An online education learning behavior trajectory tracking analysis method

Abstract

The application discloses an online education learning behavior trajectory tracking analysis method, and relates to the technical field of artificial intelligence and learning behavior analysis, wherein through collecting student visual line trajectories and click trajectories, coordinate correction, posture correction, time alignment and thermal field analysis are carried out to obtain behavior characteristics; behavior embedding vector sequences are constructed in combination with pedagogical context information, and learning intention categories are determined; a global transition probability matrix is constructed by using multi-platform collaborative analysis and a differential privacy mechanism to realize missing behavior trajectory recovery; and further, teaching regulation parameter vectors are generated based on a space-time graph, a self-attention network and cross-platform similar trajectory retrieval, so that the learning behavior analysis accuracy and the individualized teaching regulation capability are improved.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence and learning behavior analysis technology, and in particular to a method for tracking and analyzing online education learning behavior trajectories. Background Technology

[0002] In recent years, with the rapid development of internet technology, artificial intelligence technology, and online education platforms, online education has become one of the important teaching models. Online education platforms can overcome the limitations of time and space, providing students with flexible and diverse learning resources. However, at the same time, teachers find it difficult to directly observe students' attention changes, learning status, and behavioral habits during the learning process, making it difficult to effectively implement the behavioral feedback mechanisms of traditional classrooms in the online environment. How to accurately analyze students' behavioral trajectories during online learning and accordingly achieve personalized teaching adjustments has become an important research direction in the field of intelligent education.

[0003] Currently, Chinese invention patent application CN121503898A discloses an educational interactive behavior recognition system for online learning environments. This system constructs a standardized cognitive model offline based on interaction data from high-performing learning groups. In the online phase, it acquires individual learners' interaction events in real time, generating a high-dimensional cognitive trajectory representing their cognitive state. A trajectory dynamics analysis module performs dual-reference analysis: by calculating the maximum Lyapunov exponent and identifying phase transition points, it obtains intrinsic dynamic indicators representing the trajectory's stability; by calculating state deviation and path efficiency, it obtains extrinsic deviation measures of the trajectory from the standardized cognitive model. Finally, a cognitive pattern diagnosis module integrates the above indicators and generates a structured diagnostic description based on a rule base. However, the relevant technologies mainly rely on preset cognitive models and fixed rule bases to perform static analysis of learning behavior. They lack dynamic modeling mechanisms for the continuous evolution of learning behavior trajectories. In particular, they lack systematic processing capabilities for complex spatiotemporal relationships of behaviors in online education scenarios, cross-education platform behavior collaborative analysis, and recovery of missing behavior trajectories. It is difficult to accurately identify the changing trends of learning behavior and learning intentions in multiple education platforms, multiple scenarios, and complex learning states. At the same time, it is also difficult to support the dynamic generation of subsequent teaching control parameters and personalized intervention needs. Summary of the Invention

[0004] The technical problem addressed by this invention is that existing online learning behavior analysis methods primarily focus on the statistical identification or result determination of learning interaction behaviors, lacking the ability to dynamically analyze and adaptively evaluate the evolutionary process of learners' cognitive behaviors. Specifically, due to the characteristics of continuous, complex temporal changes, and significant differences in behavioral patterns in online learning interactions, learning behavior data is easily affected by short-term abnormal operations, ineffective interactions, and environmental disturbances. Traditional analysis methods using fixed rules or single behavioral features struggle to accurately reflect the learner's true cognitive state changes, easily leading to biased behavior identification, inaccurate cognitive bias analysis, and low reliability in learning state assessment. Furthermore, existing methods lack the ability to jointly analyze the correlation between the inherent evolutionary laws of learning behavior trajectories and group normative cognitive patterns, making it difficult to dynamically identify and continuously evaluate abnormal learning behaviors, cognitive deviation trends, and learning stability. Consequently, they cannot effectively support personalized teaching intervention, learning risk warning, and learning process optimization in online learning environments.

[0005] To address the aforementioned technical problems, this invention provides the following technical solution: a method for tracking and analyzing online education learning behavior, comprising the following steps: Step S1: Obtain the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process, and perform coordinate correction, posture compensation, time alignment and thermal field analysis to obtain the original behavior spot sequence and physical feature vector. Step S2: Obtain the educational context information corresponding to the behavior blob sequence, perform joint embedding processing on the educational context information and physical feature vector to obtain the behavior embedding vector sequence, and determine the intention category label; Step S3: Construct a global transition probability matrix based on the behavior blob sequences from N educational platforms, perform state deduction processing on the missing frames, and obtain the updated behavior blob sequences; Step S4: Construct a spatiotemporal graph based on the updated behavior blob sequence to obtain behavior trajectory representation vectors, and perform cross-platform similar trajectory retrieval processing to obtain similar retrieval results; Step S5: Based on the historical teaching intervention parameters and intention category labels corresponding to the similar search results, obtain the teaching regulation parameter vector.

[0006] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S1 specifically includes: Step S101: Collect the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process through the terminal camera; Among them, the trajectory points in the original gaze trajectory point sequence contain two-dimensional coordinate information in the pixel coordinate system, and the trajectory points in the original click trajectory point sequence contain two-dimensional coordinate information in the screen coordinate system. Step S102: For each trajectory point in the original line-of-sight trajectory point sequence, calculate the overhead angle between the camera optical axis and the screen plane, construct an affine transformation matrix based on the overhead angle, and map the original line-of-sight coordinates in the pixel coordinate system to the corrected line-of-sight coordinates in the screen coordinate system through the affine transformation matrix. Step S103: Synchronously collect student head posture data. The head posture data includes the translation vector of the head in three-dimensional space. Calculate the offset of the gaze point caused by the head movement based on the translation vector. Subtract the offset from the corrected gaze coordinates to obtain the compensated gaze coordinates. Step S104: For each trajectory point in the original click trajectory point sequence, obtain its two-dimensional coordinates in the screen coordinate system, and use them as the compensated click coordinates; Step S105: Align the compensated gaze coordinates and the compensated click coordinates on the timeline to form the original behavior spot sequence. Each behavior spot includes two-dimensional coordinates in the screen coordinate system, a timestamp, and an event type attribute. Step S106: Discretize the screen coordinate system into grid cells, map the coordinates of all behavior spots in the original behavior spot sequence to the corresponding grid cells, and count the cumulative dwell time and frequency of occurrence of behavior spots in each grid cell to generate a heat field distribution map of student attention.

[0007] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S1 further includes: Step S107: The heat map of student attention is converted to grayscale to obtain a grayscale heat map. The grayscale value of each grid cell in the grayscale heat map is proportional to the cumulative dwell time. Grid cell areas with grayscale values ​​greater than the first threshold are extracted as core focus areas, and grid cell areas with grayscale values ​​between the second threshold and the first threshold are extracted as general focus areas. Step S108: Count the total number of grid cells within the core focus area, and use this count as the area of ​​the core focus area; Calculate the chain code length of the boundary between the core focus area and the general focus area, and use it as the boundary perimeter; Calculate the information entropy of the probability distribution of gray values ​​in each grid cell, and use it as the spatial distribution entropy. Step S109: Perform differential calculation on the two-dimensional coordinates of the behavior spots between adjacent frames in the original behavior spot sequence in the screen coordinate system to obtain the gaze movement speed vector and the click movement speed vector. Calculate the magnitude of the gaze movement speed vector as the gaze movement rate and the magnitude of the click movement speed vector as the click movement rate. Step S110: Normalize and combine the core focus area area, boundary perimeter, spatial distribution entropy, gaze movement rate, and click movement rate to obtain the physical feature vector.

[0008] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S2 specifically includes: Step S21: For each behavioral spot, extract its corresponding educational context information, which includes the current course stage label, the current knowledge point identifier, the question type label, the course duration, and the time period number in a day. Step S22: Map the current course stage label, current knowledge point identifier, and question type label to the corresponding nodes in the pre-built knowledge graph. Use the Node2Vec algorithm to perform structural embedding encoding on the corresponding nodes to obtain structural embedding vectors. Input the course duration and the time period number in a day into the sine and cosine position encoding function to generate time embedding vectors. Step S23: Concatenate the physical feature vector, the structural embedding vector, and the temporal embedding vector to obtain the joint feature vector; Step S24: Input the joint feature vector into the first fully connected neural network and output the behavior embedding vector. Repeat steps S21 to S24 for each behavior blob in the original behavior blob sequence to obtain the behavior embedding vector sequence. Step S25: Calculate the relevance score of the behavior embedding vectors at any two positions in the behavior embedding vector sequence; The behavior embedding vectors are weighted and summed based on the relevance scores to obtain the weighted sum vector of each attention head. The weighted sum vectors of each attention head are then concatenated to obtain the mobile intent embedding sequence. Step S26: Calculate the average value of the mobile intent embedding sequence according to the time dimension to obtain the global intent vector. Calculate the cosine similarity between the global intent vector and the preset intent category center vector. Select the category with the largest cosine similarity as the intent category label output. The preset intent category labels include deep reasoning intent, information retrieval intent, comparison intent, and fatigue distraction intent.

[0009] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, the formula for calculating the correlation score is as follows: ; in, For the first The first one in the attention. The behavior embedding vector and the first Correlation scores between behavioral embedding vectors For the first Each behavior embedding vector For the first Each behavior embedding vector For the first A query matrix with attention heads For the first Key transformation matrix of an attention head For each attention head's output dimension, For sequence length, The index is the sequence length.

[0010] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S3 specifically includes: Step S31: Establish a collaborative analysis architecture among N educational platforms. Each educational platform maintains locally stored original behavioral blob sequences. The educational platforms do not directly exchange original behavioral blob sequences, where N≥2. Step S32: Each education platform divides the locally stored original behavior spot sequence into M sliding time windows according to a preset time length. For each sliding time window, the behavior spots are processed by generating thermal fields, extracting regional features, calculating motion rates, and normalizing and combining them to obtain the physical feature vectors corresponding to each sliding time window. The physical feature vectors are then mapped to the corresponding discrete state numbers using the K-means clustering algorithm. The transition frequency of the physical feature vector from the previous sliding time window to the physical feature vector of the next sliding time window in the discretized state space is counted, and a local transition probability matrix is ​​constructed. Each element in the local transition probability matrix represents the conditional probability of the next discrete state number occurring given the current discrete state number and the current intent category label. Step S33: Each education platform adds random noise to each element in the local transition probability matrix according to a preset Laplace noise scale to obtain a noisy local transition probability matrix, and sends the noisy local transition probability matrix to the central server. Step S34: The central server receives the noisy local transition probability matrix sent by all education platforms, sums the elements in the same row and column positions in the matrix and divides them by the total number of education platforms to obtain the aggregate matrix, performs non-negative truncation on the elements in the aggregate matrix, and normalizes the transition probability distribution corresponding to each condition state to obtain the global transition probability matrix. Step S35: When consecutive missing frames are detected in the behavior blob sequence, the discrete state number, two-dimensional coordinates in the screen coordinate system, and intent category label of the frame before entering the missing state are recorded and used as the starting joint state.

[0011] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S3 further includes: Step S36: Using the initial joint state as the current deduction state, repeat the following iterative process until the number of missing frames is reached: Query the state transition probability distribution corresponding to the current discrete state number and the current intent category label in the global transition probability matrix; Select the discrete state number with the highest probability value as the predicted state for the next time step; Based on the pre-established state mapping table between discrete state numbers and behavior spot coordinates, find the predicted behavior spot coordinates corresponding to the target discrete state number; Update the target discrete state number to the current discrete state number, update the predicted behavior blob coordinates to the current behavior blob coordinates, and keep the current intent category label unchanged; Step S37: Arrange the coordinates of the behavior spots corresponding to the predicted states of all next time steps in the iterative deduction process in chronological order to form a recovery trajectory. Insert the behavior spots in the recovery trajectory into the corresponding missing time positions of the original behavior spot sequence to obtain the updated behavior spot sequence.

[0012] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S4 specifically includes: Step S41: Using the grid cell containing the two-dimensional coordinates of the behavior spots in the screen coordinate system in the updated behavior spot sequence as nodes and the transition relationship between adjacent frames as edges, construct a spatiotemporal graph. Calculate the attention coefficient between each node and its neighboring nodes through a graph attention network. Based on the attention coefficient, weighted aggregate the features of the neighboring nodes to obtain a spatial feature vector sequence. Step S42: Input the updated behavior blob sequence into the self-attention network, calculate the attention weight between any two positions in the updated behavior blob sequence, obtain the self-attention output sequence, and perform pooling processing on the self-attention output sequence according to the time dimension to obtain the structural feature vector. Step S43: The global spatial vector obtained by pooling the spatial feature vector sequence is concatenated with the structural feature vector and input into the cross-attention network to obtain the behavior trajectory representation vector; Step S44: Using the current student's behavior trajectory representation vector as the query vector, calculate the hash bucket index of the query vector using the Locality Sensitive Hash Algorithm, and broadcast the hash bucket index and the parameters of the preset Locality Sensitive Hash Function to other educational platforms.

[0013] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S4 further includes: Step S45: Each other educational platform that receives the hash bucket index and parameters performs the same local sensitive hash projection on each behavior trajectory representation vector stored locally, and filters out the representation vectors that fall into the same hash bucket to form a candidate trajectory set; Step S46: The educational platform initiating the query generates a public key and a private key for the Paillier encryption algorithm, and sends the public key and the query vector to other educational platforms. The other educational platforms calculate the ciphertext of the query vector and the representation vector in the candidate trajectory set through homomorphic operation, and return all the ciphertexts to the educational platform initiating the query. The educational platform initiating the query uses the private key to decrypt each ciphertext to obtain the plaintext Euclidean distance. Step S47: Gather the plaintext Euclidean distances from all educational platforms into a list, sort them in ascending order of distance, and select the original behavioral trajectories corresponding to the top P distances as similarity search results, where P is a positive integer.

[0014] As a preferred embodiment of the online education learning behavior trajectory tracking and analysis method described in this invention, step S5 specifically includes: Step S51: Extract the historical teaching intervention parameters corresponding to each original behavioral spot sequence from the similarity search results. The historical teaching intervention parameters include the difficulty level of the pushed exercises, the frequency of prompt information, the interaction waiting time, and the content simplification coefficient. Step S52: Based on the intent category label, find the corresponding basic intervention parameter vector from the preset control strategy mapping table. The basic intervention parameter vector consists of the difficulty level of the pushed exercises, the frequency of prompt information, the interaction waiting time, and the content simplification coefficient. Step S53: Normalize and weightedly fuse the basic intervention parameter vector and the similarity retrieval results respectively to obtain the teaching regulation parameter vector.

[0015] The beneficial effects of this invention are as follows: By jointly analyzing students' gaze trajectories and click trajectories, this invention can more accurately reflect the distribution of students' attention and behavioral changes during online learning, improving the authenticity and reliability of learning behavior analysis; by introducing thermal field analysis, behavior embedding, and intent recognition mechanisms, it achieves a deeper understanding of students' learning status and intentions, improving the ability to express behavioral characteristics; by constructing a multi-platform collaborative analysis architecture and combining differential privacy and homomorphic encryption mechanisms, it achieves cross-platform joint analysis of behavioral trajectories while protecting user privacy, improving data utilization efficiency and analysis robustness; by constructing a global transition probability matrix to recover missing behavioral trajectories, it improves the continuity and completeness of behavioral trajectories; and by cross-platform similar trajectory retrieval and teaching control parameter generation, it achieves more precise personalized teaching intervention, improving the intelligence level and teaching control effect of the online education system. Attached Figure Description

[0016] Figure 1 The flowchart illustrates the steps of an online education learning behavior trajectory tracking and analysis method provided in one embodiment of the present invention. Detailed Implementation

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0018] Example, refer to Figure 1 This paper provides a method for tracking and analyzing online education learning behavior, including the following steps: Step S1: Obtain the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process, and perform coordinate correction, posture compensation, time alignment and thermal field analysis to obtain the original behavior spot sequence and physical feature vector. Step S2: Obtain the educational context information corresponding to the behavior blob sequence, perform joint embedding processing on the educational context information and physical feature vector to obtain the behavior embedding vector sequence, and determine the intention category label; Step S3: Construct a global transition probability matrix based on the behavior blob sequences from N educational platforms, perform state deduction processing on the missing frames, and obtain the updated behavior blob sequences; Step S4: Construct a spatiotemporal graph based on the updated behavior blob sequence to obtain behavior trajectory representation vectors, and perform cross-platform similar trajectory retrieval processing to obtain similar retrieval results; Step S5: Based on the historical teaching intervention parameters and intention category labels corresponding to the similar search results, obtain the teaching regulation parameter vector.

[0019] In specific implementation, step S1 includes: Step S101: Collect the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process through the terminal camera; Among them, the trajectory points in the original gaze trajectory point sequence contain two-dimensional coordinate information in the pixel coordinate system, and the trajectory points in the original click trajectory point sequence contain two-dimensional coordinate information in the screen coordinate system. Step S102: For each trajectory point in the original line-of-sight trajectory point sequence, calculate the overhead angle between the camera optical axis and the screen plane, construct an affine transformation matrix based on the overhead angle, and map the original line-of-sight coordinates in the pixel coordinate system to the corrected line-of-sight coordinates in the screen coordinate system through the affine transformation matrix. Step S103: Synchronously collect student head posture data. The head posture data includes the translation vector of the head in three-dimensional space. Calculate the offset of the gaze point caused by the head movement based on the translation vector. Subtract the offset from the corrected gaze coordinates to obtain the compensated gaze coordinates. Step S104: For each trajectory point in the original click trajectory point sequence, obtain its two-dimensional coordinates in the screen coordinate system, and use them as the compensated click coordinates; Step S105: Align the compensated gaze coordinates and the compensated click coordinates on the timeline to form the original behavior spot sequence. Each behavior spot includes two-dimensional coordinates in the screen coordinate system, a timestamp, and an event type attribute. Step S106: Discretize the screen coordinate system into grid cells, map the coordinates of all behavior spots in the original behavior spot sequence to the corresponding grid cells, and count the cumulative dwell time and frequency of occurrence of behavior spots in each grid cell to generate a heat field distribution map of student attention.

[0020] Specifically, for the acquisition of the original click trajectory point sequence, a background monitoring service is run at the terminal device's operating system level. This service can capture click events generated by the mouse or touchpad and record the coordinates and precise timestamps of the event on the screen in real time. Continuous recordings constitute the sequence. For the acquisition of the original gaze trajectory point sequence, in this embodiment, a deep learning-based computer vision method is used, implemented through a common camera built into the terminal device. This method first locates the student's face in the video stream using a face detection algorithm, and then uses an eye keypoint detection model to lock the eye area. Subsequently, a pre-trained gaze estimation neural network takes the eye image and head pose information as input and outputs a vector representing the gaze direction. By calculating the intersection of this vector and the camera image plane, a two-dimensional coordinate in the pixel coordinate system is obtained, i.e., the original gaze coordinate. This process is executed continuously at a certain frequency, arranging the original gaze coordinates of each frame in chronological order to form the original gaze trajectory point sequence.

[0021] To enable the gaze estimation neural network to accurately infer gaze direction from eye images, it needs to be pre-trained. This training process is completed in our development environment, primarily relying on a large image database containing diverse population samples. Each eye image in the database is paired with a baseline gaze direction recorded using a high-precision professional eye-tracking device. To allow the network to adapt to real-world scenarios such as lighting changes and image blurring that may occur in students' home environments, we also preprocessed the images in the database to simulate these real-world interference factors, thereby enhancing the network's adaptability. The specific training process is an iterative optimization process. An eye image and its corresponding head position information are fed into the network, which then provides an estimated gaze direction. This estimate is then compared to the baseline gaze direction corresponding to that image, and the error between the two is calculated. Based on this error, the system makes a small adjustment to all adjustable parameters within the network, aiming to make the network's next estimate even closer to the baseline direction. This process is repeated using all data in the database until the overall estimation error of the network decreases and stabilizes at an acceptablely low level, at which point we consider the network to be successfully trained. The pre-trained gaze estimation neural network comprises two parallel processing branches. The first branch specifically processes the input eye image. Upon entering this branch, the image passes through a series of convolutional processing units. These units extract useful features layer by layer from the image, progressing from basic edges and highlights to more complex high-level structures such as the iris and eyelid contours. In this way, this branch transforms the raw image pixels into a set of feature data containing key visual information. Simultaneously, the second processing branch processes the student's head pose data. This branch has a relatively simple structure; its role is to transform the head position information into a data format that can be combined with visual features. Finally, the feature data from the two branches are aggregated into the network's feature fusion section. In this section, through subsequent fully connected layers, the visual information extracted from the eye image is integrated with the head pose information for a final comprehensive analysis. Based on all the fused information, the network outputs a pair of coordinate values, which represent the calculated current gaze direction of the student.

[0022] Two-dimensional coordinate information refers to a positional identifier within a defined coordinate system. In step S101 of this scheme, the two-dimensional coordinate information specifically refers to two-dimensional coordinate information within a pixel coordinate system. This pixel coordinate system uses the single-frame image captured by the camera as a reference plane, typically with the top-left corner of the image as the origin (0,0), the positive x-axis pointing horizontally to the right, and the positive y-axis pointing vertically downwards. Therefore, a two-dimensional coordinate information consists of an abscissa (x) value and a ordinate (y) value, representing the specific pixel position of a point within that image frame.

[0023] An initial calibration procedure is used to calculate the affine transformation matrix. This procedure displays visual targets sequentially at the four corners and the center of the screen, guiding students to focus on each target one by one. As the student focuses on each target, the known coordinates of the target on the screen are recorded, along with the original gaze coordinates captured by the camera, thus obtaining multiple pairs of coordinate points. The overhead angle between the camera's optical axis and the screen plane, along with other geometric deformations, collectively determine a mapping relationship from the pixel coordinate system to the screen coordinate system. This relationship can be fully described by an affine transformation matrix. Using the collected coordinate point pairs, this affine transformation matrix can be directly solved using the least squares method. Once this matrix is ​​determined, in subsequent real-time tracking, for any acquired original gaze coordinate, a matrix multiplication operation with this affine transformation matrix can map it from the pixel coordinate system to the corrected gaze coordinates in the screen coordinate system.

[0024] The translation vector in head pose data describes the position of the head's center point relative to the camera in three-dimensional space. During initial calibration, a translation vector corresponding to a reference head position is recorded. During the learning process, the difference between the current head translation vector and the reference translation vector is calculated in real time; this difference represents the head's three-dimensional spatial displacement. An internal three-dimensional geometric model is established that can calculate an approximately equal two-dimensional screen offset based on the head's movement in a direction parallel to the screen plane; simultaneously, based on the head's movement in a direction perpendicular to the screen plane (i.e., forward and backward movement), a non-linear two-dimensional offset caused by this movement is calculated using the parallax principle. These two offsets are combined to obtain the final total offset of the gaze point on the screen caused by head movement.

[0025] The compensated gaze coordinates and compensated click coordinates are aligned on the timeline, and a high-precision timestamp is attached to each data point. Whether a compensated gaze coordinate is calculated or a compensated click coordinate is obtained from an action capturing a click event, a timestamp accurate to the millisecond is immediately associated with that coordinate. The alignment process merges the time-stamped gaze coordinate data stream and click coordinate data stream into a unified sequence. Subsequently, this mixed sequence is strictly sorted in ascending order based on the timestamp of each data point. To distinguish the data source, each data point is also assigned an event type attribute, such as labeled as gaze or click. After sorting and labeling, the final unified and ordered sequence is the student's original behavior speckle sequence.

[0026] First, the screen coordinate system is discretized into A×B grid cells. The size of the grid cells needs to be optimized. If the grid is too large, it will blur the spatial distribution details of attention; if the grid is too small, it will lead to sparse data and increased computational load. Preferably, the size of the grid cells is set to be comparable to the size of a standard interactive element (such as a button or icon) on the screen, for example, a range of 30×30 to 50×50 pixels. This ensures sufficient resolution while effectively aggregating behaviors. Then, the original behavior speckle sequence is traversed, mapping each behavior speckle to its corresponding grid cell based on its coordinates. For gaze specks, their dwell time (the difference between the timestamps of the current speckle and the next speckle) is accumulated into the cumulative dwell time of the grid cell; for all specks, their occurrence count is accumulated into the occurrence frequency of the grid cell. After the traversal, the cumulative dwell time or occurrence frequency of each grid cell can be used to generate a student attention heatmap.

[0027] This application improves the accuracy and robustness of behavior tracking in real learning environments by using affine transformation for coordinate correction and translation vector-based posture compensation, overcoming the significant errors caused by the camera's overhead angle and student head movements in traditional methods. Secondly, by aligning the compensated gaze and click coordinates on the time axis, a unified sequence of original behavior specks is constructed. This provides richer and more comprehensive information than isolated analysis of single behavior data, particularly revealing the temporal correlation between seeing and acting. Finally, transforming high-frequency original trajectory points into a grid-based student attention heatmap is an efficient feature engineering technique. This converts chaotic data streams into structured attention distribution features with clear physical meaning, providing high-quality, easily processed input for subsequent deeper analysis and serving as a crucial bridge connecting lower-level data acquisition and upper-level cognitive understanding.

[0028] In specific implementation, step S1 also includes: Step S107: The heat map of student attention is converted to grayscale to obtain a grayscale heat map. The grayscale value of each grid cell in the grayscale heat map is proportional to the cumulative dwell time. Grid cell areas with grayscale values ​​greater than the first threshold are extracted as core focus areas, and grid cell areas with grayscale values ​​between the second threshold and the first threshold are extracted as general focus areas. Step S108: Count the total number of grid cells within the core focus area, and use this count as the area of ​​the core focus area; Calculate the chain code length of the boundary between the core focus area and the general focus area, and use it as the boundary perimeter; Calculate the information entropy of the probability distribution of gray values ​​in each grid cell, and use it as the spatial distribution entropy. Step S109: Perform differential calculation on the two-dimensional coordinates of the behavior spots between adjacent frames in the original behavior spot sequence in the screen coordinate system to obtain the gaze movement speed vector and the click movement speed vector. Calculate the magnitude of the gaze movement speed vector as the gaze movement rate and the magnitude of the click movement speed vector as the click movement rate. Step S110: Normalize and combine the core focus area area, boundary perimeter, spatial distribution entropy, gaze movement rate, and click movement rate to obtain the physical feature vector.

[0029] Specifically, a linear mapping is performed based on the cumulative dwell time of each grid cell. This involves traversing all grid cells in the student attention heatmap to find the maximum cumulative dwell time value. Then, for each grid cell, its own cumulative dwell time is divided by this maximum value, resulting in a normalized ratio between 0 and 1. Finally, this ratio is multiplied by 255 and rounded to obtain the grayscale value corresponding to that grid cell. Through this process, the grayscale value of each grid cell is proportional to its cumulative dwell time, thus generating a grayscale heatmap.

[0030] The grayscale heatmap is divided into regions based on a first threshold and a second threshold to extract core focus areas and general interest areas. In this embodiment, the preferred threshold settings and their rationale are explained in Table 1. Based on the above thresholds, grid cell regions with gray values ​​greater than the first threshold are extracted as core focus areas, and grid cell regions with gray values ​​between the second and first thresholds are extracted as general focus areas.

[0031] First, the total number of grid cells within the core area of ​​focus (CIF) is counted and used as the area of ​​CIF. Then, to calculate the chain code length of the boundary between CIF and the general area of ​​interest (GA), this embodiment employs the standard chain code algorithm in image processing. First, all boundary grid cells belonging to CIF and with at least one adjacent cell belonging to GA are identified. Starting from any one boundary grid cell, the next adjacent boundary grid cell is traced clockwise. For each step, a corresponding direction code is recorded based on the direction of movement. This process continues until the starting point is returned, forming a closed coding sequence. The total number of all direction codes in this sequence is the chain code length, which is used as the boundary perimeter.

[0032] To calculate the information entropy of the probability distribution of grayscale values ​​in each grid cell, this embodiment follows the Shannon entropy calculation method in information theory. The entire grayscale heatmap is considered as a sample space of probability distributions. For each grid cell, its grayscale value is divided by the sum of the grayscale values ​​of all grid cells to obtain the probability value of that cell. Based on the method of calculating information entropy, the probability value of each grid cell is multiplied by its base-2 logarithm. The sum of the results for all grid cells is then taken as the negative of the result. The resulting value is the spatial distribution entropy, which can effectively measure the degree of student attention dispersion.

[0033] To calculate the gaze movement rate and click movement rate, this embodiment employs a motion velocity calculation method based on the coordinate difference between adjacent behavior spots to process the original behavior spot sequence. Specifically, for the calculation of the gaze movement rate, two behavior spots with the event type of gaze and which are temporally consecutive are selected from the original behavior spot sequence. The gaze movement velocity vector is calculated based on the coordinate difference and time difference between the two behavior spots, and the magnitude of this vector is the gaze movement rate. For the calculation of the click movement rate, the exact same method is used, except that the selected behavior spot pair consists of two temporally consecutive spots with the event type of click. The click movement velocity vector is calculated through optical flow field, and its magnitude is the click movement rate.

[0034] To normalize and combine the core focus area, boundary perimeter, spatial distribution entropy, gaze movement rate, and click movement rate to obtain the physical feature vector, a minimum-maximum normalization method is used. Since these five features have different dimensions and numerical ranges, directly combining them would allow features with larger numerical ranges to dominate in the subsequent model. Therefore, each feature needs to be normalized. For any feature, its normalized value is equal to its original value minus the minimum value obtained from a large amount of historical data, and then divided by the difference between the maximum and minimum values. After normalization, these five feature values ​​are scaled to between 0 and 1, possessing the same scale. Finally, these five normalized values ​​are arranged in a fixed order and concatenated into a five-dimensional vector, which is the physical feature vector obtained in this step.

[0035] In specific implementation, step S2 includes: Step S21: For each behavioral spot, extract its corresponding educational context information, which includes the current course stage label, the current knowledge point identifier, the question type label, the course duration, and the time period number in a day. Step S22: Map the current course stage label, current knowledge point identifier, and question type label to the corresponding nodes in the pre-built knowledge graph. Use the Node2Vec algorithm to perform structural embedding encoding on the corresponding nodes to obtain structural embedding vectors. Input the course duration and the time period number in a day into the sine and cosine position encoding function to generate time embedding vectors. Step S23: Concatenate the physical feature vector, the structural embedding vector, and the temporal embedding vector to obtain the joint feature vector; Step S24: Input the joint feature vector into the first fully connected neural network and output the behavior embedding vector. Repeat steps S21 to S24 for each behavior blob in the original behavior blob sequence to obtain the behavior embedding vector sequence. Step S25: Calculate the relevance score of the behavior embedding vectors at any two positions in the behavior embedding vector sequence; The behavior embedding vectors are weighted and summed based on the relevance scores to obtain the weighted sum vector of each attention head. The weighted sum vectors of each attention head are then concatenated to obtain the mobile intent embedding sequence. Step S26: Calculate the average value of the mobile intent embedding sequence along the time dimension to obtain the global intent vector. Calculate the cosine similarity between the global intent vector and the preset intent category center vector. Select the category with the largest cosine similarity as the intent category label output. The preset intent category labels include deep reasoning intent, information retrieval intent, comparison intent, and fatigue distraction intent.

[0036] Specifically, for each behavioral blob in the behavioral blob sequence, the pedagogical context information corresponding to the time of its occurrence is extracted. This information is provided by the online education platform currently used by the student through an application programming interface (API). Specifically, the platform database is queried to obtain the course status at the time the behavioral blob occurred, thereby obtaining the current course stage label (e.g., preview, listening, practice, review); the course syllabus and teaching progress are queried to obtain the current knowledge point identifier; if the student is answering questions, the question bank information is queried to obtain the question type label; at the same time, the course duration from the start of the course to the current time is recorded, as well as the time period number of the day corresponding to the current time.

[0037] The educational context information obtained in the previous step is encoded. To process the current course stage label, current knowledge point identifier, and question type label, a pre-built knowledge graph is needed. The knowledge graph construction process includes: defining entities in the education domain (such as all knowledge points, all course stages, and all question types) and using them as nodes in the graph; then defining edges between nodes based on their inherent logical relationships (such as knowledge point A being prerequisite knowledge for knowledge point B, and the practice stage following the lecture stage). When a specific label is obtained, such as "quadratic function," the corresponding node named "quadratic function" will be directly found in this pre-built knowledge graph, thus completing the mapping.

[0038] In this embodiment, the Node2Vec algorithm is used to perform structural embedding encoding on these corresponding nodes. The Node2Vec algorithm learns the neighborhood structure of each node by simulating a large number of random walks on the knowledge graph. Nodes that frequently co-occur in the walk paths are considered semantically related. The algorithm ultimately generates a low-dimensional, dense numerical vector, i.e., a structural embedding vector, for each node in the graph. This vector contains the node's position and relationship information within the entire knowledge system.

[0039] In this embodiment, the time information—the duration of the course and the time slot number within a day—is used to generate a time embedding vector using a sine and cosine position encoding function. This function uses a set of sine and cosine functions of different frequencies to transform a single time value (e.g., the course lasted 360 seconds) into a fixed-dimensional vector. This not only provides a unique vector representation for each time point but also allows the model to easily infer the relative positional relationship between any two time points.

[0040] The physical feature vector, the structural embedding vector generated in the previous step, and the temporal embedding vector are concatenated to obtain the joint feature vector. These three independent vectors are then linked end-to-end in a predetermined order (e.g., physical feature vector first, structural embedding vector in the middle, and temporal embedding vector last) to form a single vector with a longer dimension and more comprehensive information, namely the joint feature vector.

[0041] The joint feature vector is input into a first fully connected neural network. This first fully connected neural network consists of three fully connected layers, each followed by a ReLU activation function layer to introduce non-linearity, enabling the network to learn more complex feature relationships. Dropout layers can also be selectively added between layers to prevent overfitting during training. The network's role is to perform deep fusion and information extraction on the concatenated high-dimensional features, ultimately outputting a behavior embedding vector with lower dimensionality but higher information density. Repeating this process for each behavior blob in the original behavior blob sequence yields a one-to-one sequence of behavior embedding vectors.

[0042] To infer a student's dynamic intent from a sequence of behavioral embedding vectors, this embodiment utilizes a self-attention mechanism. Specifically, to calculate the relevance score between behavioral embedding vectors at any two positions, three distinct derived vectors are generated for each behavioral embedding vector in the sequence: a query vector, a key vector, and a value vector. These derived vectors are obtained by multiplying the original behavioral embedding vector with different weight matrices learned during training. The query vector of one behavioral embedding vector is then multiplied by the key vectors of all other behavioral embedding vectors. After scaling and normalization, the relevance score of that behavioral embedding vector to all other vectors is obtained.

[0043] Based on the calculated relevance scores, the behavior embedding vectors are weighted and summed. Specifically, the value vector corresponding to each behavior embedding vector in the sequence is multiplied by its relevance score calculated in the previous step; this relevance score is the weight for this summation. Then, all these weighted value vectors are summed to obtain a weighted sum vector, which is an updated vector representation of a behavior after incorporating information from all other relevant behaviors in the sequence. The calculation formula is as follows: ; in, In the first The first one in the attention. The weighted sum vector corresponding to each behavior embedding vector For the first The first one in the attention. The behavior embedding vector and the first The correlation score between the behavioral embedding vectors For the first The value matrix of each attention head, For the first Each behavior embedding vector The sequence length; To understand the complex relationships between behaviors from different perspectives and subspaces, multiple attention heads are set up in parallel. Each attention head has its own weight matrix learned independently during training. Table 2 illustrates these weight matrices, which serve as core parameters of the weighting process; By concatenating the weighted sum vectors of each attention point along the feature dimension, the final mobile intent embedding sequence is obtained, and its calculation formula is as follows: ; in, In order to be with the first The motion intent embedding vector corresponding to each position For splicing operations, For the number of attention heads, In the first The first one in the attention. The weighted summation vector corresponding to each behavior embedding vector; The final intent category label is determined based on the mobile intent embedding sequence. First, the sequence needs to be processed along the time dimension. Here, the time dimension refers to the direction of time flow represented by the order of the behavior embedding vectors in the sequence. The average value of the sequence along the time dimension is calculated, which is to add all the vectors in the sequence and divide by the number of vectors, thereby compressing the entire sequence into a global intent vector that can represent the overall behavioral characteristics within that time period.

[0044] The cosine similarity between the global intent vector and each of the four preset intent category center vectors is calculated. These four center vectors are preset parameters, and their setting method and reasoning are explained in Table 3. After calculating the cosine similarity between the current student's global intent vector and the four preset center vectors, the category with the highest similarity value will be selected and output as the final intent category label for this learning behavior.

[0045] In practice, the formula for calculating the relevance score is as follows: ; in, For the first The first one in the attention. The behavior embedding vector and the first Correlation scores between behavioral embedding vectors For the first Each behavior embedding vector For the first Each behavior embedding vector For the first A query matrix with attention heads For the first Key transformation matrix of an attention head For each attention head's output dimension, For sequence length, The index is the sequence length.

[0046] In specific implementation, step S3 includes: Step S31: Establish a collaborative analysis architecture among N educational platforms. Each educational platform maintains locally stored original behavioral blob sequences. The educational platforms do not directly exchange original behavioral blob sequences, where N≥2. Step S32: Each education platform divides the locally stored original behavior spot sequence into M sliding time windows according to a preset time length. For each sliding time window, the behavior spots are processed by generating thermal fields, extracting regional features, calculating motion rates, and normalizing and combining them to obtain the physical feature vectors corresponding to each sliding time window. The physical feature vectors are then mapped to the corresponding discrete state numbers using the K-means clustering algorithm. The transition frequency of the physical feature vector from the previous sliding time window to the physical feature vector of the next sliding time window in the discretized state space is counted, and a local transition probability matrix is ​​constructed. Each element in the local transition probability matrix represents the conditional probability of the next discrete state number occurring given the current discrete state number and the current intent category label. Step S33: Each education platform adds random noise to each element in the local transition probability matrix according to a preset Laplace noise scale to obtain a noisy local transition probability matrix, and sends the noisy local transition probability matrix to the central server. Step S34: The central server receives the noisy local transition probability matrix sent by all education platforms, sums the elements in the same row and column positions in the matrix and divides them by the total number of education platforms to obtain the aggregate matrix, performs non-negative truncation on the elements in the aggregate matrix, and normalizes the transition probability distribution corresponding to each condition state to obtain the global transition probability matrix. Step S35: When consecutive missing frames are detected in the behavior blob sequence, the discrete state number, two-dimensional coordinates in the screen coordinate system, and intent category label of the frame before entering the missing state are recorded and used as the starting joint state.

[0047] It should be noted that the collaborative analytics architecture comprises a central server and N participating educational platforms (as clients). The central server is responsible for model aggregation and coordination but does not access any raw data. Each educational platform performs data processing and initial model training locally, exchanging only privacy-preserving, highly aggregated model parameters with the central server, such as the noisy local transition probability matrix in this embodiment. Importantly, the educational platforms do not directly exchange any data, especially raw behavioral speckle sequences containing user personal information, thereby ensuring user privacy and the data sovereignty of each educational platform while achieving data value sharing.

[0048] Each educational platform needs to process the locally stored raw behavioral blob sequences to construct a local transition probability matrix. First, the physical feature vectors of each frame within the time window need to be quantized. In this embodiment, the K-means clustering algorithm is used to perform this processing. The training process of this algorithm is completed offline: first, a large-scale representative sample set is extracted from the massive historical physical feature vectors. Then, the K-means clustering algorithm is applied to this sample set, and the algorithm automatically divides these continuous vectors into K clusters. Each cluster represents a similar physical behavioral state, such as highly concentrated, fast browsing, or small-scale exploration, and is represented by a centroid. After the algorithm training is completed, each cluster is assigned a unique discrete state number.

[0049] When a new physical feature vector is obtained, the Euclidean distance between this vector and the centroids of all K clusters is calculated, and the nearest centroid is found. The discrete state number corresponding to this centroid is the result of mapping the physical feature vector after state quantization. After state quantization, a local transition probability matrix can be constructed. This matrix is ​​a three-dimensional matrix, the dimensions of which are determined by the number of discrete state numbers, the number of intent category labels, and the number of discrete state numbers. All original behavior blob sequences are traversed locally, and the transition frequency from the physical feature vector of the previous frame to the physical feature vector of the next frame in the discretized state space is counted. Specifically, for each pair of adjacent frames, the corresponding triple (previous frame discrete state number, current intent category label, next frame discrete state number) is recorded. A frequency counter is maintained to count all observed triples. After the traversal, the local transition probability matrix is ​​obtained by normalizing the frequency of each triple by dividing it by the total frequency of all possible next frame states given (previous frame discrete state number, current intent category label). Each element in the matrix represents the conditional probability of a specific discrete state number appearing in the next frame, given the current discrete state number and the current intent category label.

[0050] The preset Laplace noise scale is a key parameter for achieving differential privacy protection, directly determining the intensity of added random noise. In this embodiment, the scale is set based on two more fundamental concepts: global sensitivity and privacy budget. Global sensitivity measures the maximum potential impact of changes to a single user's data on the output; for the process of constructing the local transition probability matrix in this embodiment, the global sensitivity can be set to 1. The privacy budget is a pre-set positive number used to quantify the strength of privacy protection; the smaller the value, the more stringent the privacy protection requirements. To achieve a good balance between providing strong privacy protection and maintaining model usability, this embodiment preferably sets the privacy budget to 0.5. Based on the above settings, the preset Laplace noise scale is the global sensitivity divided by the privacy budget, resulting in 2. Therefore, in this embodiment, the preset Laplace noise scale is set to 2. Specifically, the calculation process for adding random noise to each element of the local transition probability matrix according to a preset Laplace noise scale is as follows: Assume that an educational platform has calculated a row in a local transition probability matrix, where the row represents a transition probability vector, for example, [0.1, 0.7, 0.2]. First, noise is added to the first element 0.1 of this vector. A random number is drawn from a Laplace distribution with a mean of 0 and a scale parameter of 2, let's say -0.08. Then, the new element after adding noise is 0.1 + (-0.08) = 0.02. Next, noise is generated independently for the second element 0.7. Let's say the randomly drawn number is +0.15. Then, the new element is 0.7 + 0.15 = 0.85. Finally, noise is generated for the third element 0.2. Let's say the randomly drawn number is -0.05. Then, the new element is 0.2 + (-0.05) = 0.15. After this process, the original probability row vector [0.1, 0.7, 0.2] is transformed into a noisy row vector [0.02, 0.85, 0.15]. This vector is the corresponding part of the final noisy local transition probability matrix and is sent to the central server.

[0051] Adding noise among multiple distrustful educational platforms aims to achieve collaborative analysis that both shares data value and strictly protects user privacy. Directly uploading precise local transition probability matrices poses a privacy risk. By adding random noise, we obfuscate the original matrix, making it mathematically impossible to deduce any individual information from it. The Laplace noise mechanism is employed because it not only provides quantifiable privacy guarantees, but its zero-mean property ensures that when the noisy matrices from numerous educational platforms are aggregated and averaged on a central server, the random noise cancels out. This guarantees that the final global transition probability matrix approximates the true global data distribution, thus ensuring the accuracy of subsequent analysis while building a secure and reliable collaborative analysis architecture.

[0052] To add random noise to each element of the local transition probability matrix according to a preset Laplace noise scale, a random number is generated from a Laplace distribution with a mean of 0 and a scale parameter of b, and this random number is added to each element of the matrix. This process is performed independently on all elements of the matrix, ultimately resulting in a noisy local transition probability matrix. The educational platform then sends this noisy local transition probability matrix to the central server.

[0053] In steps S34 and S35, the central server performs model aggregation and prepares for subsequent missing frame inference. After receiving the noisy local transition probability matrices sent by all educational platforms, the central server sums the elements at the same row and column positions in these matrices and then divides by the total number of educational platforms to obtain the aggregation matrix. According to the theory of differential privacy, the random noise added by multiple educational platforms will cancel each other out during the aggregation and averaging process, so that the aggregation result can approximate the global statistical characteristics of the sum of all educational platform data. Since some elements in the aggregation matrix may have negative values ​​or not satisfy the probability distribution constraints, the aggregation matrix is ​​further subjected to non-negative truncation and normalization processing to obtain the global transition probability matrix. When processing a behavior blob sequence, if consecutive missing frames are detected, the discrete state number, behavior blob coordinates, and intent category label corresponding to the frame before entering the missing state are immediately recorded, and these three are treated as a whole to form the initial joint state for state inference.

[0054] Compared to traditional centralized data analysis methods or data-sharing methods that do not consider privacy protection, traditional methods centrally store and analyze all users' raw data, posing significant risks of privacy leaks and data security vulnerabilities, or creating data silos among educational platforms, failing to leverage collective intelligence. This application achieves differential privacy protection by establishing a collaborative analysis architecture, combining local computation of the local transition probability matrix with the addition of Laplace noise. This means that the central server and any other participating party cannot deduce specific behavioral data of any single educational platform or even any single user from the received noisy local transition probability matrix, thus securely aggregating the wisdom of multiple parties' data while complying with increasingly stringent global data privacy regulations. Furthermore, the limited data volume and user diversity of a single educational platform may lead to biases in the models trained on it. This solution aggregates the noisy local transition probability matrices of N educational platforms on a central server to generate a global transition probability matrix. This matrix integrates behavioral patterns from different educational platforms and user groups, making it more universal and robust than the local matrix of any single educational platform, and more accurately reflecting the general patterns of online learning behavior. Finally, in response to the common problem of missing data in online behavior tracking, this solution transforms the complex continuous behavior problem into a discrete Markov process problem by quantizing the state and constructing a transition probability matrix. By accurately recording the initial joint state in step S35, it provides clear and complete initial conditions for subsequent state deduction based on the global transition probability matrix. This allows for the completion of missing data in a more scientific way based on the statistical laws of large-scale data, rather than simply ignoring or incorrectly interpolating.

[0055] In specific implementation, step S3 also includes: Step S36: Using the initial joint state as the current deduction state, repeat the following iterative process until the number of missing frames is reached: Query the state transition probability distribution corresponding to the current discrete state number and the current intent category label in the global transition probability matrix; Select the discrete state number with the highest probability value as the predicted state for the next time step; Based on the pre-established state mapping table between discrete state numbers and behavior spot coordinates, find the predicted behavior spot coordinates corresponding to the target discrete state number; Update the target discrete state number to the current discrete state number, update the predicted behavior blob coordinates to the current behavior blob coordinates, and keep the current intent category label unchanged; Step S37: Arrange the coordinates of the behavior spots corresponding to the predicted states of all next time steps in the iterative deduction process in chronological order to form a recovery trajectory. Insert the behavior spots in the recovery trajectory into the corresponding missing time positions of the original behavior spot sequence to obtain the updated behavior spot sequence.

[0056] Specifically, starting with the initial joint state as the current inference state, the process is repeated until the number of generated predicted states reaches the number of detected missing frames. The first step of the iteration process is to query the global transition probability matrix. Using the current discrete state number and current intent category label in the current inference state as indices, the corresponding state transition probability distribution is found in the global transition probability matrix. This distribution is a vector where each element represents the probability of transitioning from the current state to the next possible discrete state. The second step of the iteration process is to select the target discrete state number with the highest probability value as the predicted state for the next time step based on the above probability distribution. This is a deterministic maximum a posteriori probability inference, i.e., selecting the most likely next behavioral state. The third step of the iteration process is to find the predicted behavioral blob coordinates corresponding to the target discrete state number selected in the previous step, based on a pre-established state mapping table between discrete state numbers and behavioral blob coordinates. This state mapping table is constructed synchronously during K-means clustering in step S32. During clustering, not only are the physical feature vectors clustered to obtain discrete state numbers, but the two-dimensional coordinates of the behavioral blobs assigned to each cluster in the screen coordinate system are also recorded simultaneously. For each cluster, the average coordinates of all behavior blob coordinates within that cluster are calculated and used as the typical behavior blob coordinates corresponding to that discrete state number. Therefore, the state mapping table records the correspondence between each discrete state number and its corresponding typical behavior blob coordinates. During a lookup, the typical behavior blob coordinates corresponding to that discrete state number are returned as the predicted behavior blob coordinates for that time step.

[0057] A pre-established state mapping table 4 between discrete state numbers and behavior blob coordinates; The final step in the iterative process is to update the state for the next iteration. The target discrete state number selected in the previous step is updated to the current discrete state number for the next iteration, and the coordinates of the found predicted behavior blob are updated to the current behavior blob coordinates for the next iteration. In this deduction, we assume that the student's macroscopic learning intention remains stable during the short period of absence; therefore, the current intention category label remains unchanged.

[0058] After completing the same number of iterative deductions as the number of missing frames, a series of predicted states for the next time step are obtained. In step S37, the coordinates of the predicted behavior spots found in each iteration, along with the deduction's virtual timestamp and the unchanged event type attribute, are arranged in chronological order to form the recovery trajectory. Subsequently, all the behavior spots in this recovery trajectory are inserted as a whole into the corresponding missing time positions in the original behavior spot sequence. This insertion operation fills in the blank time periods in the original sequence caused by missing data, ultimately resulting in a temporally continuous and uninterrupted updated behavior spot sequence.

[0059] Traditional methods, such as direct deletion or simple linear interpolation, either result in information loss or introduce erroneous data that does not reflect actual behavior. This solution, through iterative deduction based on a global transition probability matrix, achieves data completion that is more consistent with behavioral logic and relies on large-scale collective intelligence. Utilizing a global transition probability matrix aggregated from N educational platforms, the basis for state deduction is no longer limited to the finite data of a single user, but represents the most widespread and universal learning behavior transition patterns. This makes the prediction of missing frames more accurate and robust. Furthermore, this solution not only predicts missing states but also recovers the specific behavioral blob coordinates through a state mapping table, generating a complete recovery trajectory, thus ensuring the dual continuity of the updated behavioral blob sequence in both time and space. This scientific and refined data completion method provides a high-quality, uninterrupted data foundation for subsequent spatiotemporal graph construction and trajectory analysis, greatly improving the accuracy and reliability of the entire analysis method.

[0060] In specific implementation, step S4 includes: Step S41: Using the grid cell containing the two-dimensional coordinates of the behavior spots in the screen coordinate system in the updated behavior spot sequence as nodes and the transition relationship between adjacent frames as edges, construct a spatiotemporal graph. Calculate the attention coefficient between each node and its neighboring nodes through a graph attention network. Based on the attention coefficient, weighted aggregate the features of the neighboring nodes to obtain a spatial feature vector sequence. Step S42: Input the updated behavior blob sequence into the self-attention network, calculate the attention weight between any two positions in the updated behavior blob sequence, obtain the self-attention output sequence, and perform pooling processing on the self-attention output sequence according to the time dimension to obtain the structural feature vector. Step S43: The global spatial vector obtained by pooling the spatial feature vector sequence is concatenated with the structural feature vector and input into the cross-attention network to obtain the behavior trajectory representation vector; Step S44: Using the current student's behavior trajectory representation vector as the query vector, calculate the hash bucket index of the query vector using the Locality Sensitive Hash Algorithm, and broadcast the hash bucket index and the parameters of the preset Locality Sensitive Hash Function to other educational platforms.

[0061] Specifically, a graph attention network is used to process the node relationships in the spatiotemporal graph. First, the grid cell containing each behavior blob in the updated behavior blob sequence is taken as a node, and the corresponding behavior feature is taken as the node feature. Then, for each node, all neighboring nodes with edge connections are traversed. For the current node and each neighboring node, the node features of both are extracted and input into the attention weight calculation module to obtain the attention coefficient between the current node and its corresponding neighboring node. This attention coefficient represents the importance of neighboring nodes to the current node. To avoid feature imbalance caused by an excessively large weight for any one neighboring node, the attention coefficients of all neighboring nodes are further normalized so that the sum of all neighboring node attention coefficients is 1. Then, the node feature of each neighboring node is multiplied by its corresponding attention coefficient, and all results are accumulated to obtain the aggregated feature of the current node, calculated using the following formula: ; in, For nodes The corresponding spatial feature vector, For nodes The corresponding set of neighboring nodes, For nodes with neighboring nodes Attention coefficient between them Neighboring nodes The corresponding node feature vector; This aggregation process allows neighboring nodes with higher attention coefficients to contribute more to the current node, while those with lower attention coefficients contribute less, thus automatically highlighting neighboring nodes more closely related to the current learning behavior, ultimately resulting in a spatial feature vector sequence. In this embodiment, the range of neighboring nodes is preferably set to nodes that are temporally adjacent to each other in two consecutive frames and nodes with a spatial distance of no more than two grid cells. If the neighbor range is too small, it will be difficult to capture the spatial correlation in continuous learning behavior; if the neighbor range is too large, it will easily introduce irrelevant nodes and increase noise. Therefore, the above range can achieve a good balance between spatial correlation and computational complexity.

[0062] A self-attention network is used to process the updated behavior blob sequence. The updated behavior blob sequence is read chronologically, and each behavior blob is mapped to a corresponding behavior feature vector. Subsequently, query features, key features, and value features are generated. For any two positions in the sequence, the correlation between the corresponding query feature and key feature is calculated to obtain the attention weight between the positions. Based on the attention weight, the value features corresponding to each position are weighted and fused to obtain the self-attention output sequence. Then, the self-attention output sequence is pooled along the time dimension to obtain the structure feature vector. The calculation formula is as follows: ; in, For structural feature vectors, The length of the updated behavioral blob sequence, For the self-attention output sequence, the first... The output vector corresponding to each position.

[0063] This structural feature vector can comprehensively represent long-term dependencies in a behavior sequence, temporal correlation patterns between behaviors, and the overall structural features of the learned behaviors. To avoid excessive interference from distant behaviors, in this embodiment, the global dependency weights are normalized, and preferably, the maximum weight of a single behavior is limited to no more than 30% of the total weights, thereby improving the stability of the structural feature vector.

[0064] In step S43, the spatial feature vector sequence is first processed by pooling. Preferably, a global average pooling method is used. Specifically, all vectors in the spatial feature vector sequence are averaged along their corresponding dimensions to obtain a fixed-length global spatial vector. Using global average pooling preserves the overall spatial distribution trend, reduces the influence of local abnormal nodes, and avoids changes in vector dimensions with the length of the behavior sequence. Then, the global spatial vector and the structural feature vector are concatenated end-to-end in a preset order to form a fused vector. For example, the global spatial vector can be arranged in the first half, and the structural feature vector in the second half. The concatenated fused vector contains both the spatial distribution characteristics of student behavior and the temporal structural characteristics of student behavior. Subsequently, the fused vector is input into a cross-attention network to further analyze the correlation between spatial and temporal behaviors, the interaction patterns between different learning stages, and the changing trends of student behavior, ultimately outputting a behavior trajectory representation vector.

[0065] A preset locality-sensitive hash function (LSH) is used to achieve fast approximate retrieval of high-dimensional behavioral trajectory representation vectors. Traditional Euclidean distance comparison methods are computationally intensive, while LSH can map similar vectors to the same or nearby hash buckets, thus reducing the computational complexity of cross-educational platform similar trajectory retrieval. In this embodiment, a random projection LSH algorithm is used to process the behavioral trajectory representation vectors. First, multiple sets of random projection vectors are pre-generated as parameters of the preset LSH. To achieve a good balance between retrieval precision and recall, these parameters need to be optimally set. In this embodiment, the relevant parameter settings are shown in Table 5: Each set of random projection vectors is multiplied by the behavior trajectory representation vector. A dot product is output when the dot product is greater than 0, and 0 when it is less than or equal to 0. All binary results are combined in a fixed order to form a hash code, and the corresponding number is the hash bucket index. Then, the hash bucket index, the random projection vector parameters (i.e., the random projection vectors used as parameters for the preset locality-sensitive hash function), and the locality-sensitive hash function number are broadcast to other educational platforms. Other educational platforms use the same locality-sensitive hash function parameters to perform the same processing on their local behavior trajectory representation vectors, thereby quickly filtering out candidate trajectory sets that fall into the same hash bucket.

[0066] Compared to traditional cross-educational platform behavior retrieval methods, this application firstly achieves rapid filtering of behavior trajectory representation vectors through a Locality Sensitive Hashing (LSH) algorithm, avoiding full distance calculation for all behavior trajectories. This significantly reduces the computational complexity of cross-educational platform similar trajectory retrieval and improves retrieval efficiency. Secondly, by broadcasting only the hash bucket index and LSH function parameters instead of directly transmitting the original behavior trajectory representation vectors, this application effectively reduces the risk of cross-platform data leakage and improves the security of user behavior data. Furthermore, this application incorporates the Paillier encryption algorithm to implement ciphertext operations during candidate trajectory distance calculation. This allows each educational platform to complete cross-educational platform similarity calculations even without access to the original behavior trajectory representation vectors of other platforms, thus simultaneously ensuring the accuracy of similar trajectory retrieval, multi-educational platform collaboration capabilities, and user privacy protection. Finally, by jointly retrieving behavior trajectories from multiple educational platforms, this application can obtain richer historical learning behavior patterns, thereby improving the accuracy and robustness of generating teaching control parameter vectors.

[0067] In practice, step S4 also includes: Step S45: Each other educational platform that receives the hash bucket index and parameters performs the same local sensitive hash projection on each behavior trajectory representation vector stored locally, and filters out the representation vectors that fall into the same hash bucket to form a candidate trajectory set; Step S46: The educational platform initiating the query generates a public key and a private key for the Paillier encryption algorithm, and sends the public key and the query vector to other educational platforms. The other educational platforms calculate the ciphertext of the query vector and the representation vector in the candidate trajectory set through homomorphic operation, and return all the ciphertexts to the educational platform initiating the query. The educational platform initiating the query uses the private key to decrypt each ciphertext to obtain the plaintext Euclidean distance. Step S47: Gather the plaintext Euclidean distances from all educational platforms into a list, sort them in ascending order of distance, and select the original behavioral trajectories corresponding to the top P distances as similarity search results, where P is a positive integer.

[0068] Specifically, each other educational platform that receives the hash bucket index and parameters from the educational platform that initiated the query needs to perform the same Local Sensitive Hash (LSH) projection on each behavior trajectory representation vector stored locally. Specifically, the educational platform uses the parameters of the preset LSH function included in the broadcast (e.g., the set of randomly generated unit vectors and the segmentation threshold) to perform the exact same calculation process as step S44 on each behavior trajectory representation vector in its local historical database. Each local vector is then multiplied by the set of random unit vectors, and the result is binarized and concatenated into a hash code. The calculated hash code is then compared with the hash bucket index received in the broadcast. If they are identical, it means that the local behavior trajectory representation vector and the query vector fall into the same bucket in the LSH space. All representation vectors falling into the same hash bucket are selected and grouped together to form a candidate trajectory set.

[0069] To accurately calculate the distance between the query vector and each vector in the candidate trajectory set while protecting privacy, the educational platform initiating the query first generates a public and private key for the Paillier encryption algorithm locally. The Paillier encryption algorithm is a public-key cryptosystem that supports both additive and scalar multiplication homomorphism. After generating the key pair, the platform encrypts the query vector using the public key and sends the ciphertext of the public key and query vector to other platforms. Upon receiving the public key and query vector, each platform performs the following ciphertext calculation for each representation vector in its local candidate trajectory set: it needs to calculate the ciphertext of the squared Euclidean distance between the representation vector and the query vector. Since the Paillier encryption algorithm directly supports the ciphertext calculation of vector inner products, and the squared Euclidean distance can be expanded to the sum of the squares of the moduli of the two vectors minus twice their inner product, other educational platforms can securely calculate the encrypted result of the squared distance using the public key through a series of homomorphic addition and scalar multiplication operations, without knowing the plaintext of the query vector. This encrypted result is the ciphertext of the squared Euclidean distance. After the calculation is complete, other educational platforms will return all these ciphertexts to the educational platform that initiated the query. Finally, after receiving all the ciphertexts returned from other platforms, the educational platform that initiated the query will use its locally held private key to decrypt each ciphertext. Due to the correctness of the Paillier encryption algorithm, the decrypted result is the true, unencrypted plaintext Euclidean distance.

[0070] The educational platform initiating the query needs to perform a final sorting and filtering of all returned distances. The plaintext Euclidean distances from all educational platforms will be aggregated into a list. Each item in this list contains the distance value and the source information of the corresponding behavioral trajectory (e.g., educational platform ID and trajectory ID), as shown in Table 6. After obtaining this list, it is sorted in ascending order of distance. The sorted list places the trajectories with the smallest distance at the top, indicating that these trajectories are most similar to the query trajectory. Finally, the original behavioral trajectories corresponding to the top P distances are selected as the similarity retrieval results. The parameter P is a positive integer representing the number of most similar trajectories to be returned. In this embodiment, P is set to 10, which provides a sufficiently diverse range of high-quality similar cases, making the subsequent parameter fusion process more robust and representative. If the value of P is too small (e.g., less than 5), there are too few reference samples, making it susceptible to the influence of a few extreme cases, resulting in a greater degree of randomness in the decision. If the value of P is too large (e.g., greater than 20), some distant neighbor trajectories with low similarity will be introduced. These trajectories may contain noise information that is inconsistent with the current context, which may interfere with the accuracy of the decision and unnecessarily increase the computational burden of subsequent processing. Therefore, 10 is an optimal value that strikes a good balance between ensuring a sufficient number of high-quality reference cases and avoiding the introduction of too much irrelevant information.

[0071] In specific implementation, step S5 includes: Step S51: Extract the historical teaching intervention parameters corresponding to each original behavioral spot sequence from the similar search results. The historical teaching intervention parameters include the difficulty level of the pushed exercises, the frequency of prompt messages, the interaction waiting time, and the content simplification coefficient. Step S52: Based on the intent category label, find the corresponding basic intervention parameter vector from the preset control strategy mapping table. The basic intervention parameter vector consists of the difficulty level of the pushed exercises, the frequency of prompt information, the interaction waiting time, and the content simplification coefficient. Step S53: Normalize and weightedly fuse the basic intervention parameter vector and the similarity retrieval results respectively to obtain the teaching regulation parameter vector.

[0072] Specifically, for each original behavioral speckle sequence in the similarity search results, its associated historical records are queried to extract the historical teaching intervention parameters used on that student at that time. These parameters constitute P groups of historical parameters, each group including the difficulty level of the pushed exercises, the frequency of prompt messages, the interaction waiting time, and the content simplification coefficient. In parallel, in step S52, based on the current student's intention category label determined in step S2, the corresponding basic intervention parameter vector is searched from a preset control strategy mapping table. This preset control strategy mapping table is pre-developed by educational psychology experts and senior teachers based on teaching experience, providing a theoretically optimal, benchmark intervention strategy for each learning intention, as shown in Table 7; By looking up a table, a basic intervention parameter vector is obtained, consisting of the difficulty level of the pushed exercises, the frequency of prompt messages, the interaction waiting time, and the content simplification coefficient.

[0073] The basic intervention parameter vector and the similarity retrieval results (i.e., historical teaching intervention parameters of group P) need to be normalized and weighted to obtain the final teaching regulation parameter vector. First, the basic intervention parameter vector and the historical teaching intervention parameters of group P are normalized to map all parameters to the same scale for subsequent weighted fusion. Then, the average value of the normalized historical parameters of group P is calculated to obtain an average historical intervention vector representing the group's experience. Next, the normalized basic intervention parameter vector and the average historical intervention vector are weighted and summed. The weights used here are preset to balance the importance of theoretical strategies and group experience. The weighted fusion process involves multiplying the basic intervention parameter vector by its corresponding weight, multiplying the average historical intervention vector by its corresponding weight, and then adding the two weighted vectors together.

[0074] The parameters for the weighted fusion process are shown in Table 8; Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0075] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the protection scope of the present invention. All data acquisition actions in this application are carried out in compliance with the relevant data protection laws and policies of the country where the application is located and with the authorization granted by the owner of the corresponding device.

Claims

1. An online education learning behavior trajectory tracking analysis method, characterized in that, Includes the following steps: Step S1: Obtain the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process, and perform coordinate correction, posture compensation, time alignment and thermal field analysis to obtain the original behavior spot sequence and physical feature vector. Step S2: Obtain the educational context information corresponding to the behavior blob sequence, perform joint embedding processing on the educational context information and physical feature vector to obtain the behavior embedding vector sequence, and determine the intention category label; Step S3: Construct a global transition probability matrix based on the behavior blob sequences from N educational platforms, perform state deduction processing on the missing frames, and obtain the updated behavior blob sequences; Step S4: Construct a spatiotemporal graph based on the updated behavior blob sequence to obtain behavior trajectory representation vectors, and perform cross-platform similar trajectory retrieval processing to obtain similar retrieval results; Step S5: Based on the historical teaching intervention parameters and intention category labels corresponding to the similar search results, obtain the teaching regulation parameter vector.

2. The online education learning behavior trajectory tracking analysis method of claim 1, wherein, Step S1 specifically includes: Step S101: Collect the original line-of-sight trajectory point sequence and the original click trajectory point sequence of the student during the learning process through the terminal camera; Among them, the trajectory points in the original gaze trajectory point sequence contain two-dimensional coordinate information in the pixel coordinate system, and the trajectory points in the original click trajectory point sequence contain two-dimensional coordinate information in the screen coordinate system. Step S102: For each trajectory point in the original line-of-sight trajectory point sequence, calculate the overhead angle between the camera optical axis and the screen plane, construct an affine transformation matrix based on the overhead angle, and map the original line-of-sight coordinates in the pixel coordinate system to the corrected line-of-sight coordinates in the screen coordinate system through the affine transformation matrix. Step S103: Synchronously collect student head posture data. The head posture data includes the translation vector of the head in three-dimensional space. Calculate the offset of the gaze point caused by the head movement based on the translation vector. Subtract the offset from the corrected gaze coordinates to obtain the compensated gaze coordinates. Step S104: For each trajectory point in the original click trajectory point sequence, obtain its two-dimensional coordinates in the screen coordinate system, and use them as the compensated click coordinates; Step S105: Align the compensated gaze coordinates and the compensated click coordinates on the timeline to form the original behavior spot sequence. Each behavior spot includes two-dimensional coordinates in the screen coordinate system, a timestamp, and an event type attribute. Step S106: Discretize the screen coordinate system into grid cells, map the coordinates of all behavior spots in the original behavior spot sequence to the corresponding grid cells, and count the cumulative dwell time and frequency of occurrence of behavior spots in each grid cell to generate a heat field distribution map of student attention.

3. The online education learning behavior trajectory tracking analysis method of claim 2, wherein, Step S1 also includes: Step S107: The heat map of student attention is converted to grayscale to obtain a grayscale heat map. The grayscale value of each grid cell in the grayscale heat map is proportional to the cumulative dwell time. Grid cell areas with grayscale values ​​greater than the first threshold are extracted as core focus areas, and grid cell areas with grayscale values ​​between the second threshold and the first threshold are extracted as general focus areas. Step S108: Count the total number of grid cells within the core focus area, and use this as the area of ​​the core focus area; Calculate the chain code length of the boundary between the core focus area and the general focus area, and use it as the boundary perimeter; Calculate the information entropy of the probability distribution of gray values ​​in each grid cell, and use it as the spatial distribution entropy. Step S109: Perform differential calculation on the two-dimensional coordinates of the behavior spots between adjacent frames in the original behavior spot sequence in the screen coordinate system to obtain the gaze movement speed vector and the click movement speed vector. Calculate the magnitude of the gaze movement speed vector as the gaze movement rate and the magnitude of the click movement speed vector as the click movement rate. Step S110: Normalize and combine the core focus area area, boundary perimeter, spatial distribution entropy, gaze movement rate, and click movement rate to obtain the physical feature vector.

4. The online education learning behavior trajectory tracking and analysis method as described in claim 3, characterized in that, Step S2 specifically includes: Step S21: For each behavioral spot, extract its corresponding educational context information, which includes the current course stage label, the current knowledge point identifier, the question type label, the course duration, and the time period number in a day. Step S22: Map the current course stage label, current knowledge point identifier, and question type label to the corresponding nodes in the pre-built knowledge graph. Use the Node2Vec algorithm to perform structural embedding encoding on the corresponding nodes to obtain structural embedding vectors. Input the course duration and the time period number in a day into the sine and cosine position encoding function to generate time embedding vectors. Step S23: Concatenate the physical feature vector, the structural embedding vector, and the temporal embedding vector to obtain the joint feature vector; Step S24: Input the joint feature vector into the first fully connected neural network and output the behavior embedding vector. Repeat steps S21 to S24 for each behavior blob in the original behavior blob sequence to obtain the behavior embedding vector sequence. Step S25: Calculate the relevance score of the behavior embedding vectors at any two positions in the behavior embedding vector sequence; The behavior embedding vectors are weighted and summed based on the relevance scores to obtain the weighted sum vector of each attention head. The weighted sum vectors of each attention head are then concatenated to obtain the mobile intent embedding sequence. Step S26: Calculate the average value of the mobile intent embedding sequence according to the time dimension to obtain the global intent vector. Calculate the cosine similarity between the global intent vector and the preset intent category center vector. Select the category with the largest cosine similarity as the intent category label output. The preset intent category labels include deep reasoning intent, information retrieval intent, comparison intent, and fatigue distraction intent.

5. The online education learning behavior trajectory tracking and analysis method as described in claim 4, characterized in that, The formula for calculating the relevance score is: ； in, For the first The first one in the attention. The behavior embedding vector and the first Correlation scores between behavioral embedding vectors For the first Each behavior embedding vector For the first Each behavior embedding vector For the first A query matrix with attention heads For the first Key transformation matrix of an attention head For each attention head's output dimension, For sequence length, The index is the sequence length.

6. The online education learning behavior trajectory tracking and analysis method as described in claim 5, characterized in that, Step S3 specifically includes: Step S31: Establish a collaborative analysis architecture among N educational platforms. Each educational platform maintains locally stored original behavioral blob sequences. The educational platforms do not directly exchange original behavioral blob sequences, where N≥2. Step S32: Each education platform divides the locally stored original behavior spot sequence into M sliding time windows according to a preset time length. It performs thermal field generation, regional feature extraction, motion rate calculation and normalization combination processing on the behavior spots in each sliding time window to obtain the physical feature vector corresponding to each sliding time window. The physical feature vector is then mapped to the corresponding discrete state number through the K-means clustering algorithm. The transition frequency of the physical feature vector from the previous sliding time window to the physical feature vector of the next sliding time window in the discretized state space is counted, and a local transition probability matrix is ​​constructed. Each element in the local transition probability matrix represents the conditional probability of the next discrete state number occurring given the current discrete state number and the current intent category label. Step S33: Each education platform adds random noise to each element in the local transition probability matrix according to a preset Laplace noise scale to obtain a noisy local transition probability matrix, and sends the noisy local transition probability matrix to the central server. Step S34: The central server receives the noisy local transition probability matrix sent by all education platforms, sums the elements in the same row and column positions in the matrix and divides them by the total number of education platforms to obtain the aggregate matrix, performs non-negative truncation on the elements in the aggregate matrix, and normalizes the transition probability distribution corresponding to each condition state to obtain the global transition probability matrix. Step S35: When consecutive missing frames are detected in the behavior blob sequence, the discrete state number, two-dimensional coordinates in the screen coordinate system, and intent category label of the frame before entering the missing state are recorded and used as the starting joint state.

7. The online education learning behavior trajectory tracking and analysis method as described in claim 6, characterized in that, Step S3 also includes: Step S36: Using the initial joint state as the current deduction state, repeat the following iterative process until the number of missing frames is reached: Query the state transition probability distribution corresponding to the current discrete state number and the current intent category label in the global transition probability matrix; Select the discrete state number with the highest probability value as the predicted state for the next time step; Based on the pre-established state mapping table between discrete state numbers and behavior spot coordinates, find the predicted behavior spot coordinates corresponding to the target discrete state number; Update the target discrete state number to the current discrete state number, update the predicted behavior blob coordinates to the current behavior blob coordinates, and keep the current intent category label unchanged; Step S37: Arrange the coordinates of the behavior spots corresponding to the predicted states of all next time steps in the iterative deduction process in chronological order to form a recovery trajectory. Insert the behavior spots in the recovery trajectory into the corresponding missing time positions of the original behavior spot sequence to obtain the updated behavior spot sequence.

8. The online education learning behavior trajectory tracking and analysis method as described in claim 7, characterized in that, Step S4 specifically includes: Step S41: Using the grid cell containing the two-dimensional coordinates of the behavior spots in the screen coordinate system in the updated behavior spot sequence as nodes and the transition relationship between adjacent frames as edges, construct a spatiotemporal graph. Calculate the attention coefficient between each node and its neighboring nodes through a graph attention network. Based on the attention coefficient, weighted aggregate the features of the neighboring nodes to obtain a spatial feature vector sequence. Step S42: Input the updated behavior blob sequence into the self-attention network, calculate the attention weight between any two positions in the updated behavior blob sequence, obtain the self-attention output sequence, and perform pooling processing on the self-attention output sequence according to the time dimension to obtain the structural feature vector. Step S43: The global spatial vector obtained by pooling the spatial feature vector sequence is concatenated with the structural feature vector and input into the cross-attention network to obtain the behavior trajectory representation vector; Step S44: Using the current student's behavior trajectory representation vector as the query vector, calculate the hash bucket index of the query vector using the Locality Sensitive Hash Algorithm, and broadcast the hash bucket index and the parameters of the preset Locality Sensitive Hash Function to other educational platforms.

9. The online education learning behavior trajectory tracking and analysis method as described in claim 8, characterized in that, Step S4 also includes: Step S45: Each other educational platform that receives the hash bucket index and parameters performs the same local sensitive hash projection on each behavior trajectory representation vector stored locally, and filters out the representation vectors that fall into the same hash bucket to form a candidate trajectory set; Step S46: The educational platform initiating the query generates a public key and a private key for the Paillier encryption algorithm, and sends the public key and the query vector to other educational platforms. The other educational platforms calculate the ciphertext of the query vector and the representation vector in the candidate trajectory set through homomorphic operation, and return all the ciphertexts to the educational platform initiating the query. The educational platform initiating the query uses the private key to decrypt each ciphertext to obtain the plaintext Euclidean distance. Step S47: Gather the plaintext Euclidean distances from all educational platforms into a list, sort them in ascending order of distance, and select the original behavioral trajectories corresponding to the top P distances as similarity search results, where P is a positive integer.

10. The online education learning behavior trajectory tracking and analysis method as described in claim 9, characterized in that, Step S5 specifically includes: Step S51: Extract the historical teaching intervention parameters corresponding to each original behavioral spot sequence from the similarity search results. The historical teaching intervention parameters include the difficulty level of the pushed exercises, the frequency of prompt information, the interaction waiting time, and the content simplification coefficient. Step S52: Based on the intent category label, find the corresponding basic intervention parameter vector from the preset control strategy mapping table. The basic intervention parameter vector consists of the difficulty level of the pushed exercises, the frequency of prompt information, the interaction waiting time, and the content simplification coefficient. Step S53: Normalize and weightedly fuse the basic intervention parameter vector and the similarity retrieval results respectively to obtain the teaching regulation parameter vector.

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