Fine-grained knowledge point mastering analysis method based on local graph convolution

Abstract

The invention discloses a fine-grained knowledge point mastering analysis method based on local graph convolution, and the method comprises the steps: S1, collecting the learning behavior data of students, and constructing an initial knowledge graph based on the learning behavior data; s2, establishing a local graph convolution model based on the initial knowledge graph; s3, updating and generating a knowledge graph with personalized features; s4, based on the personalized knowledge graph, generating a knowledge point mastering condition table by calculating a mastering degree index of each knowledge point; s5, performing clustering analysis on the knowledge points of which the mastering degree indexes are lower than a preset threshold value in the knowledge point mastering condition table; s6, generating knowledge blind spot group feature vectors; and S7, generating a learning strategy for each knowledge blind spot group according to the feature vectors of the knowledge blind spot groups. According to the invention, refined evaluation and real-time dynamic tracking of knowledge point mastering are realized.

Description

Technical Field

[0001] The present invention relates to the field of intelligent learning technology, and in particular to a fine-grained knowledge point mastery and 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 conduct quantitative evaluation based on students' learning frequency, accuracy or learning time indicators of a certain knowledge point and infer students' mastery through these basic data. Traditional methods have significant limitations and are difficult to meet the needs in terms of accuracy, real-time and personalized analysis of knowledge mastery.

[0003] First, in terms of accuracy, existing technologies make it difficult to achieve fine-grained analysis of the mastery of knowledge points, especially the dynamic relationships between adjacent or related knowledge points. Traditional statistical methods ignore the graph structure features between knowledge points and cannot deeply analyze the relationship between each knowledge point in the student learning process, resulting in relatively rough results of knowledge mastery assessment. At the same time, simple statistical indicators are difficult to identify students’ real weaknesses in certain knowledge points and cannot provide students with accurate learning suggestions.

[0004] Secondly, the existing technology also has shortcomings in real-time performance. The existing mastery analysis methods mostly use periodic statistics or static analysis methods, which cannot timely update the knowledge graph structure and knowledge mastery according to students' real-time learning behavior. It is difficult to timely identify new problems that students encounter during the learning process, which leads to a lack of timeliness in learning guidance for students and makes it difficult to effectively support teachers' teaching adjustments and personalized guidance.

[0005] In addition, existing technologies also have obvious shortcomings in personalized analysis and adaptive adjustment. The current knowledge mastery analysis methods usually use the same analysis model for all students, which makes it difficult to dynamically adapt to students' individual learning needs and changes in knowledge structure, and cannot achieve personalized updates of knowledge graphs. The one-size-fits-all analysis model makes it impossible to teach students in accordance with their aptitude and provide effective personalized learning support for each student, which ultimately affects the effectiveness of personalized learning.

[0006] To sum up, the existing technology has the following main shortcomings: first, the accuracy and granularity of knowledge point mastery assessment are low, making it difficult to capture the dynamic relationship between knowledge points; second, the real-time performance of knowledge mastery analysis is poor, making it difficult to dynamically reflect students' learning progress and weak links; finally, the existing technology lacks personalization and adaptive adjustment capabilities and cannot effectively meet students' personalized learning needs, making it difficult to provide learning support that is tailored to students' needs. Summary of the invention

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

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

[0009] S1. Collect students' learning behavior data, and construct an initial knowledge graph containing multiple knowledge points and their associations based on the learning behavior data, where each knowledge point in the knowledge graph is a node in the graph, and the associations between different knowledge points are edges in the graph;

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

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

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

[0013] S5, performing cluster analysis on the knowledge points in the knowledge point mastery status table whose mastery index is lower than a preset threshold, using a clustering algorithm to group the knowledge points with low mastery, and generating a knowledge blind spot grouping table, wherein the knowledge blind spot grouping table identifies knowledge blind spot groups with similar mastery characteristics and structural characteristics, and the knowledge points in each knowledge blind spot group have similar knowledge weaknesses and learning disability manifestations in the graph structure;

[0014] S6, extracting the characteristics of each knowledge blind spot group based on the knowledge blind spot grouping table, analyzing the weak characteristics of the knowledge points in each group, and generating a knowledge blind spot group feature vector;

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

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

[0017] S11. Collect students’ learning progress data i , the learning progress data includes the student’s learning progress at each knowledge point, where i is the number of the knowledge point, P iThe value range of is 0 to 1, 0 means not learned, 1 means fully mastered, and the learning progress data is used to characterize the learning status of students at each knowledge point;

[0018] S12. Collect students’ learning frequency data F i ,The learning frequency data includes the number of times students study each knowledge point. The learning frequency data is used to reflect the review or repeated learning of students on a specific knowledge point;

[0019] S13. Collect students’ learning feedback data i ,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, where 0 indicates incorrect feedback and 1 indicates correct feedback. The learning feedback data is used to evaluate the accuracy of students’ understanding of the knowledge points;

[0020] S14. Collect students’ knowledge mastery data C i ,The knowledge mastery data includes the students’ comprehensive mastery of each knowledge point,C i Based on the student's learning progress P on knowledge point i i , learning frequency F i and learning feedback R i The weighted calculation of is:

[0021] C i =w1·P i +w2·F i +w3·R i ;

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

[0023] S15. Based on the collected learning progress data, learning frequency data, learning feedback data and mastery data, an initial knowledge graph is constructed containing multiple knowledge points and their associations. Each knowledge point in the knowledge graph is a node, and the associations between different knowledge points are edges in the graph. The associations are calculated based on the correlation of the students' learning behavior data on the knowledge points. The knowledge point association parameter L is defined. ij Represents the strength of association between knowledge point i and knowledge point j:

[0024]

[0025] Among them, L ij The value range is from 0 to 1, where 0 means no association and 1 means complete association.

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

[0027] S21, based on the initial knowledge graph, define the neighborhood N(i) of each knowledge point node i, wherein 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 , used to indicate the strength of association between knowledge points;

[0028] S22, define the initial feature vector X for each knowledge point node i i , the initial eigenvector X i Based on the learning progress data P of this knowledge point i , learning frequency F i , learning feedback data R i and knowledge mastery data C i composition:

[0029]

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

[0031] S23. Define a trainable convolution kernel weight matrix Where d is the implicit feature dimension, for each knowledge point node i, the normalized association parameter The implicit feature vector H of node i is calculated by weighted summing the features of neighboring nodes j in the neighborhood N(i) i :

[0032]

[0033] Among them, σ(·) is a nonlinear activation function, is the bias vector; is the normalized correlation parameter, defined as:

[0034]

[0035] S24, for the latent feature vector H i Perform multi-layer graph convolution operations to capture high-order neighborhood information, and the feature vector of the lth layer for:

[0036]

[0037] Where l = 1, 2, ..., L, is the weight matrix and bias vector of the lth layer, and L is the number of convolutional layers;

[0038] S25, after L layers of convolution, the final feature vector Z of each knowledge point node i is obtained i =H i (L), L2 regularization is used for Z i After regularization, the final eigenvector Z i Used to characterize the deep knowledge association and relative mastery relationship between knowledge point i and its neighboring nodes.

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

[0040] S31. The student's latest learning behavior data D i (t) Input local graph convolution model;

[0041] S32, according to the students' personalized learning process, through the implicit feature vector Z i And the latest learning behavior data D i (t) updating the feature vector in the initial knowledge graph to generate a personalized knowledge graph, wherein the node feature vector in the personalized knowledge graph Defined as:

[0042]

[0043] Among them, α is the attenuation coefficient, which is used to control the historical feature X i The balance between the feature and the current feature, ranging from 0 to 1.

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

[0045] S41. Feature vector based on personalized knowledge graph The learning frequency data F in i (t), learning feedback data R i (t) and learning time data T i (t), calculate the mastery index M of knowledge point i i :

[0046]

[0047] Among them, β1, β2, and β3 are weight coefficients for mastery calculation;

[0048] S42, the mastery index M of each knowledge point i Summarize and generate a table of knowledge points mastered:

[0049] M={M1,M2,…,M n};

[0050] Among them, n is the total number of knowledge points in the knowledge graph;

[0051] S43. Knowledge point mastery table M is used to quantify students’ mastery of each knowledge point and represent students’ learning progress on different knowledge points.

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

[0053] S51, set the mastery threshold θ, used to filter out the low mastery knowledge points in the knowledge point mastery status table M, if the mastery index M of the knowledge point i is i <θ, then the knowledge point is marked as a low-mastery knowledge point;

[0054] S52, for the knowledge point set S={i|M i <θ} is used for feature extraction, based on the structural feature vector Z in the knowledge graph i and Mastery Index M i Construct the feature matrix Q:

[0055]

[0056] Among them, i1,i2,…,i k is the number of the knowledge point with low mastery, Z i is the structural feature vector of knowledge point i, and the feature matrix Q is used to characterize the similarity characteristics of low-mastery knowledge points in the knowledge graph structure;

[0057] S53, apply the K-means improved clustering algorithm based on mastery weighting to the feature matrix Q to identify similar groups in 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 , 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:

[0058]

[0059] Among them, γ is the mastery weight coefficient, ranging from 0 to 1, which is used to balance the influence of the structural characteristics of knowledge points and the mastery on the clustering results, ∥Z i -μ j ∥ 2 Represents the structural feature vector Z of knowledge point i i With group center μ j The Euclidean distance between i is the mastery index of knowledge point i, which is used to weight and adjust the importance of knowledge points in the cluster. A lower mastery value will increase the weight and emphasize the contribution of knowledge points with low mastery in the cluster. ∈ is a small positive number;

[0060] The objective function of the mastery-weighted K-means clustering algorithm combines the structural characteristics of knowledge points and mastery indicators to achieve mastery-weighted fine-grained clustering and identify knowledge blind spot groups with similar mastery difficulties and learning barriers.

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

[0062] S61, based on the knowledge blind spot grouping table, for each knowledge blind spot group G j The knowledge point feature vector Z in i Aggregate and extract the overall features of each knowledge blind spot group, and define the group feature vector Z j for:

[0063]

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

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

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

[0067]

[0068] Among them, T j The knowledge blind spot group G j The feature vector contains the overall structural characteristics and mastery statistical characteristics of the knowledge points in the group.

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

[0070] S71. Analyze the learning needs of each knowledge blind spot group according to its feature vector and generate a learning strategy, wherein the learning strategy specifically includes learning resource recommendation, exercise question allocation and learning path adjustment plan;

[0071] S72, learning resource recommendation: determining the type and quantity of learning resources according to the mastery and structural characteristics of the knowledge points in the knowledge blind spot group, wherein the learning resources include video tutorials, knowledge explanations, case analysis and summary materials, and providing step-by-step learning resources for knowledge points with low mastery;

[0072] S73. Exercise assignment: Targeted exercise questions are assigned to students based on the complexity and mastery of the knowledge points in the knowledge blind spot group. The question types include basic comprehension questions, application questions, and comprehensive high-level questions. For knowledge points with low mastery and high relevance, exercise questions are given priority to consolidate learning. At the same time, the difficulty of the questions should be matched with the students' current level.

[0073] S74. Learning path adjustment plan: Optimize students' learning paths based on the characteristics of knowledge blind spot groups so that knowledge points with low mastery and strong relevance appear first in the learning paths. 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, so that students can concentrate on overcoming their weaknesses while covering related knowledge in the path.

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

[0075] (1) The present invention adopts local graph convolution technology. When constructing the student knowledge graph, it captures the fine-grained features of each knowledge point through 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 student's mastery. The present invention obtains high-order neighborhood information through multi-layer convolution operations, and integrates the subtle differences and correlations between knowledge points into the model, thereby fully reflecting the student's mastery status in the assessment. By updating the knowledge graph structure and mastery status in real time, the assessment results of the present invention can instantly reflect the student's learning dynamics 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 knowledge points with low mastery by features and generate personalized learning strategies, so that the system can provide each student with exclusive learning resources, practice questions and path optimization solutions, thereby effectively covering the students' knowledge gaps. Traditional analysis methods are difficult to dynamically adapt to students' learning progress. The present invention enables the system to perform real-time personalized adjustments to each student's learning behavior through personalized updates of the knowledge graph, ensuring that learning resources and strategies match students' needs, significantly improving the accuracy and adaptability of personalized analysis.

[0077] (3) The present invention automatically generates an optimized learning path based on the feature vector of the knowledge blind spot group, so that students can give priority to learning knowledge points with strong relevance and high importance, thereby efficiently improving their mastery level. Traditional learning paths are often fixed patterns and cannot flexibly adjust priorities. The present invention dynamically optimizes the learning path through a detailed analysis of the structural characteristics of knowledge points, making it more adaptable to the individual situation of students, and strengthening learning 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, so that students can 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. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

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

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

[0081] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

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

[0083] S1. Collect students' learning behavior data, and build an initial knowledge graph containing multiple knowledge points and their associations based on the learning behavior data. Each knowledge point in the knowledge graph is a node in the graph, and the associations between different knowledge points are edges in the graph.

[0084] S2. Based on the initial knowledge graph, a local graph convolution model is established to 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 the convolution kernel, extract the local feature matrix of the knowledge point, and obtain the feature vector of each knowledge point node;

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

[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. Perform cluster analysis on the knowledge points whose mastery index is lower than the preset threshold in the knowledge point mastery status table, group the knowledge points with low mastery using a clustering algorithm, 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 disability performances 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 a learning strategy for each knowledge blind spot group according to the knowledge blind spot group feature vector.

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

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

[0092] S12. Collect students’ learning frequency data F i ,The learning frequency data includes the number of times students study each knowledge point. The learning frequency data is used to reflect the review or repeated learning of students on a specific knowledge point;

[0093] S13. Collect students’ learning feedback data i ,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, where 0 indicates incorrect feedback and 1 indicates correct feedback. The learning feedback data is used to evaluate the accuracy of students’ understanding of the knowledge points;

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

[0095] C i =w1·P i +w2·Fi +w3·R i ;

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

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

[0098]

[0099] Among them, L ij The value range is from 0 to 1, where 0 means no association and 1 means complete association.

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

[0101] S21. Based on the initial knowledge graph, define the neighborhood N(i) of each knowledge point node i. The neighborhood N(i) includes all neighboring knowledge point nodes j directly connected to node i. There is an association parameter L between nodes i and j. ij , used to indicate the strength of association between knowledge points;

[0102] S22, define the initial feature vector X for each knowledge point node i i , the initial eigenvector X i Based on the learning progress data P of this knowledge point i , learning frequency F i , learning feedback data R i and knowledge mastery data C i composition:

[0103]

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

[0105] S23. Define a trainable convolution kernel weight matrix Where d is the implicit feature dimension, for each knowledge point node i, the normalized association parameter The implicit feature vector H of node i is calculated by weighted summing the features of neighboring nodes j in the neighborhood N(i) i :

[0106]

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

[0108]

[0109] S24, for the latent feature vector H i Perform multi-layer graph convolution operations to capture high-order neighborhood information, and the feature vector of the lth layer for:

[0110]

[0111] Where l = 1, 2, ..., L, and is the weight matrix and bias vector of the lth layer, and L is the number of convolutional layers;

[0112] S25, after L layers of convolution, the final feature vector of each knowledge point node i is obtained L2 regularization is used for Z i After regularization, the final eigenvector Z i Used to characterize the deep knowledge association and relative mastery relationship between knowledge point i and its neighboring nodes.

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

[0114] S31. The student's latest learning behavior data D i (t) Input local graph convolution model;

[0115] S32, according to the students' personalized learning process, through the implicit feature vector Z i And the latest learning behavior data D i (t) Update the feature vector in the initial knowledge graph to generate a personalized knowledge graph. The node feature vector in the personalized knowledge graph Defined as:

[0116]

[0117] Among them, α is the attenuation coefficient, which is used to control the historical feature X i The balance between the feature and the current feature, ranging from 0 to 1.

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

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

[0120]

[0121] Among them, β1, β2, and β3 are weight coefficients for mastery calculation;

[0122] S42, the mastery index M of each knowledge point i Summarize and generate a table of knowledge points mastered:

[0123] M={M1,M2,…,M n};

[0124] Among them, n is the total number of knowledge points in the knowledge graph;

[0125] S43. Knowledge point mastery table M is used to quantify students’ mastery of each knowledge point and represent students’ learning progress on different knowledge points.

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

[0127] S51, set the mastery threshold θ, used to filter out the low mastery knowledge points in the knowledge point mastery status table M, if the mastery index M of the knowledge point i is i <θ, then the knowledge point is marked as a low-mastery knowledge point;

[0128] S52, for the knowledge point set S={i|M i <θ} is used for feature extraction, based on the structural feature vector Z in the knowledge graph i and Mastery Index M i Construct the feature matrix Q:

[0129]

[0130] Among them, i1,i2,…,i k is the number of the knowledge point with low mastery, Z i is the structural feature vector of knowledge point i, and the feature matrix Q is used to characterize the similarity characteristics of low-mastery knowledge points in the knowledge graph structure;

[0131] S53, apply the K-means improved clustering algorithm based on mastery weighting to the feature matrix Q to identify similar groups in 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 , 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] Among them, γ is the mastery weight coefficient, ranging from 0 to 1, which is used to balance the influence of the structural characteristics of knowledge points and the mastery on the clustering results, ∥Z i -μ j ∥ 2 Represents the structural feature vector Z of knowledge point i i With group center μ j The Euclidean distance between i is the mastery index of knowledge point i, which is used to weight and adjust the importance of knowledge points in the cluster. A lower mastery value will increase the weight and emphasize the contribution of knowledge points with low mastery in the cluster. ∈ is a small positive number;

[0134] The objective function of the mastery-weighted K-means clustering algorithm combines the structural characteristics of knowledge points and mastery indicators to achieve mastery-weighted fine-grained clustering and identify knowledge blind spot groups with similar mastery difficulties and learning barriers.

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

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

[0137]

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

[0139] S62. For each knowledge blind spot group G j Calculate the mean of the knowledge points mastered within the group and variance Used to evaluate the concentration and deviation of knowledge points mastered by the group;

[0140] S63, based on group feature vector Z j , group mastery mean and variance Generate the feature vector T for each knowledge blind spot group j :

[0141]

[0142] Among them, T j The knowledge blind spot group G j The feature vector contains the overall structural characteristics and mastery statistical characteristics of the knowledge points in the group.

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

[0144] S71. Analyze the learning needs of each knowledge blind spot group according to its feature vector and generate a learning strategy. The learning strategy specifically includes learning resource recommendation, exercise question allocation and learning path adjustment plan.

[0145] S72, learning resource recommendation: Determine the type and quantity of learning resources based on the mastery and structural characteristics of the knowledge points in the knowledge blind spot group. Learning resources include video tutorials, knowledge explanations, case analysis and summary materials. Priority will be given to providing step-by-step learning resources for knowledge points with low mastery.

[0146] S73. Exercise assignment: Targeted exercise questions are assigned to students based on the complexity and mastery of the knowledge points in the knowledge blind spot group. The question types include basic comprehension questions, application questions, and comprehensive high-level questions. For knowledge points with low mastery and high relevance, exercise questions are given priority to consolidate learning. At the same time, the difficulty of the questions should be matched with the students' current level.

[0147] S74. Learning path adjustment plan: Optimize students' learning paths based on the characteristics of knowledge blind spot groups so that knowledge points with low mastery and strong relevance appear first in the learning paths. 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, so that students can concentrate on overcoming their weaknesses while covering related knowledge in the path.

[0148] Embodiment 1:

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

[0150] In the school's eighth grade mathematics course, students need to learn multiple fine-grained knowledge points including "identification of quadratic function graphs", "vertex formulas of quadratic functions", "opening directions of quadratic functions" and "quadratic function application problems". Due to the different difficulty levels of each knowledge point, students' understanding and mastery of the knowledge points vary greatly. In the traditional education model, teachers can often only infer students' mastery based on test scores or classroom performance, and it is difficult to fully and accurately understand each student's mastery of these knowledge points.

[0151] During the teaching process, each student's learning behavior data is automatically collected through the school's intelligent learning platform. Students perform online exercises, watch teaching videos, and participate in question-and-answer discussions in the system every day. All learning behavior data are recorded by the system, including learning frequency, accuracy, learning time, and students' feedback in specific exercises. The system first builds an initial knowledge graph for each student based on these data, representing each student's learning situation in the quadratic function module.

[0152] The knowledge graph is composed of various fine-grained knowledge point nodes, and the association relationship between the nodes reflects the logical connection between the knowledge points. In Example 1, there is a strong association between the "vertex formula of the quadratic function" and the "opening direction of the quadratic function". 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 perform feature aggregation on the neighboring nodes of each node, thereby extracting the features of each knowledge point.

[0153] When the system detects that students have a high learning frequency and a low accuracy rate in "quadratic function image recognition", the system marks the mastery of this knowledge point as "low mastery" and performs feature aggregation and mastery evaluation on related 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, so that students can review and practice the weak knowledge points first.

[0154] In Example 1, Student A showed a high accuracy rate when practicing the calculation of the "quadratic function vertex formula" many times, but made frequent mistakes in solving the "quadratic function application problem". Through cluster analysis, the system classified the "quadratic function application problem" as a low-mastery knowledge point and automatically adjusted the learning strategy. The system recommended a detailed teaching video of this knowledge point to Student A and provided targeted application question exercises. At the same time, the knowledge points "vertex formula" and "opening direction" closely related to this knowledge point were placed in the priority position of the learning path.

[0155] During the entire learning process, the system will regularly generate a "knowledge point mastery table" to record student A's real-time mastery of each knowledge point. In order to evaluate the effectiveness of the present invention, the system will quantitatively analyze the learning effect of each student and compare it with the mastery evaluation under traditional teaching methods.

[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 invention and the traditional method in terms of improving students' mastery, learning efficiency and personalized adaptability.

[0157] In terms of the improvement of mastery, the method of the present invention: after 3 weeks of study, the average mastery of students in "quadratic function image recognition" increased by 23%, in "quadratic function opening direction" increased by 19%, and in "quadratic function application problems" increased by 27%. Traditional method: under the traditional evaluation method, the average mastery of students in the same period increased by 12%, 8% and 15%. It can be seen that the mastery of each knowledge point of the method of the present invention is significantly higher than that of the traditional method, especially in the mastery of complex application problems, the performance of students under the guidance of the system is more significant.

[0158] In terms of learning efficiency, the method of the present invention: within a 3-week period, the average number of exercises completed by students was 40, and the average teaching video viewing time was 120 minutes; each student completed an average of 3 reviews of low-mastery knowledge points, and the system made 4 dynamic adjustments to the learning path during the entire learning process. Traditional method: within the same learning cycle, students completed an average of 55 exercises, and the average teaching video viewing time was 180 minutes, but the review frequency of low-mastery knowledge points was only 1 time, and there was no dynamic adjustment of the learning path. The data show that the method of the present invention is superior to the traditional method in terms of the number of exercises and video viewing time. The system improves learning efficiency by optimizing and adjusting personalized learning paths and review frequencies.

[0159] In terms of personalized adaptability, the method of the present invention: the system dynamically adjusts the intensity of learning resources according to each student's knowledge blind spots and learning progress. 48 out of 50 students received personalized learning path suggestions and targeted exercise assignments during the learning process. Traditional methods: no personalized resource and path adjustment plan is provided, and all students use the same teaching resources and exercise question bank. The method of the present invention shows significant advantages in personalized learning strategies. The personalized adjustment plan helps most students solve their weak links in a short period of time and improves their learning outcomes.

[0160] Through the method of the present invention, the school has achieved accurate grasp of students' learning situation in the "quadratic function" module, so that students' learning paths and resource usage are more in line with individual needs, achieving the effect of improving learning efficiency and mastering accuracy. The fine-grained and dynamic adaptability of the present invention in knowledge point mastering analysis not only provides students with accurate learning feedback, but also provides teachers with targeted teaching support, which significantly improves the problems of inaccurate evaluation and inflexible adjustment in traditional teaching methods.

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

[0162] The present invention adopts local graph convolution technology. When constructing the student knowledge graph, it captures the fine-grained features of each knowledge point through 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 student's mastery. The present invention obtains high-order neighborhood information through multi-layer convolution operations, and integrates the subtle differences and correlations between knowledge points into the model, thereby fully reflecting the student's mastery status in the assessment. By updating the knowledge graph structure and mastery status in real time, the assessment results of the present invention can instantly reflect the student's learning dynamics and make the teaching feedback more agile.

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

[0164] The present invention automatically generates an optimized learning path based on the feature vector of the knowledge blind spot group, so that students can give priority to learning knowledge points with strong relevance and high importance, thereby efficiently improving their mastery level. Traditional learning paths are often fixed patterns and cannot flexibly adjust priorities. The present invention dynamically optimizes the learning path through a detailed analysis of the structural characteristics of the knowledge points, making it more adaptable to the individual circumstances of students, and strengthening learning 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, so that students can more efficiently achieve the goal of comprehensive mastery.

[0165] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A fine-grained knowledge point mastery and analysis method based on local graph convolution, characterized in that: The steps include: S1. Collect students' learning behavior data, and construct an initial knowledge graph containing multiple knowledge points and their associations based on the learning behavior data, where each knowledge point in the knowledge graph is a node in the graph, and the associations between different knowledge points are edges in the graph; S2. Based on the initial knowledge graph, a local graph convolution model is established to perform feature aggregation on the neighboring nodes of each knowledge point node in the knowledge graph, perform weighted operations on the features of the neighboring knowledge points through the convolution kernel, extract the local feature matrix of the knowledge point, and obtain the feature vector of each knowledge point node; S3. Input the students’ learning behavior data into the local graph convolution model, and update and generate a knowledge graph with personalized characteristics according to the students’ personalized learning process; S4. Based on the personalized knowledge graph, generate a knowledge point mastery status table by calculating the mastery index of each knowledge point; S5, performing cluster analysis on the knowledge points in the knowledge point mastery status table whose mastery index is lower than a preset threshold, using a clustering algorithm to group the knowledge points with low mastery, and generating a knowledge blind spot grouping table, wherein the knowledge blind spot grouping table identifies knowledge blind spot groups with similar mastery characteristics and structural characteristics, and the knowledge points in each knowledge blind spot group have similar knowledge weaknesses and learning disability manifestations in the graph structure; S6, extracting the characteristics of each knowledge blind spot group based on the knowledge blind spot grouping table, analyzing the weak characteristics of the knowledge points in each group, and generating a knowledge blind spot group feature vector; S7. Generate a learning strategy for each knowledge blind spot group according to the knowledge blind spot group feature vector.

2. According to claim 1, a fine-grained knowledge point mastery and analysis method based on local graph convolution is characterized in that: The S1 comprises the following specific steps: S11. Collect students’ learning progress data i , the learning progress data includes the student’s learning progress at each knowledge point, where i is the number of the knowledge point, P i The value range of is 0 to 1, 0 means not learned, 1 means fully mastered, and the learning progress data is used to characterize the learning status of students at each knowledge point; S12. Collect students’ learning frequency data F i ,The learning frequency data includes the number of times students study each knowledge point. The learning frequency data is used to reflect the review or repeated learning of students on a specific knowledge point; S13. Collect students’ learning feedback data i ,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, where 0 indicates incorrect feedback and 1 indicates correct feedback. The learning feedback data is used to evaluate the accuracy of students’ understanding of the knowledge points; S14. Collect students’ knowledge mastery data C i ,The knowledge mastery data includes the students’ comprehensive mastery of each knowledge point,C i Based on the student's learning progress P on knowledge point i i , learning frequency F i and learning feedback R i The weighted calculation of is: C i =w1·P i +w2·F i +w3·R i ; Among them, w1, w2, w3 are the weight coefficients of progress, frequency and feedback respectively, and they satisfy w1+w2+w3=1; S15. Based on the collected learning progress data, learning frequency data, learning feedback data and mastery data, an initial knowledge graph is constructed containing multiple knowledge points and their associations. Each knowledge point in the knowledge graph is a node, and the associations between different knowledge points are edges in the graph. The associations are calculated based on the correlation of the students' learning behavior data on the knowledge points. The knowledge point association parameter L is defined. ij Represents the strength of association between knowledge point i and knowledge point j: Among them, L ij The value range is from 0 to 1, where 0 means no association and 1 means complete association.

3. According to claim 1, a fine-grained knowledge point mastery and analysis method based on local graph convolution is characterized in that: The S2 comprises the following specific steps: S21, based on the initial knowledge graph, define the neighborhood N(i) of each knowledge point node i, wherein 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 , used to indicate the strength of association between knowledge points; S22, define the initial feature vector X for each knowledge point node i i , the initial eigenvector X i Based on the learning progress data P of this knowledge point i , learning frequency F i , learning feedback data R i and knowledge mastery data C i composition: Among them, X i is a four-dimensional column vector, representing the learning status and mastery of knowledge point i; S23. Define a trainable convolution kernel weight matrix Where d is the implicit feature dimension, for each knowledge point node i, the normalized association parameter The implicit feature vector H of node i is calculated by weighted summing the features of neighboring nodes j in the neighborhood N(i) i : Among them, σ(·) is a nonlinear activation function, is the bias vector; is the normalized correlation parameter, defined as: S24, for the latent feature vector H i Perform multi-layer graph convolution operations to capture high-order neighborhood information, and the feature vector of the lth layer for: Where l = 1, 2, ..., L, and is the weight matrix and bias vector of the lth layer, and L is the number of convolutional layers; S25, after L layers of convolution, the final feature vector of each knowledge point node i is obtained L2 regularization is used for Z i After regularization, the final eigenvector Z i Used to characterize the deep knowledge association and relative mastery relationship between knowledge point i and its neighboring nodes.

4. According to claim 1, a fine-grained knowledge point mastery and analysis method based on local graph convolution is characterized in that: The S3 comprises the following specific steps: S31. The student's latest learning behavior data D i (t) Input local graph convolution model; S32, according to the students' personalized learning process, through the implicit feature vector Z i And the latest learning behavior data D i (t) updating the feature vector in the initial knowledge graph to generate a personalized knowledge graph, wherein the node feature vector in the personalized knowledge graph Defined as: Among them, α is the attenuation coefficient, which is used to control the historical feature X i The balance between the feature and the current feature, ranging from 0 to 1.

5. According to claim 1, a fine-grained knowledge point mastery and analysis method based on local graph convolution is characterized in that: The S4 comprises the following specific steps: S41. Feature vector based on personalized knowledge graph The learning frequency data F in i (t), learning feedback data R i (t) and learning time data T i (t), calculate the mastery index M of knowledge point i i : Among them, β1, β2, and β3 are weight coefficients for mastery calculation; S42, the mastery index M of each knowledge point i Summarize and generate a table of knowledge points mastered: M={M1,M2,…,M n }; Among them, n is the total number of knowledge points in the knowledge graph; S43. Knowledge point mastery table M is used to quantify students’ mastery of each knowledge point and represent students’ learning progress on different knowledge points.

6. According to claim 1, a method for fine-grained knowledge point mastery and analysis based on local graph convolution is characterized in that: The S5 comprises the following specific steps: S51, set the mastery threshold θ, used to filter out the low mastery knowledge points in the knowledge point mastery status table M, if the mastery index M of the knowledge point i is i <θ, then the knowledge point is marked as a low-mastery knowledge point; S52, for the knowledge point set S={i|M i <θ} is used for feature extraction, based on the structural feature vector Z in the knowledge graph i and Mastery Index M i Construct the feature matrix Q: Among them, i1,i2,…,i k is the number of the knowledge point with low mastery, Z i is the structural feature vector of knowledge point i, and the feature matrix Q is used to characterize the similarity characteristics of low-mastery knowledge points in the knowledge graph structure; S53, apply the K-means improved clustering algorithm based on mastery weighting to the feature matrix Q to identify similar groups in 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 , 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: Among them, γ is the mastery weight coefficient, ranging from 0 to 1, which is used to balance the influence of the structural characteristics of knowledge points and the mastery on the clustering results, ∥Z i -μ j ∥ 2 Represents the structural feature vector Z of knowledge point i i With group center μ j The Euclidean distance between i is the mastery index of knowledge point i, which is used to weight and adjust the importance of knowledge points in the cluster. A lower mastery value will increase the weight and emphasize the contribution of knowledge points with low mastery in the cluster. ∈ is a small positive number; The objective function of the mastery-weighted K-means clustering algorithm combines the structural characteristics of knowledge points and mastery indicators to achieve mastery-weighted fine-grained clustering and identify knowledge blind spot groups with similar mastery difficulties and learning barriers.

7. According to claim 1, a fine-grained knowledge point mastery and analysis method based on local graph convolution is characterized in that: The S6 comprises the following specific steps: S61, based on the knowledge blind spot grouping table, for each knowledge blind spot group G j The knowledge point feature vector Z in i Aggregate and extract the overall features of each knowledge blind spot group, and define the group feature vector for: Among them, |G j | for group G j The number of knowledge points in Z i is the feature vector of knowledge point i, and the group feature vector Used to characterize the knowledge blind spot group G j The overall learning weakness characteristics of the knowledge points; S62. For each knowledge blind spot group G j Calculate the mean of the knowledge points mastered within the group and variance Used to evaluate the concentration and deviation of knowledge points mastered by the group; S63, based on group feature vector Group mastery mean and variance Generate the feature vector T for each knowledge blind spot group j : Among them, T j The knowledge blind spot group G j The feature vector contains the overall structural characteristics and mastery statistical characteristics of the knowledge points in the group.

8. According to claim 1, a method for fine-grained knowledge point mastery and analysis based on local graph convolution is characterized in that: The S7 comprises the following specific steps: S71, for each knowledge blind spot group, analyzing the learning needs according to its feature vector, and generating a learning strategy, wherein the learning strategy specifically includes learning resource recommendation, exercise question allocation, and learning path adjustment plan; S72, learning resource recommendation: determining the type and quantity of learning resources according to the mastery and structural characteristics of the knowledge points in the knowledge blind spot group, wherein the learning resources include video tutorials, knowledge explanations, case analysis and summary materials, and providing step-by-step learning resources for knowledge points with low mastery; S73. Exercise assignment: Targeted exercise questions are assigned to students based on the complexity and mastery of the knowledge points in the knowledge blind spot group. The question types include basic comprehension questions, application questions, and comprehensive high-level questions. For knowledge points with low mastery and high relevance, exercise questions are given priority to consolidate learning. At the same time, the difficulty of the questions should be matched with the students' current level. S74. Learning path adjustment plan: Optimize students' learning paths based on the characteristics of knowledge blind spot groups so that knowledge points with low mastery and strong relevance appear first in the learning paths. 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, so that students can concentrate on overcoming their weaknesses while covering related knowledge in the path.

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