Fine-grained Knowledge Point Mastery Analysis Method Based on Local Graph Convolution

Abstract

The present invention discloses a fine-grained knowledge point mastery analysis method based on local graph convolution. S1: Collect the learning behavior data of students and construct an initial knowledge graph based on the learning behavior data; S2: Establish a local graph convolution model based on the initial knowledge graph; S3: Update and generate a knowledge graph with personalized features; S4: Based on the personalized knowledge graph, generate a knowledge point mastery situation table by calculating the mastery degree index of each knowledge point; S5: Conduct cluster analysis on the knowledge points with mastery degree indexes lower than the preset threshold in the knowledge point mastery situation table; S6: Generate a feature vector of the knowledge blind spot group; S7: Generate learning strategies for each knowledge blind spot group according to the feature vector of the knowledge blind spot group. The present invention realizes the refined evaluation and real-time dynamic tracking of knowledge point mastery.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent learning, and particularly relates to a fine-grained knowledge point mastery analysis method based on local graph convolution. Background Art

[0002] Traditional knowledge point mastery analysis mainly relies on statistical data of learning records or simple correlation analysis between knowledge points. Traditional methods usually quantify and evaluate based on indicators such as the learning frequency, correct rate, or learning duration of a certain knowledge point by a student, and infer the student's mastery situation through these basic data. Traditional methods have significant limitations and are difficult to meet the requirements in terms of the accuracy, real-time nature, and personalized analysis of knowledge mastery.

[0003] Firstly, in terms of accuracy, the existing technology is difficult to achieve fine-grained analysis of knowledge point mastery, especially unable to effectively capture the dynamic associations between adjacent or related knowledge points. Traditional statistical methods ignore the graph structure features between knowledge points and cannot deeply analyze the mutual relationships of each knowledge point in the student's learning process, resulting in relatively rough results of knowledge mastery assessment. At the same time, simple statistical indicators are difficult to identify the true weak points of students in certain knowledge points and cannot provide precise learning suggestions for students.

[0004] Secondly, the existing technology also has deficiencies in terms of real-time nature. Existing mastery analysis methods mostly adopt phased statistics or static analysis means and cannot update the knowledge graph structure and knowledge mastery situation in a timely manner according to the real-time learning behaviors of students, making it difficult to timely identify new problems generated by students during the learning process. As a result, the learning guidance for students lacks timeliness and is difficult to effectively support the teaching adjustment and personalized guidance of teachers.

[0005] In addition, the existing technology also has obvious shortcomings in terms of personalized analysis and adaptive adjustment. Currently, knowledge mastery analysis methods usually adopt the same analysis model for all students and are difficult to dynamically adapt to the individual learning needs and knowledge structure changes of students, unable to achieve personalized updates of the knowledge graph. The one-size-fits-all analysis mode leads to the inability to teach students in accordance with their aptitude and difficult to provide effective personalized learning support for each student, ultimately affecting the effect of personalized learning.

[0006] In summary, the existing technology mainly has the following disadvantages: Firstly, the accuracy and fine-grained nature of knowledge point mastery assessment are low, and it is difficult to capture the dynamic associations between knowledge points; Secondly, the real-time nature of knowledge mastery analysis is poor, and it is difficult to dynamically reflect the learning progress and weak links of students; Finally, the existing technology lacks personalized and adaptive adjustment capabilities, unable to effectively meet the personalized learning needs of students, and difficult to provide learning support for teaching students in accordance with their aptitude. Summary of the Invention

[0007] An object of the present invention is to propose a fine-grained knowledge point mastery analysis method based on local graph convolution, and the present invention realizes refined evaluation and real-time dynamic tracking of knowledge point mastery.

[0008] A fine-grained knowledge point mastery analysis method based on local graph convolution according to an embodiment of the present invention includes the following steps:

[0009] S1. Collect the learning behavior data of students, and construct an initial knowledge graph containing multiple knowledge points and their association relationships based on the learning behavior data. Each knowledge point in the knowledge graph is used as a node in the graph, and the association relationships between different knowledge points are used as edges in the graph;

[0010] S2. Based on the initial knowledge graph, establish a local graph convolution model, aggregate the features of the neighboring nodes of each knowledge point node in the knowledge graph, perform weighted operations on the features of the neighboring knowledge points through a convolution kernel, extract the local feature matrix of the knowledge points, and obtain the feature vectors of each knowledge point node;

[0011] S3. Input the learning behavior data of students into the local graph convolution model, and update and generate a knowledge graph with personalized features according to the personalized learning progress of students;

[0012] S4. Based on the personalized knowledge graph, generate a knowledge point mastery situation table by calculating the mastery index of each knowledge point;

[0013] S5. Perform clustering analysis on the knowledge points whose mastery indexes in the knowledge point mastery situation table are lower than the preset threshold, use a clustering algorithm to group the knowledge points with low mastery, and generate a knowledge blind spot grouping table. The knowledge blind spot grouping table identifies knowledge blind spot groups with similar mastery characteristics and structural characteristics. The knowledge points in each knowledge blind spot group have similar knowledge weaknesses and learning obstacle performances in the graph structure;

[0014] S6. Extract the features of each knowledge blind spot group based on the knowledge blind spot grouping table, analyze the weak characteristics of the knowledge points in each group, and generate a knowledge blind spot group feature vector;

[0015] S7. Generate learning strategies for each knowledge blind spot group according to the knowledge blind spot group feature vector.

[0016] Optionally, the S1 includes the following specific steps:

[0017] S11. Collect the learning progress data P i , the learning progress data includes the learning progress of students in each knowledge point, where i is the number of the knowledge point, P iThe value range of [parameter] is from 0 to 1. 0 indicates not learned, and 1 indicates fully mastered. The learning progress data is used to characterize the learning status of students in each knowledge point;

[0018] S12. Collect the learning frequency data F of students i , where the learning frequency data includes the number of times students learn each knowledge point, and the learning frequency data is used to reflect the review or repeated learning of students for specific knowledge points;

[0019] S13. Collect the learning feedback data R of students i , where the learning feedback data includes the feedback results of students on each knowledge point. The value of the learning feedback data is 0 or 1. 0 indicates wrong feedback, and 1 indicates correct feedback. The learning feedback data is used to evaluate the accuracy of students' understanding of knowledge points;

[0020] S14. Collect the knowledge mastery data C of students i , where the knowledge mastery data includes the comprehensive mastery of students on each knowledge point. C i is obtained through the weighted calculation of the learning progress P i of students on knowledge point i, i learning frequency F i and learning feedback R:

[0021] C i = w1·P i + w2·F i + w3·R i ;

[0022] where w1, w2, and w3 are the weight coefficients of progress, frequency, and feedback respectively, and satisfy w1 + w2 + w3 = 1;

[0023] S15. Based on the collected learning progress data, learning frequency data, learning feedback data, and mastery data, construct an initial knowledge graph including multiple knowledge points and their association relationships. Each knowledge point in the knowledge graph is used as a node, and the association relationships between different knowledge points are used as edges in the graph. The association relationships are calculated based on the correlation of students' learning behavior data on knowledge points. Define the knowledge point association parameter L ij to represent the association strength between knowledge point i and knowledge point j:

[0024]

[0025] where L ij has a value range from 0 to 1. 0 indicates no association, and 1 indicates full association.

[0026] Optionally, S2 includes the following specific steps:

[0027] S21. Define the neighborhood N(i) of each knowledge point node i based on the initial knowledge graph. The neighborhood N(i) includes all adjacent knowledge point nodes j directly connected to node i, and there is an association parameter L ij between node i and node j, which is used to represent the association strength between knowledge points;

[0028] S22. Define the initial feature vector X i for each knowledge point node i. The initial feature vector X i is composed of the learning progress data P i , learning frequency F i , learning feedback data R i and knowledge mastery data C i :

[0029]

[0030] Among them, X i is a four-dimensional column vector, representing the learning situation and mastery degree of knowledge point i;

[0031] S23. Define the trainable convolutional kernel weight matrix where d is the dimension of the hidden feature. For each knowledge point node i, use the normalized association parameter to calculate the hidden feature vector H i of node i by weighted summation of the features of adjacent nodes j in the neighborhood N(i):

[0032]

[0033] Among them, σ(·) is a non-linear activation function, is the bias vector; is the normalized association parameter, defined as:

[0034]

[0035] S24. Perform multi-layer graph convolution operations on the hidden feature vector H i to capture high-order neighborhood information. The feature vector of the l-th layer is:

[0036]

[0037] Among them, l = 1, 2,..., L, are the weight matrix and bias vector of the l-th layer, and L is the number of convolution layers;

[0038] S25. After L layers of convolution, obtain the final feature vector Z i = H i (L), L2 regularization is used for Z i for regularization processing, and the final feature vector Z i is used to represent the deep knowledge association degree and relative mastery degree relationship between knowledge point i and its neighboring nodes.

[0039] Optionally, S3 includes the following specific steps:

[0040] S31. Input the latest learning behavior data D i (t) of the student into the local graph convolutional model;

[0041] S32. According to the personalized learning process of the student, update the feature vectors in the initial knowledge graph through the latent feature vector Z i and the latest learning behavior data D i (t) to generate a personalized knowledge graph, and the node feature vectors in the personalized knowledge graph are defined as:

[0042]

[0043] where α is the attenuation coefficient, used to control the balance between the historical feature X i and the current feature, and its value range is from 0 to 1.

[0044] Optionally, S4 includes the following specific steps:

[0045] S41. Based on the learning frequency data F in the feature vectors of the personalized knowledge graph i (t), learning feedback data R i (t) and learning duration data T i (t), calculate the mastery index M i of knowledge point i:

[0046]

[0047] where β1, β2, and β3 are the weight coefficients for mastery calculation;

[0048] S42. Aggregate the mastery indices M i of each knowledge point to generate a knowledge point mastery situation table:

[0049] M = {M1, M2,..., M n};

[0050] where n is the total number of knowledge points in the knowledge graph;

[0051] The knowledge point mastery situation table M is used to quantify the mastery degree of each knowledge point by the student and represent the learning progress of the student on different knowledge points.

[0052] Optionally, S5 includes the following specific steps:

[0053] S51. Set a mastery threshold θ for screening low-mastery knowledge points in the knowledge point mastery situation table M. If the mastery index M of knowledge point i i < θ, then mark this knowledge point as a low-mastery knowledge point;

[0054] S52. Extract features from the set S of knowledge points marked as low-mastery, i.e., S = {i|M i < θ}, and construct a feature matrix Q based on the structural feature vector Z in the knowledge graph i and the mastery index M i :

[0055]

[0056] where i1, i2,..., i k are the numbers of low-mastery knowledge points, Z i is the structural feature vector of knowledge point i, and the feature matrix Q is used to characterize the similarity features of low-mastery knowledge points in the knowledge graph structure;

[0057] S53. Apply the K-means improved clustering algorithm weighted by mastery to the feature matrix Q to identify similar groups among low-mastery knowledge points, determine the number of groups K, and divide the knowledge point set S into K knowledge blind spot groups G1, G2,..., G K , and the knowledge points in each knowledge blind spot group have similar knowledge weakness features and learning obstacle manifestations. The objective function of the mastery-weighted K-means clustering algorithm is defined as:

[0058]

[0059] where γ is the mastery weight coefficient, and its value range is from 0 to 1, which is used to balance the influence of the structural features and mastery of knowledge points on the clustering result. ∥Z i - μ j ∥ 2 represents the Euclidean distance between the structural feature vector Z i of knowledge point i and the group center μ j , M i is the mastery index of knowledge point i, which is used to weightedly adjust the importance of knowledge points in clustering. A lower mastery value will increase the weight, emphasizing the contribution of knowledge points with low mastery in clustering, and ∈ is a small positive number;

[0060] The objective function of the mastery weighted K-means clustering algorithm realizes fine-grained clustering with mastery weighting by combining the structural characteristics of knowledge points and the mastery index, and identifies groups of knowledge blind spots with similar mastery difficulties and learning obstacles.

[0061] Optionally, the S6 includes the following specific steps:

[0062] S61. Aggregate the knowledge point feature vectors Z j in each knowledge blind spot group G i to extract the overall features of each knowledge blind spot group, and define the group feature vector Z j as:

[0063]

[0064] where |G j | is the number of knowledge points in group G j Z i is the feature vector of knowledge point i, and the group feature vector Z j is used to represent the overall learning weakness characteristics of the knowledge points in the knowledge blind spot group G j ;

[0065] S62. Calculate the mean M j of the mastery degrees of the knowledge points within each knowledge blind spot group G j and the variance σ j 2 to evaluate the concentration and deviation of the mastery of the knowledge points within the group;

[0066] S63. Generate the feature vector T of each knowledge blind spot group based on the group feature vector group mastery mean and variance j :

[0067]

[0068] where T j is the feature vector of the knowledge blind spot group G j and contains the overall structural characteristics and mastery statistical characteristics of the knowledge points within the group.

[0069] Optionally, the S7 includes the following specific steps:

[0070] S71. For each knowledge blind spot group, analyze the learning needs according to its feature vector and generate learning strategies, and the learning strategies specifically include learning resource recommendations, practice question assignments, and learning path adjustment plans;

[0071] S72. Learning resource recommendation: Determine the type and quantity of learning resources according to the mastery degree and structural characteristics of the knowledge points in the knowledge blind spot group. The learning resources include video tutorials, knowledge explanations, case analyses, and summary materials. Step-by-step learning resources are provided preferentially for the knowledge points with lower mastery degrees.

[0072] S73. Practice question assignment: Assign targeted practice questions to students based on the complexity and mastery degree of the knowledge points within the knowledge blind spot group. The question types include basic comprehension questions, application questions, and comprehensive advanced questions. For the knowledge points with lower mastery degrees and high relevance, practice questions are provided preferentially to consolidate learning, and at the same time, the difficulty of the questions matches the current level of the students.

[0073] S74. Learning path adjustment plan: Optimize the learning path of students based on the characteristics of the knowledge blind spot group, so that the knowledge points with low mastery degrees and strong relevance appear in the learning path preferentially. The learning path adjustment plan includes reordering the learning order of knowledge points, suggesting to review weak knowledge points, and increasing the learning frequency of related knowledge points, enabling students to concentrate on overcoming weaknesses and covering related knowledge in the path at the same time.

[0074] The beneficial effects of the present invention are as follows:

[0075] (1) The present invention adopts the local graph convolution technology, captures the fine-grained features of each knowledge point by aggregating the features of neighborhood nodes when constructing the student knowledge graph, thereby making the knowledge mastery evaluation more accurate. Traditional methods usually rely on single statistical data and are difficult to accurately reflect the student's mastery situation. However, the present invention obtains high-order neighborhood information through multi-layer convolution operations, integrates the subtle differences and correlation degrees between knowledge points into the model, and thus comprehensively reflects the student's mastery situation in the evaluation. By updating the knowledge graph structure and mastery situation in real time, the evaluation results of the present invention can immediately reflect the learning dynamics of students and make the teaching feedback more agile.

[0076] (2) The present invention designs an automatic grouping method for knowledge blind spots based on cluster analysis to group the knowledge points with low mastery degrees according to their characteristics and generate personalized learning strategies, enabling the system to provide exclusive learning resources, practice questions, and path optimization plans for each student, thereby effectively covering the knowledge gaps of students. Traditional analysis methods are difficult to dynamically adapt to the learning progress of students. However, the present invention makes the system able to perform real-time personalized adjustment for each student's learning behavior through personalized updating of the knowledge graph, ensuring that the learning resources and strategies match the needs of students, and significantly improving the accuracy and adaptability of personalized analysis.

[0077] (3) The present invention automatically generates an optimized learning path based on the feature vectors of the knowledge blind spot group, enabling students to preferentially learn knowledge points with strong relevance and high importance, thereby efficiently improving the mastery level. Traditional learning paths are often in a fixed mode and cannot flexibly adjust priorities. The present invention dynamically optimizes the learning path through a detailed analysis of the structural features of knowledge points, making it more adaptable to the individual situations of students. Intensive learning is carried out in areas with low mastery. By highlighting weak knowledge points and related knowledge modules in the learning path, the learning efficiency and effect are significantly improved, enabling students to more efficiently achieve the goal of comprehensive mastery. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. They are used in conjunction with the embodiments of the present invention to explain the present invention and do not constitute a limitation to the present invention. In the accompanying drawings:

[0079] Figure 1 is a flowchart of a fine-grained knowledge point mastery analysis method based on local graph convolution proposed by the present invention;

[0080] Figure 2 is a schematic diagram of generating a knowledge blind spot grouping table based on clustering analysis in a fine-grained knowledge point mastery analysis method based on local graph convolution proposed by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0081] Now, the present invention will be further described in detail with reference to the accompanying drawings. These drawings are all simplified schematic diagrams, only illustrating the basic structure of the present invention in a schematic manner, so they only show the components related to the present invention.

[0082] Referring to Figure 1 - Figure 2 , a fine-grained knowledge point mastery analysis method based on local graph convolution includes the following steps:

[0083] S1. Collect the learning behavior data of students, and construct an initial knowledge graph containing multiple knowledge points and their association relationships based on the learning behavior data. Each knowledge point in the knowledge graph is used as a node in the graph, and the association relationships between different knowledge points are used as edges in the graph;

[0084] S2. Based on the initial knowledge graph, establish a local graph convolution model, aggregate the features of adjacent nodes of each knowledge point node in the knowledge graph, perform weighted operations on the features of adjacent knowledge points through a convolution kernel, extract the local feature matrix of the knowledge points, and obtain the feature vectors of each knowledge point node;

[0085] S3. Input the learning behavior data of students into the local graph convolution model, and update and generate a knowledge graph with personalized features according to the personalized learning process of students;

[0086] S4. Based on the personalized knowledge graph, generate a knowledge point mastery status table by calculating the mastery index of each knowledge point;

[0087] S5. Conduct a clustering analysis on the knowledge points with mastery indices lower than the preset threshold in the knowledge point mastery status table. Use the clustering algorithm to group the knowledge points with low mastery, generating a knowledge blind spot grouping table. The knowledge blind spot grouping table identifies knowledge blind spot groups with similar mastery characteristics and structural characteristics. The knowledge points in each knowledge blind spot group have similar knowledge weaknesses and learning obstacle manifestations in the graph structure;

[0088] S6. Extract the characteristics of each knowledge blind spot group based on the knowledge blind spot grouping table, analyze the weak characteristics of the knowledge points in each group, and generate a knowledge blind spot group feature vector;

[0089] S7. Generate learning strategies for each knowledge blind spot group according to the knowledge blind spot group feature vector.

[0090] In this embodiment, S1 includes the following specific steps:

[0091] S11. Collect the learning progress data P i of the students. The learning progress data includes the learning progress of the students in each knowledge point, where i is the number of the knowledge point, and the value range of P i is from 0 to 1. 0 indicates not learned, and 1 indicates fully mastered. The learning progress data is used to represent the learning status of the students in each knowledge point;

[0092] S12. Collect the learning frequency data F i of the students. The learning frequency data includes the number of learning times of the students in each knowledge point. The learning frequency data is used to reflect the review or repeated learning situation of the students for specific knowledge points;

[0093] S13. Collect the learning feedback data R i of the students. The learning feedback data includes the feedback results of the students on each knowledge point. The value of the learning feedback data is 0 or 1. 0 indicates wrong feedback, and 1 indicates correct feedback. The learning feedback data is used to evaluate the understanding accuracy of the students on the knowledge points;

[0094] S14. Collect the knowledge mastery data C i of the students. The knowledge mastery data includes the comprehensive mastery situation of the students on each knowledge point. C i is obtained through the weighted calculation of the learning progress P i , learning frequency F i and learning feedback R i of the students on the knowledge point i:

[0095] C i = w1·P i + w2·Fi + w3·R i ;

[0096] Among them, w1, w2, and w3 are the weight coefficients of progress, frequency, and feedback respectively, and satisfy w1 + w2 + w3 = 1;

[0097] S15. Construct an initial knowledge graph containing multiple knowledge points and their association relationships based on the collected learning progress data, learning frequency data, learning feedback data, and mastery data. Each knowledge point in the knowledge graph is used as a node, and the association relationships between different knowledge points are used as edges in the graph. The association relationships are calculated based on the correlation of students' learning behavior data on the knowledge points, and the knowledge point association parameter L is defined ij represents the association strength between knowledge point i and knowledge point j:

[0098]

[0099] Among them, L ij ranges from 0 to 1, where 0 means no association and 1 means complete association.

[0100] In this embodiment, S2 includes the following specific steps:

[0101] S21. Define the neighborhood N(i) of each knowledge point node i based on the initial knowledge graph. The neighborhood N(i) includes all adjacent knowledge point nodes j directly connected to node i, and there is an association parameter L ij between node i and node j, which is used to represent the association strength between knowledge points;

[0102] S22. Define an initial feature vector X i for each knowledge point node i. The initial feature vector X i is composed of the learning progress data P i , learning frequency F i , learning feedback data R i and knowledge mastery data C i :

[0103]

[0104] Among them, X i is a four-dimensional column vector, representing the learning situation and mastery degree of knowledge point i;

[0105] S23. Define a trainable convolutional kernel weight matrix where d is the hidden feature dimension. For each knowledge point node i, use the normalized association parameter to perform a weighted sum of the features of adjacent nodes j in the neighborhood N(i) to calculate the hidden feature vector H i of node i:

[0106]

[0107] Among them, σ(·) is a non-linear activation function, is a bias vector; is a normalized correlation parameter, defined as:

[0108]

[0109] S24. Perform multi-layer graph convolution operations on the hidden feature vector H i to capture high-order neighborhood information. The feature vector of the l-th layer is:

[0110]

[0111] where l = 1, 2, …, L, and are the weight matrix and bias vector of the l-th layer, and L is the number of convolution layers;

[0112] S25. After L layers of convolution, obtain the final feature vector of each knowledge point node i. Use L2 regularization to perform regularization processing on Z i . The final feature vector Z i is used to represent the deep knowledge association degree and relative mastery degree relationship between the knowledge point i and its neighboring nodes.

[0113] In this embodiment, S3 includes the following specific steps:

[0114] S31. Input the latest learning behavior data D i (t) of the student into the local graph convolution model;

[0115] S32. According to the personalized learning process of the student, update the feature vector in the initial knowledge graph through the hidden feature vector Z i and the latest learning behavior data D i (t) to generate a personalized knowledge graph. The node feature vector in the personalized knowledge graph is defined as:

[0116]

[0117] where α is an attenuation coefficient, used to control the balance between the historical feature X i and the current feature, and its value range is from 0 to 1.

[0118] In this embodiment, S4 includes the following specific steps:

[0119] S41. Feature vector based on the personalized knowledge graph The learning frequency data F i (t), learning feedback data R i (t) and learning duration data T i (t), calculate the mastery index M of knowledge point i i :

[0120]

[0121] where β1, β2, and β3 are the weight coefficients for calculating the mastery degree;

[0122] S42. Aggregate the mastery indices M of each knowledge point i to generate a knowledge point mastery status table:

[0123] M = {M1, M2, …, M n};

[0124] where n is the total number of knowledge points in the knowledge graph;

[0125] S43. The knowledge point mastery status table M is used to quantify the mastery degree of each knowledge point by students and represent the learning progress of students on different knowledge points.

[0126] In this embodiment, S5 includes the following specific steps:

[0127] S51. Set a mastery degree threshold θ to screen the low-mastery knowledge points in the knowledge point mastery status table M. If the mastery index M of knowledge point i i < θ, then mark this knowledge point as a low-mastery knowledge point;

[0128] S52. Extract features from the set S = {i | M i < θ} of marked low-mastery knowledge points. Based on the structural feature vector Z i in the knowledge graph and the mastery index M i construct a feature matrix Q:

[0129]

[0130] where i1, i2, …, i k are the numbers of low-mastery knowledge points, Z i is the structural feature vector of knowledge point i, and the feature matrix Q is used to represent the similarity features of low-mastery knowledge points in the knowledge graph structure;

[0131] S53. Apply the improved K-means clustering algorithm with mastery weighted to the feature matrix Q to identify similar groups in the low-mastery knowledge points, determine the number of groups K, and divide the knowledge point set S into K knowledge blind spot groups G1, G2, …, G K , where the knowledge points in each knowledge blind spot group have similar knowledge weakness characteristics and learning obstacle manifestations. The objective function of the mastery weighted K-means clustering algorithm is defined as:

[0132]

[0133] where γ is the mastery weight coefficient, and its value range is from 0 to 1, which is used to balance the influence of the structural characteristics and mastery of knowledge points on the clustering result. ∥Z i -μ j ∥ 2 represents the Euclidean distance between the structural feature vector Z i of knowledge point i and the group center μ j , M i is the mastery index of knowledge point i, which is used to weighted adjust the importance of knowledge points in clustering. A lower mastery value will increase the weight, emphasizing the contribution of knowledge points with low mastery in clustering. ∈ is a small positive number;

[0134] By combining the structural characteristics and mastery index of knowledge points, the objective function of the mastery weighted K-means clustering algorithm realizes the fine-grained clustering with mastery weighted, and identifies knowledge blind spot groups with similar mastery difficulties and learning obstacles.

[0135] In this embodiment, S6 includes the following specific steps:

[0136] S61. Aggregate the feature vectors Z j of the knowledge points in each knowledge blind spot group G i based on the knowledge blind spot grouping table, extract the overall features of each knowledge blind spot group, and define the group feature vector Z j as:

[0137]

[0138] where |G j | is the number of knowledge points in group G j , Z i is the feature vector of knowledge point i, and the group feature vector Z j is used to represent the overall learning weakness characteristics of the knowledge points in the knowledge blind spot group G j ;

[0139] S62. Calculate the mean j and variance of the mastery of the knowledge points within each knowledge blind spot group G For evaluating the centrality and deviation of knowledge points mastery within a group;

[0140] S63. Based on the group feature vector Z j , the average group mastery degree and variance generate the feature vector T of each knowledge blind spot group j :

[0141]

[0142] where T j is the feature vector of the knowledge blind spot group G j , which contains the overall structural features and mastery degree statistical characteristics of the knowledge points within the group.

[0143] In this embodiment, S7 includes the following specific steps:

[0144] S71. For each knowledge blind spot group, analyze the learning needs according to its feature vector and generate learning strategies, which specifically include learning resource recommendation, exercise question assignment, and learning path adjustment plan;

[0145] S72. Learning resource recommendation: Determine the type and quantity of learning resources according to the mastery degree and structural features of the knowledge points in the knowledge blind spot group. The learning resources include video tutorials, knowledge explanations, case analyses, and summary materials. Provide step-by-step learning resources preferentially for the knowledge points with lower mastery degrees;

[0146] S73. Exercise question assignment: Allocate targeted exercise questions for students based on the complexity and mastery degree of the knowledge points within the knowledge blind spot group. The question types include basic comprehension questions, application questions, and comprehensive advanced questions. Provide exercise questions preferentially to consolidate learning for the knowledge points with lower mastery degrees and high relevance, and at the same time, the question difficulty matches the students' current level;

[0147] S74. Learning path adjustment plan: Optimize the students' learning paths based on the features of the knowledge blind spot groups, so that the knowledge points with low mastery degrees and strong relevance appear preferentially in the learning paths. The learning path adjustment plan includes reordering the learning order of knowledge points, suggesting to review weak knowledge points, and increasing the learning frequency of related knowledge points, enabling students to concentrate on overcoming weaknesses and covering related knowledge in the path.

[0148] Example 1:

[0149] In the intelligent education system of a middle school, the school hopes to conduct a fine-grained analysis of the students' knowledge point mastery so that teachers can track each student's knowledge weaknesses in real time and provide personalized learning plans. Example 1 takes the mathematical knowledge module of "quadratic functions" as the scenario to demonstrate the application of the present invention in the analysis of students' knowledge point mastery.

[0150] In the second-year junior high school mathematics curriculum of this school, students need to learn multiple fine-grained knowledge points, including "recognition of quadratic function graphs", "vertex formula of quadratic functions", "opening direction of quadratic functions", and "application problems of quadratic functions". Due to the different difficulties of each knowledge point, there are significant differences in students' understanding and mastery of knowledge points. In the traditional education model, teachers can only infer students' mastery levels based on test scores or classroom performance, and it is difficult to comprehensively and accurately understand each student's mastery of these knowledge points.

[0151] In the teaching process, the learning behavior data of each student is automatically collected through the school's intelligent learning platform. Students conduct online exercises, watch teaching videos, and participate in Q&A discussions in the system every day, and all learning behavior data is recorded by the system, including learning frequency, correct rate, learning duration, and students' feedback in specific exercises. The system first constructs an initial knowledge graph for each student based on this data, representing each student's learning situation in the quadratic function module.

[0152] This knowledge graph is composed of nodes of each fine-grained knowledge point, and the association relationships between nodes reflect the logical connections between knowledge points. In Example 1, there is a strong association between the "vertex formula of quadratic functions" and the "opening direction of quadratic functions" because understanding the application of the vertex formula requires mastering the knowledge of the opening direction. During the graph construction process, the system uses the local graph convolution method of the present invention to aggregate the features of adjacent nodes of each node, thereby extracting the features of each knowledge point.

[0153] When the system monitors that a student has a high learning frequency but a low correct rate in "recognition of quadratic function graphs", the system marks the mastery level of this knowledge point as "low mastery level", and conducts feature aggregation and mastery level evaluation on the relevant knowledge points around this knowledge point. The system also adjusts the student's learning path according to the personalized learning path optimization scheme of the present invention, enabling the student to preferentially review and practice this weak knowledge point.

[0154] In Example 1, student A showed a high correct rate in multiple calculations of the "vertex formula of quadratic functions", but frequently made mistakes in the problem-solving process of "application problems of quadratic functions". Through cluster analysis, the system classified the "application problems of quadratic functions" into the knowledge points with low mastery level and automatically adjusted the learning strategy. The system recommended a detailed teaching video of this knowledge point to student A and provided targeted application problem exercises, and at the same time placed the knowledge points "vertex formula" and "opening direction" closely related to this knowledge point in the priority position of the learning path.

[0155] Throughout the learning process, the system regularly generates a "Knowledge Point Mastery Table" to record the real-time mastery of each knowledge point by Student A. To evaluate the effectiveness of the present invention, the system conducts a quantitative analysis of the learning effects of each student and compares it with the mastery evaluation under the traditional teaching method.

[0156] After implementing the invention, the system selected the learning behavior data of 50 students and used the learning cycle (3 weeks) of the quadratic function module as the observation period to compare the differences between the method of the present invention and the traditional method in terms of students' mastery improvement, learning efficiency, and personalized adaptability.

[0157] Regarding the improvement in mastery, for the method of the present invention: After 3 weeks of learning, the average mastery of students in "identifying quadratic function graphs" increased by 23%, in "the opening direction of quadratic functions" by 19%, and in "application problems of quadratic functions" by 27%. For the traditional method: Under the traditional evaluation method, the average mastery improvement of students within the same period was 12%, 8%, and 15%. It can be seen that the method of the present invention has a significantly higher improvement amplitude in mastery of each knowledge point than the traditional method, especially in the mastery of complex application problems, and the performance of students under the guidance of the system is more remarkable.

[0158] In terms of learning efficiency, for the method of the present invention: The average number of practice questions completed by students within a 3-week period was 40, and the average viewing duration of teaching videos was 120 minutes; each student completed an average of 3 reviews of knowledge points with low mastery, and the system made 4 dynamic adjustments to the learning path throughout the learning process. For the traditional method: Within the same learning period, the average number of practice questions completed by students was 55, and the average viewing duration of teaching videos was 180 minutes, but the review frequency of knowledge points with low mastery was only 1 time, and there was no dynamic adjustment of the learning path. The data shows that the method of the present invention is superior to the traditional method in both the number of practice questions and the viewing duration of videos. The system improves learning efficiency through optimized adjustment of personalized learning paths and review frequencies.

[0159] In terms of personalized adaptability, for the method of the present invention: The system dynamically adjusts the intensity of learning resources according to the knowledge blind spots and learning progress of each student. 48 out of 50 students received personalized learning path suggestions and targeted practice question assignments during the learning process. For the traditional method: No personalized resource and path adjustment plan was provided, and all students used the same teaching resources and practice question banks. The method of the present invention shows significant advantages in personalized learning strategies. The personalized adjustment plan helps most students solve weak links in a short time and improves learning effectiveness.

[0160] Through the method of the present invention, the school has achieved an accurate grasp of the students' learning situation in the "quadratic function" module, making the students' learning paths and resource usage more in line with individual needs, achieving the effects of improving learning efficiency and mastery accuracy. The fine-grainedness and dynamic adaptability of the present invention in knowledge point mastery analysis not only provide accurate learning feedback for students, but also provide targeted teaching support for teachers, significantly improving the problems of inaccurate assessment and inflexible adjustment in traditional teaching methods.

[0161] The data results of this Example 1 show that applying the fine-grained knowledge point mastery analysis method based on local graph convolution of the present invention in an intelligent education system can effectively improve students' knowledge mastery, enhance learning efficiency, and have higher personalized adaptability, thus comprehensively achieving personalized teaching goals.

[0162] The present invention adopts local graph convolution technology. When constructing the students' knowledge graph, it captures the fine-grained features of each knowledge point through the feature aggregation of neighborhood nodes, thereby making the knowledge mastery assessment more accurate. Traditional methods usually rely on single statistical data and are difficult to accurately reflect the students' mastery situation. However, the present invention obtains high-order neighborhood information through multi-layer convolution operations, integrates the subtle differences and correlation degrees between knowledge points into the model, and thus comprehensively reflects the students' mastery status in the assessment. By real-time updating the knowledge graph structure and mastery situation, the assessment results of the present invention can immediately reflect the students' learning dynamics and make teaching feedback more agile.

[0163] The present invention designs an automatic grouping method for knowledge blind spots based on cluster analysis to group the knowledge points with low mastery degree according to features and generate personalized learning strategies, enabling the system to provide exclusive learning resources, practice questions, and path optimization plans for each student, thereby effectively covering the students' knowledge gaps. Traditional analysis methods are difficult to dynamically adapt to the students' learning progress. However, the present invention makes the system able to perform real-time personalized adjustment for each student's learning behavior through personalized updating of the knowledge graph, ensuring that the learning resources and strategies match the students' needs, and significantly improving the accuracy and adaptability of personalized analysis.

[0164] The present invention automatically generates an optimized learning path based on the feature vectors of knowledge blind spot groups, enabling students to preferentially learn knowledge points with strong relevance and high importance, thereby efficiently improving the mastery level. Traditional learning paths are often in a fixed mode and cannot flexibly adjust priorities. The present invention dynamically optimizes the learning path through a detailed analysis of the structural features of knowledge points, making it more adaptable to the individual situation of students. Intensive learning is carried out in areas with low mastery degree, and by highlighting weak knowledge points and related knowledge modules in the learning path, the learning efficiency and effect are significantly improved, enabling students to more efficiently achieve the goal of comprehensive mastery.

[0165] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution of the present invention and its inventive concept, making equivalent substitutions or changes, shall be covered by the protection scope of the present invention.

Claims

1. A fine-grained knowledge point mastery analysis method based on local graph convolution, characterized in that It includes the following steps: S1. Collect the learning behavior data of students, and construct an initial knowledge graph containing multiple knowledge points and their association relationships based on the learning behavior data. Each knowledge point in the knowledge graph is used as a node in the graph, and the association relationships between different knowledge points are used as edges in the graph; S2. Based on the initial knowledge graph, establish a local graph convolutional model, aggregate the features of adjacent nodes of each knowledge point node in the knowledge graph, perform weighted operations on the features of adjacent knowledge points through a convolutional kernel, extract the local feature matrix of the knowledge points, and obtain the feature vectors of each knowledge point node; S3. Input the learning behavior data of students into the local graph convolutional model, and update and generate a knowledge graph with personalized features according to the personalized learning process of students; S4. Based on the knowledge graph with personalized features, generate a knowledge point mastery situation table by calculating the mastery index of each knowledge point; S5. Perform clustering analysis on the knowledge points with mastery indexes lower than the preset threshold in the knowledge point mastery situation table, use the clustering algorithm to group the knowledge points with low mastery, and generate a knowledge blind spot grouping table. The knowledge blind spot grouping table identifies knowledge blind spot groups with similar mastery feature and structural features. The knowledge points in each knowledge blind spot group have similar knowledge weaknesses and learning obstacle performances in the graph structure; S6. Extract the features of each knowledge blind spot group based on the knowledge blind spot grouping table, analyze the weak characteristics of the knowledge points in each group, and generate knowledge blind spot group feature vectors; S7. Generate learning strategies for each knowledge blind spot group according to the knowledge blind spot group feature vectors; The S3 includes the following specific steps: Input the latest learning behavior data D i (t) of the student into the local graph convolutional model; According to the personalized learning process of students, through the implicit feature vector Z i and the latest learning behavior data D i (t) update the feature vectors in the initial knowledge graph to generate a personalized knowledge graph; The S4 includes the following specific steps: Feature vector X based on personalized knowledge graph i (t) The learning frequency data F i (t), learning feedback data R i (t) and learning duration data T i (t), calculate the mastery index M of knowledge point i i , and summarize the mastery index M of each knowledge point i to generate a knowledge point mastery situation table M. The knowledge point mastery situation table M is used to quantify the mastery degree of each knowledge point by students and represent the learning progress of students on different knowledge points; The S5 includes the following specific steps: Set the mastery threshold θ to screen for low-mastery knowledge points in the knowledge point mastery situation table M. If the mastery index M of knowledge point i i < θ, then mark this knowledge point as a low-mastery knowledge point; For the knowledge point set S = {i|M i <θ} marked as low mastery, feature extraction is performed, and based on the structural feature vector Z i in the knowledge graph and the mastery index M i a feature matrix Q is constructed; Apply the improved K-means clustering algorithm weighted by mastery degree to the feature matrix Q to identify similar groups in the low-mastery knowledge points, determine the number of groups K, and divide the knowledge point set S into K knowledge blind spot groups G1, G2, …, G K , and the knowledge points in each knowledge blind spot group have similar knowledge weakness characteristics and learning obstacle manifestations; The objective function of the mastery weighted K-means clustering algorithm realizes mastery weighted fine-grained clustering by combining the structural features and mastery indexes of knowledge points, and identifies knowledge blind spot groups with similar mastery difficulties and learning obstacles.

2. The fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, wherein The S1 includes the following specific steps: S11. Collect the learning progress data P of students i , where the learning progress data includes the learning progress of students at each knowledge point, where i is the number of the knowledge point, and P i ranges from 0 to 1. 0 indicates not learned, and 1 indicates fully mastered. The learning progress data is used to characterize the learning status of students at each knowledge point; S12. Collect the learning frequency data F of students i , where the learning frequency data includes the number of times a student learns each knowledge point, and the learning frequency data is used to reflect the review or repeated learning of a student for a specific knowledge point; S13. Collect the learning feedback data R of students i , where the learning feedback data includes the feedback results of students on each knowledge point. The value of the learning feedback data is 0 or 1. 0 indicates an incorrect feedback, and 1 indicates a correct feedback. The learning feedback data is used to evaluate the accuracy of students' understanding of knowledge points; S14. Collect the knowledge mastery data C of students i , where the knowledge mastery data includes the comprehensive mastery of each knowledge point by students, C i through the weighted calculation of the learning progress P of students on knowledge point i i , learning frequency F i and learning feedback R i is obtained: C i = w1·P i + w2·F i + w3·R i ; Wherein, w1, w2, and w3 are the weight coefficients of progress, frequency, and feedback respectively, and satisfy w1 + w2 + w3 = 1; S15. Construct an initial knowledge graph containing multiple knowledge points and their association relationships based on the collected learning progress data, learning frequency data, learning feedback data, and mastery data. Each knowledge point in the knowledge graph serves as a node, and the association relationships between different knowledge points serve as the edges in the graph. The association relationships are calculated based on the correlation of students' learning behavior data on the knowledge points, and define the knowledge point association parameter L ij indicating the association strength between knowledge point i and knowledge point j: Among them, L ij has a value range from 0 to 1, where 0 indicates no association and 1 indicates full association.

3. The fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that The S2 includes the following specific steps: S21. Define the neighborhood N(i) of each knowledge point node i based on the initial knowledge graph. The neighborhood N(i) includes all neighboring knowledge point nodes j directly connected to node i, and there is an association parameter L between node i and node j ij , which is used to represent the association strength between knowledge points; S22. Define an initial feature vector X for each knowledge point node i i , where the initial feature vector X i consists of the learning progress data P i of this knowledge point, the learning frequency F i , the learning feedback data R i and the knowledge mastery data C i : Among them, X i is a four-dimensional column vector representing the learning situation and mastery level of knowledge point i; S23. Define a trainable convolutional kernel weight matrix where d is the dimension of the latent feature. For each knowledge point node i, use the normalized correlation parameter to perform a weighted sum of the features of neighboring nodes j in the neighborhood N(i) to calculate the latent feature vector H of node i i : wherein, σ(·) is a non-linear activation function, is a bias vector; is a normalized correlation parameter, defined as: S24. For the implicit feature vector H i perform multi-layer graph convolutional operations to capture high-order neighborhood information. The feature vector of the l-th layer is as follows: where \(l = 1, 2, \ldots, L\), and are the weight matrix and bias vector of the \(l\)-th layer, and \(L\) is the number of convolutional layers; S25. After L-layer convolution, the final feature vector of each knowledge point node i is obtained. Use L2 regularization for Z i Perform regularization processing, and the final feature vector Z i is used to characterize the deep knowledge correlation and relative mastery relationship between knowledge point i and its neighboring nodes.

4. A fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that The S3 includes the following specific steps: S31. Input the latest learning behavior data D i (t) of the student into the local graph convolutional model; S32. According to the personalized learning process of the student, update the feature vectors in the initial knowledge graph through the implicit feature vector Z i and the latest learning behavior data D i (t) to generate a personalized knowledge graph, and the node feature vectors in the personalized knowledge graph are defined as: Among them, α is the attenuation coefficient, which is used to control the balance between the historical feature X i and the current feature, and its value range is from 0 to 1.

5. The fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that The S4 includes the following specific steps: S41. Feature vector based on the personalized knowledge graph The learning frequency data F i (t), the learning feedback data R i (t) and the learning duration data T i (t), calculate the mastery index M i : Wherein, β1, β2, and β3 are the weight coefficients for mastery calculation; S42. Aggregate the mastery index M of each knowledge point i to generate a knowledge point mastery status table: M = {M1, M2, …, M n}; Wherein, n is the total number of knowledge points in the knowledge graph; S43. The knowledge point mastery situation table M is used to quantify the mastery degree of students for each knowledge point and represent the learning progress of students on different knowledge points.

6. The fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that The S5 includes the following specific steps: S51. Set a mastery threshold θ for screening low-mastery knowledge points in the knowledge point mastery situation table M. If the mastery index M of knowledge point i i < θ, then mark this knowledge point as a low-mastery knowledge point; S52. Extract features from the set of knowledge points S = {i|M i <θ}, and construct a feature matrix Q based on the structural feature vector Z i in the knowledge graph and the mastery index M i : Among them, i1, i2, …, i k are the numbers of the low - mastery knowledge points, and Z i is the structure feature vector of knowledge point i. The feature matrix Q is used to characterize the similarity features of low - mastery knowledge points in the knowledge graph structure; S53. Apply the improved K-means clustering algorithm with mastery-degree weighting to the feature matrix Q to identify similar groups in the low-mastery knowledge points, determine the number of groups K, and divide the knowledge point set S into K knowledge blind spot groups G1, G2, …, G K , where the knowledge points in each knowledge blind spot group have similar knowledge weakness characteristics and learning obstacle manifestations. The objective function of the mastery-degree weighted K-means clustering algorithm is defined as: Among them, γ is the mastery weight coefficient, with a value range from 0 to 1, which is used to balance the influence of the structural characteristics of knowledge points and the mastery degree on the clustering result, ||Z i - μ j || 2 represents the Euclidean distance between the structural feature vector Z i of knowledge point i and the group center μ j , M i is the mastery degree index of knowledge point i, which is used to weightedly adjust the importance of knowledge points in clustering. The lower the mastery degree value, the greater the weight, emphasizing the contribution of knowledge points with low mastery degree in clustering. ∈ is a small positive number; The objective function of the mastery weighted K-means clustering algorithm realizes mastery weighted fine-grained clustering by combining the structural features and mastery indexes of knowledge points, and identifies knowledge blind spot groups with similar mastery difficulties and learning obstacles.

7. A fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that, The S6 includes the following specific steps: S61. Aggregate the knowledge point feature vectors Z in each knowledge blind spot group G based on the knowledge blind spot grouping table j to extract the overall features of each knowledge blind spot group and define the group feature vector i as follows: ​ Among them, |G j | is the number of knowledge points in group G j , Z i is the feature vector of knowledge point i, and the group feature vector is used to represent the overall learning weakness characteristics of the knowledge points in the knowledge blind spot group G j ; S62. For each knowledge blind spot group G j Calculate the mean of the mastery levels of the knowledge points within the group and the variance for evaluating the centralization and deviation of the mastery of the knowledge points within the group; S63. Group feature vector-based Group mastery mean and variance Generate the feature vector T of each knowledge blind spot group j : Among them, T j is the feature vector of the knowledge blind spot group G j , which contains the overall structural features and mastery degree statistical characteristics of the knowledge points within the group.

8. A fine-grained knowledge point mastery analysis method based on local graph convolution according to claim 1, characterized in that The S7 includes the following specific steps: S71. For each knowledge blind spot group, analyze the learning needs according to its feature vector and generate learning strategies. The learning strategies specifically include learning resource recommendation, exercise question assignment, and learning path adjustment plan; S72. Learning resource recommendation: Determine the types and quantities of learning resources based on the mastery levels and structural characteristics of the knowledge points in the knowledge blind spot group. The learning resources include video tutorials, knowledge explanations, case analyses, and summary materials. Step-by-step learning resources are preferentially provided for knowledge points with low mastery levels. S73. Practice question assignment: Assign targeted practice questions to students according to the complexity and mastery levels of the knowledge points within the knowledge blind spot group. The types of questions include basic comprehension questions, application questions, and comprehensive advanced questions. For knowledge points with low mastery levels and high relevance, practice questions are preferentially provided to consolidate learning, and the difficulty of the questions matches the students' current levels. S74. Learning path adjustment plan: Optimize the students' learning paths based on the characteristics of the knowledge blind spot group, so that knowledge points with low mastery levels and strong relevance appear in the learning paths preferentially. The learning path adjustment plan includes reordering the learning order of knowledge points, suggesting review of weak knowledge points, and increasing the learning frequency of related knowledge points, enabling students to focus on overcoming weaknesses while covering related knowledge in the path.

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