high empirical efficacy under most of the alternative hypotheses, suggesting that the new tests are more widely applicable and perform more consistently.The experimental results show that this angle-based trajectory detection method provides real-time detection of various trajectory curves in a generic way that can more accurately reflect the human motion trajectories that may occur in real-world situations on campus. Although SCED’s algorithm has a stronger generality in terms of trajectory types, the advantages of the algorithm proposed in this chapter, which does not require sample training and a more targeted curve type discrimination, allow this algorithm to work better with the same hardware configuration.


## 6.2. Results of Classroom Aberrant Behaviour Detection

After validation with publicly available datasets, we found that EM and MV metrics can be used as evaluation criteria for anomaly detection algorithms in unsupervised cases. We use the EM and MV metrics to compare unsupervised anomaly detection algorithms on student behaviour data. Since the algorithms work similarly on data of different sizes, this experiment uses behavioural data of 2000 students for anomaly detection for better presentation. As the EM and MV metrics of the algorithms differed significantly, the EM metrics of the original OCSVM algorithm were expanded by a factor of 10,000, and the MV metrics of the original LOF and OCSVM algorithms were reduced by a factor of 1,000 and 10,000, respectively, for the sake of visualisation of the plots, and the experimental results are shown in Figure8.Figure 8
EM score curve.In Figure8, the EM metrics for the improved iForest algorithm (Bt-iForest), iForest, OCSVM, and LOF algorithms are 7.995E − 4, 7.965E − 4, 3.987E − 8, and 3.971E − 4, respectively. The legend of the improved iForest algorithm shows that the grey star-shaped line is always above the other curves, indicating that this algorithm has the best detection effect. As the number of RNN layers increases, the accuracy of the model tends to increase and then decrease. This is because when the number of RNN layers is shallow, the representational power of the model has difficulty fitting the distribution of the training data; while when the number of RNN layers increases, the representational power of the model increases whenever the complexity of the model structure increases; when the number of RNN layers is too deep, the training of the RNN suffers from gradient disappearance and gradient explosion due to the constant multiplication of the cyclic weight matrix. Therefore, too deep RNN models are difficult to converge in training, resulting in a sharp drop inaccuracy.Comparing the relative positions of the curves in Figure9 shows that the metrics of the BASE method improved when combined with the temporal attention mechanism and the spatial attention mechanism alone, respectively, and the metrics improved more when combined with the spatial attention mechanism alone. This is because, in the RNN + ST approach, we only assign weights to candidates’ spatial motion patterns without corresponding weight scaling to information about candidates’ motion differences in the temporal dimension, which leads to many false detections or missed detections when the algorithm inputs inconsistent and contradictory information about candidates in the process of identifying certain abnormal behaviours.Figure 9
Classroom state analysis.As can be seen in Figure9, a greater proportion of students with poorer mental health status played on their mobile phones and dozed off, with the sum of the two behaviours exceeding 85%, along with correspondingly poorer academic performance, while a greater proportion of students with less mental stress listened to and read books, with correspondingly better academic performance. Although both hand-raising and standing were less frequent among all students, students who engaged in classroom behaviour of raising their hands and standing for teacher–student interaction were in a better mental state whenever this occurred.As students who are prone to risky behaviour on campus are often students who are psychologically stressed, and psychologically stressed students are more likely and at risk of abnormal behaviour. Therefore, student classroom behaviour from the Campus Health video was used to identify students who were playing on their mobile phones and sleeping in the classroom behaviour. Students who played with their mobile phones and slept for more than 75% of the 120 lessons were marked as students with high psychological stress and poor heart health and recorded in the Campus Smart Health system and given higher-level warnings in subsequent chapters for abnormal behaviours and risky actions of students with poor heart health.Two hundred face categories with a total of 18,000 images were then divided into a training set and a test set according to 8 : 2 and fed into the ABASNet network for training. The models were tested in the test set at different iteration counts. The network tends to fit when the number of iterations reaches 382, and the highest accuracy of face recognition is achieved when the number of iterations is around 463. Therefore, the face recognition model at iteration number 463 was chosen for student identification in hazardous areas.


## 7. Conclusion

This paper firstly introduces some common methods of pose estimation and abnormal behaviour detection. To be able to better extract the features of behaviour, this thesis uses key points of the human skeleton based on pose recognition as features and designs an abnormal behaviour detection algorithm for the campus environment. A specific analysis is made based on the needs of the project and an improved approach is proposed based on the existing advanced posture estimation and behaviour recognition algorithms. This paper proposes a deep learning-based method for identifying students’ classroom behavioural states based on the relationship between students’ classroom behaviour and their mental health states. Then, a MECN head is proposed to improve the accuracy of student behaviour recognition, and at the same time, migration learning is combined to reduce the number of network iterations and prevent network overfitting. The numerical simulation results show that the new test has high empirical efficacy under most of the alternative hypotheses, which indicates that the new test is more widely applicable and performs more consistently. Finally, reasonable assumptions about students’ mental health status are made based on their classroom behavioural status. A campus abnormal behaviour detection method that uses skeletal key points as behaviour recognition feature points and combines spatiotemporal graph convolutional networks for human behaviour recognition is proposed. The temporal and spatial graphs are modelled separately, and temporal features and spatial features are fully extracted using temporal changes of the same joint point and spatial configurations between joint points and joints, and experiments are expected to demonstrate the accuracy of this method.



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