Teaching-assisting knowledge graph and construction method thereof

Abstract

The invention aims to provide a teaching-assisting knowledge graph and a construction method thereof, and relates to the technical field of education data processing. The method comprises the following steps: constructing a teaching aid evaluation matrix according to learning behavior data, teaching aid resource data and learning stage data of a user; decomposing the teaching-assistant evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix through a non-negative matrix factorization algorithm; and constructing a knowledge graph according to the teaching aid evaluation matrix, the educational knowledge mastery degree matrix and the educational knowledge association degree matrix. According to the knowledge graph construction method, the relationship among the educational knowledge nodes, the learning stage nodes and the teaching-assisted resource nodes is integrated, the influence degrees of different teaching-assisted resources on the educational knowledge nodes in different learning stages of the user can be distinguished by analyzing knowledge mastering and resource use conditions, the teaching-assisted resources can be efficiently screened, and the teaching-assisted resources can be conveniently and rapidly screened. A user is helped to discover weak links in a learning process, and a learning plan and a learning method are optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of educational data processing, and in particular to a teaching-aiding knowledge graph and a construction method thereof. Background Art

[0002] Knowledge graph is a structured knowledge representation method that can represent entities, concepts, and the relationships between them through nodes and edges. In a knowledge graph, nodes usually represent various types of entities, such as people, places, objects, or abstract concepts, while edges represent the diverse relationships between these entities. This structure can not only effectively present the complex associations in large knowledge systems, but also help users understand the knowledge content more intuitively through visualization. The application of knowledge graphs covers many fields, such as search engine optimization, recommendation systems, and intelligent question-answering systems, demonstrating its powerful information organization and management capabilities.

[0003] In the field of education, knowledge graphs provide strong support for the integration of educational resources. It realizes the systematic organization and management of knowledge by linking educational resources with entities and relationships in knowledge graphs. This connection not only helps students understand the relationship between knowledge points more intuitively, but also enables students to explore related content independently through knowledge graphs, thereby improving the efficiency and depth of learning. In addition, teachers can also use knowledge graphs to design course structures more clearly, evaluate students' learning effects, identify knowledge weaknesses, and adjust teaching strategies in a targeted manner. Overall, knowledge graphs show great potential in the field of education and help build a more scientific and efficient learning environment.

[0004] However, there are many types of educational resources on the market, with scattered sources, and the relationship between educational resources and knowledge points is complex. Building a comprehensive and accurate knowledge graph faces many challenges. Existing technologies and tools are insufficient in establishing precise relationships between resources, knowledge points, and learning stages, and are difficult to handle large-scale data and complex relationships, making it difficult for students and teachers to effectively integrate and utilize rich educational resources, thus limiting the realization of personalized and efficient learning experiences. Summary of the invention

[0005] The purpose of the present invention is to provide a knowledge graph that combines teaching and auxiliary teaching and a method for constructing it, so as to efficiently screen teaching and auxiliary teaching resources, help users discover weak links in the learning process, optimize learning plans and methods, and provide users with comprehensive learning support.

[0006] The purpose of the present invention is achieved by the following technical means: In a first aspect, the present invention provides a method for constructing a knowledge graph that is both teaching-assisted and supplementary, comprising the steps of: Constructing a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data, and learning stage data; the elements of the teaching aid evaluation matrix represent the teaching aid evaluation index of a certain teaching aid resource at a certain user learning stage; The teaching aid evaluation matrix is ​​decomposed into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm; the elements of the educational knowledge mastery degree matrix represent the mastery degree index of a certain educational knowledge by the user at a certain learning stage; the elements of the educational knowledge association degree represent the correlation degree between a certain teaching aid resource and a certain educational knowledge; A knowledge graph is constructed based on a teaching aid evaluation matrix, an educational knowledge mastery degree matrix and an educational knowledge association degree matrix; the nodes of the knowledge graph include educational knowledge nodes, learning stage nodes and teaching aid resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set by the educational knowledge mastery degree matrix; the edges between the teaching aid resource nodes and the educational knowledge nodes are set by the educational knowledge association degree matrix; the edges between the learning stage nodes and the teaching aid resource nodes are set by the teaching aid evaluation matrix.

[0007] Preferably, the step of constructing a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data, and learning stage data comprises the following steps: Collect learning behavior data, teaching resources data and learning stage data involved in the user's learning process; Clean the collected learning behavior data, teaching resource data, and learning stage data, and process missing values, noise data, and outliers; A teaching aid evaluation matrix is ​​constructed based on learning behavior data, teaching aid resource data and learning stage data; the rows of the teaching aid evaluation matrix represent the user learning stage, which is obtained through the learning stage data; the columns of the teaching aid evaluation matrix represent the teaching aid resource identifier, which is obtained through the teaching aid resource data.

[0008] Preferably, the teaching aid evaluation index is calculated by weighted average of the user's concentration, participation, learning time and exercise score rate in the process of using the teaching aid resources.

[0009] Preferably, the method of decomposing the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm comprises the steps of: Randomly initialize the educational knowledge mastery degree matrix and the educational knowledge association degree matrix, and set the sizes of the educational knowledge mastery degree matrix and the educational knowledge association degree matrix; Set the maximum number of iterations and error threshold; Iteratively update the educational knowledge mastery degree matrix and the educational knowledge association degree matrix and calculate the matrix approximation error until the maximum number of iterations is reached or the matrix approximation error is less than the error threshold.

[0010] Preferably, the mastery index is expressed as: ; The degree of correlation is expressed as: ; in, Represents the educational knowledge mastery matrix, It represents the user's mastery of the kth educational knowledge in the i-th learning stage in the current iteration; represents the educational knowledge correlation matrix, Indicates the degree of relevance between the j-th teaching resource and the k-th educational knowledge in the current iteration; represents the teaching aid evaluation matrix; The matrix approximation error is expressed as: ; in, It represents the matrix approximation error of the iter-th iteration, and F represents the Frobenius norm.

[0011] Preferably, the method further comprises the steps of: The knowledge graph is updated by a non-dominated sorting genetic algorithm.

[0012] Preferably, the updating of the knowledge graph by a non-dominated sorting genetic algorithm comprises the steps of: The population is generated by random initialization, and each individual in the population represents an update plan for the knowledge graph.

[0013] The fitness parameter group of each individual in the population is calculated through the fitness function group; the population is divided into several non-dominated levels according to the fitness parameter group, the non-dominated level of each individual is recorded and the crowding distance of each individual is calculated; Perform selection, crossover and mutation operations on individuals in the population according to the non-dominated rank and crowding distance of each individual; Merge the offspring individuals into the population, recalculate the non-dominated rank and crowding distance of each individual, and select a new population based on the non-dominated rank and crowding distance of each individual; Iterate until the stopping condition is met, and output the final Pareto frontier as a knowledge graph set; The sum of the fitness parameters of each individual in the knowledge graph set is calculated according to the preset weights, and the knowledge graph is updated according to the individual with the highest sum of fitness parameters.

[0014] Preferably, the fitness function group includes an accuracy evaluation function, a connectivity evaluation function and a simplicity evaluation function; and the fitness parameter group includes an accuracy evaluation parameter, a connectivity evaluation parameter and a simplicity evaluation parameter.

[0015] Preferably, the accuracy evaluation function is expressed as: ; in, Represents an update scheme for an individual in a population, i.e. a knowledge graph, represents the value of the i-th row and j-th column of the actual teaching aid evaluation matrix, Represents an individual The value of the i-th row and j-th column of the teaching aid evaluation matrix; m and n are the number of rows and columns of the teaching aid evaluation matrix respectively; The connectivity evaluation function is expressed as: ; Where: N is the total number of nodes of individual G, x is the node number; is the number of nearest neighbors of node x; is the total number of edges between the nearest nodes of node x; The simplicity evaluation parameter is expressed as: ; in, is the total number of edges in individual G.

[0016] Preferably, the sum of the fitness parameters is expressed as: ; in, , and They are the preset weights for the accuracy evaluation function, connectivity evaluation function, and simplicity evaluation function respectively.

[0017] In the second aspect, the present invention provides a knowledge graph that is both teaching and auxiliary, and the knowledge graph teaching and auxiliary is constructed by constructing an evaluation matrix, an educational knowledge mastery degree matrix, and an educational knowledge association degree matrix. The nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching auxiliary resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set by the educational knowledge mastery degree matrix; the edges between the teaching auxiliary resource nodes and the educational knowledge nodes are set by the educational knowledge association degree matrix; the edges between the learning stage nodes and the teaching auxiliary resource nodes are set by the teaching auxiliary evaluation matrix.

[0018] The teaching aid evaluation matrix is ​​constructed based on the user's learning behavior data, teaching aid resource data and learning stage data; the elements of the teaching aid evaluation matrix represent the teaching aid evaluation index of a certain teaching aid resource at a certain user learning stage; The educational knowledge mastery degree matrix and the educational knowledge association degree matrix are obtained by decomposing the teaching aid evaluation matrix through a non-negative matrix decomposition algorithm; the elements of the educational knowledge mastery degree matrix represent the user's mastery degree index of a certain educational knowledge at a certain learning stage; the elements of the educational knowledge association degree represent the correlation degree between a certain teaching aid resource and a certain educational knowledge.

[0019] The beneficial effects of the present invention are: This application constructs a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data and learning stage data to achieve the evaluation of the teaching aid resources used by the user at different learning stages; decomposes the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix through a non-negative matrix decomposition algorithm to achieve a detailed analysis of the user's educational knowledge mastery degree and the degree of association between teaching aid knowledge; constructs the nodes and edges of the knowledge graph through the teaching aid evaluation matrix, the educational knowledge mastery degree matrix and the educational knowledge association degree matrix to achieve a graphical representation of the relationship between educational knowledge, learning stages and teaching aid resources. The construction method of the knowledge graph of this application integrates the relationship between educational knowledge nodes, learning stage nodes and teaching aid resource nodes. It can help to efficiently screen teaching aid resources by analyzing knowledge mastery and resource usage, and identifying the degree of influence of different teaching aid resources on educational knowledge points at different learning stages of users, helping users discover weak links in the learning process, optimizing learning plans and means, and providing users with comprehensive learning support.

[0020] The embodiment of the present application can optimize multiple objectives simultaneously through the non-dominated sorting genetic algorithm. Specifically, through the Pareto optimal solution set, the non-dominated sorting genetic algorithm finds the best balance between different objectives, making the knowledge graph update more comprehensive and reasonable; and through fast non-dominated sorting, the non-dominated sorting genetic algorithm can efficiently screen and sort the population, improve the computational efficiency, and can improve the computational efficiency and reduce the computational complexity compared to the traditional genetic algorithm.

[0021] The embodiment of the present application uses accuracy, connectivity and simplicity as the comprehensive evaluation targets of the sum of fitness parameters to ensure a balance between different targets. Since the knowledge graph in the final Pareto front has different specific characteristics, the embodiment can select the knowledge graph that is suitable for the specific application scenario by adjusting the preset weights, which helps to enhance the applicability of the knowledge graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0024] Figure 1 A flow chart of a method for constructing a knowledge graph that combines teaching and auxiliary learning according to an embodiment of the present invention; Figure 2 A schematic diagram of a process of decomposing a teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm according to an embodiment of the present invention; Figure 3 A schematic diagram of a flow chart of a method for constructing a knowledge graph that provides both teaching and assistance according to another embodiment of the present invention; Figure 4 This is a schematic diagram of a process for updating the knowledge graph through a non-dominated sorting genetic algorithm according to another embodiment of the present invention. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0027] In addition, the descriptions of "first", "second", etc. in the present invention are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0028] The purpose of the present invention is to provide a knowledge graph that combines teaching and auxiliary teaching and a method for constructing it, so as to efficiently screen teaching and auxiliary teaching resources, help users discover weak links in the learning process, optimize learning plans and methods, and provide users with comprehensive learning support.

[0029] Example 1 Please refer to Figure 1 , a method for constructing a knowledge graph that is both teaching and auxiliary, comprising the steps of: S1. Construct a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data and learning stage data; the rows of the teaching aid evaluation matrix represent the user's learning stage, the columns represent the teaching aid resource identifiers, and the elements of the teaching aid evaluation matrix represent the teaching aid evaluation indicators for a certain teaching aid resource at a certain user learning stage.

[0030] Furthermore, the construction of a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data, and learning stage data includes the following steps: S11, collecting learning behavior data, teaching resources data and learning stage data involved in the user's learning process; Among them, learning behavior data refers to various behavioral data generated by users during the learning process, such as video viewing time, question answering accuracy, homework submission status, etc.

[0031] The supplementary teaching resource data is a digital representation of the content of the supplementary teaching materials. The sources of the supplementary teaching materials include textbook content, homework, reference books, learning videos, etc. In one embodiment, the supplementary teaching resource data is stored through an independent supplementary teaching resource ID. Specifically, for a certain chapter in a certain textbook content, the corresponding supplementary teaching resource data can be represented in the form of "resource ID: unique identifier; resource type: textbook content, homework, reference book or learning video; resource name: specific name of supplementary teaching material; supplementary teaching material identifier: unique identifier of different types of supplementary teaching materials; chapter identifier: identifier of the specific chapter corresponding to the supplementary teaching material; resource content: specific content or link of the supplementary teaching material". For example, a supplementary teaching resource data identifier is {"resource ID": "001", "resource type": "textbook content", "resource name": "High school mathematics compulsory course one", "supplementary teaching material identifier": "textbook-high school mathematics-compulsory course one", "chapter identifier": "Chapter 1-sets and functions", "resource content": "concept of sets, operations on sets..."}.

[0032] Learning stage data is used to reflect the current learning stage of the user. Learning stage data can be obtained through user registration information, learning progress, etc.

[0033] S12. Clean the collected learning behavior data, teaching resource data, and learning stage data, process missing values, noise data, and outliers, and ensure the reliability and accuracy of the data.

[0034] S13, construct a teaching aid evaluation matrix based on learning behavior data, teaching aid resource data and learning stage data; Among them, the rows of the teaching aid evaluation matrix represent the user's learning stage, which is obtained through the learning stage data; the columns of the teaching aid evaluation matrix represent the teaching aid resource identifiers, which are obtained through the teaching aid resource data; the matrix elements in the teaching aid evaluation matrix represent the teaching aid evaluation indicators of a certain user's learning stage for a certain teaching aid resource, which are obtained through comprehensive analysis of learning behavior data.

[0035] In one embodiment, the teaching aid evaluation index is calculated by weighted average of the user's concentration, participation, learning time and exercise score rate in the process of using the teaching aid resources. The methods for obtaining the concentration include: Sensor data: use mouse and keyboard activity monitoring or wearable devices (such as smart bracelets) to obtain users' behavioral and physiological data to infer their concentration level; log analysis: analyze users' operation records on the platform and pay attention to behaviors such as frequent page switching or long-term stay on a specific page.

[0036] The methods for obtaining the engagement include: server logs, analyzing the user's active time on the platform, number of visits, and type and frequency of participation in activities; NLP technology, evaluating the user's engagement by analyzing the user's interaction frequency or speech content in the discussion area.

[0037] The method for obtaining the learning time includes: client log, recording the user's login time and logout time on the platform to calculate the learning time; server log, analyzing the user's learning session time and calculating the learning time through timestamp records; sensor data, using mouse and keyboard activity records to identify the actual time invested in learning.

[0038] The methods for obtaining the exercise score rate include: platform data, directly obtaining the performance data of users in various exercises and tests on various online learning platforms; real-time scoring, using a camera or a mobile phone camera to take pictures of the exercises currently completed by the user, and using computer vision technology such as OCR (optical character recognition) technology to identify the exercises and the user's answers, comparing the identified answers with the standard answers, and calculating the user's exercise score rate in real time.

[0039] S2. Decompose the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix through a non-negative matrix decomposition algorithm; the rows of the educational knowledge mastery degree matrix represent the user's learning stage, the columns represent the educational knowledge identifiers, and the elements of the educational knowledge mastery degree matrix represent the user's mastery degree index of a certain educational knowledge at a certain learning stage; the rows of the educational knowledge association degree matrix represent the educational knowledge identifiers, the columns represent the teaching aid resource identifiers, and the elements of the educational knowledge association degree matrix represent the degree of correlation between a certain teaching aid resource and a certain educational knowledge.

[0040] Among them, the non-negative matrix factorization (NMF) algorithm is a matrix decomposition technology that is widely used in recommendation systems, image processing, text mining and other fields. It can decompose a non-negative matrix into two non-negative matrices, thereby revealing the potential low-dimensional structure in the data. The purpose of this application to construct a knowledge graph that combines teaching and auxiliary materials is to provide students with different teaching and auxiliary materials at different stages of learning to improve learning efficiency and effectiveness. In order to achieve personalized recommendations, it is necessary to understand the students' mastery of various educational knowledge and the relationship between teaching and auxiliary materials and educational knowledge. This purpose is achieved through the non-negative matrix decomposition algorithm.

[0041] It should be noted that educational knowledge refers to the educational knowledge points involved in the user's learning process. In order to distinguish the conventional technical term "knowledge point" in the field of educational data technology from the field of knowledge graph technology, the educational knowledge points involved in the user's learning process are recorded as "educational knowledge" in this article.

[0042] For further information, see Figure 2 The method of decomposing the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm comprises the following steps: S21, randomly initialize the educational knowledge mastery degree matrix and the educational knowledge association degree matrix, set the sizes of the educational knowledge mastery degree matrix and the educational knowledge association degree matrix to m×k and k×n; the size of the teaching aid evaluation matrix is ​​recorded as m×n, wherein m, n and k are all positive integers.

[0043] S22, setting the maximum number of iterations and error threshold; S23, iteratively updating the educational knowledge mastery degree matrix and the educational knowledge association degree matrix and calculating the matrix approximation error until the maximum number of iterations is reached or the matrix approximation error is less than the error threshold; In the iterative process, the mastery index is expressed as: ; The degree of correlation is expressed as: ; in, Represents the educational knowledge mastery matrix, It represents the user's mastery of the kth educational knowledge in the i-th learning stage in the current iteration; represents the educational knowledge correlation matrix, Indicates the degree of relevance between the j-th teaching resource and the k-th educational knowledge in the current iteration; represents the teaching aid evaluation matrix; The (i, k)th item represents the product of the transposed product of the teaching aid evaluation matrix and the educational knowledge association degree matrix. The (i, k)th item represents the result of multiplying the educational knowledge mastery degree matrix, the educational knowledge association degree matrix, and the transpose of the educational knowledge association degree matrix. The (k,j)th item represents the product of the transpose of the educational knowledge mastery matrix and the teaching aid evaluation matrix. The (k, j)th item representing the transpose of the educational knowledge mastery degree matrix and the product of the educational knowledge mastery degree matrix and the educational knowledge association degree matrix; The matrix approximation error is specifically expressed as: ; in, It represents the matrix approximation error of the iter-th iteration, and F represents the Frobenius norm.

[0044] This embodiment decomposes the high-dimensional teaching aid evaluation matrix into a low-dimensional education knowledge mastery degree matrix and an education knowledge association degree matrix, thereby extracting the potential education knowledge mastery degree and education knowledge association degree, and providing a data basis for the subsequent construction of a knowledge graph to intuitively display the relationship between educational knowledge, user learning stage and teaching aid resources.

[0045] S3. Construct a knowledge graph based on the teaching aid evaluation matrix, the educational knowledge mastery degree matrix and the educational knowledge association degree matrix; the nodes of the knowledge graph include educational knowledge nodes, learning stage nodes and teaching aid resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set by the educational knowledge mastery degree matrix; the edges between the teaching aid resource nodes and the educational knowledge nodes are set by the educational knowledge association degree matrix; the edges between the learning stage nodes and the teaching aid resource nodes are set by the teaching aid evaluation matrix.

[0046] This application constructs a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data and learning stage data to achieve the evaluation of the teaching aid resources used by the user at different learning stages; decomposes the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix through a non-negative matrix decomposition algorithm to achieve a detailed analysis of the user's educational knowledge mastery degree and the degree of association between teaching aid knowledge; constructs the nodes and edges of the knowledge graph through the teaching aid evaluation matrix, the educational knowledge mastery degree matrix and the educational knowledge association degree matrix to achieve a graphical representation of the relationship between educational knowledge, learning stages and teaching aid resources. The construction method of the knowledge graph of this application integrates the relationship between educational knowledge nodes, learning stage nodes and teaching aid resource nodes. It can help to efficiently screen teaching aid resources by analyzing knowledge mastery and resource usage, and identifying the degree of influence of different teaching aid resources on educational knowledge points at different learning stages of users, helping users discover weak links in the learning process, optimizing learning plans and means, and providing users with comprehensive learning support.

[0047] In order to more intuitively illustrate how to construct a knowledge graph according to this embodiment, a small amount of high school mathematics related content is used as an example for explanation.

[0048] The knowledge points, supplementary teaching resources and learning stages focused on in this example are as follows: Knowledge points: Definition and properties of functions (K1), trigonometric functions (K2), derivatives (K3), permutations and combinations (K4) Teaching resources: handouts (T1), exercise books (T2), video explanations (T3), test papers (T4) Study period: Semester 1 (S1), Semester 2 (S2) In step S1, a teaching aid evaluation matrix is ​​constructed, assuming that the teaching aid evaluation indicators of students using various teaching aid resources (T1, T2, T3, T4) at different learning stages (S1, S2) are obtained from the user learning behavior data.

[0049] The teaching aid evaluation matrix constructed according to the teaching aid evaluation indicators is as follows: | T1 | T2 | T3 | T4 | --| -- | -- | -- | -- | S1 | 0.8| 0.7| 0.6| 0.5|; S2 | 0.7| 0.9| 0 | 0.6| In step S2, the teaching aid evaluation matrix is ​​decomposed by a non-negative matrix decomposition algorithm, and the following is obtained after decomposition: Educational knowledge mastery matrix: | K1 | K2 | K3 | K4 | -- | -- | -- | -- | -- | S1 | 0.9| 0.6| 0.2| 0.4|; S2 | 0.8| 0.7| 0.5| 0.6| Educational knowledge correlation degree matrix: | T1 | T2 | T3 | T4 | -- | -- | -- | -- | -- | K1 | 0.8| 0.7| 0.6| 0.5| K2 | 0.6| 0.8| 0.7| 0.4|; K3 | 0 | 0.7| 0.9| 0.6| K4 | 0.4| 0.6| 0.5| 0.7| In step S3, a knowledge graph is constructed based on the teaching aid evaluation matrix, the educational knowledge mastery matrix, and the educational knowledge association matrix, including: 1. Create a node: Create learning phase nodes: S1, S2; Create educational knowledge nodes: K1, K2, K3, K4; Create teaching resource nodes: T1, T2, T3, T4; 2. Create edges: Edges between learning stage nodes and educational knowledge nodes: S1-K1 (weight 0.9), S1-K2 (weight 0.6), S1-K3 (weight 0.2), S1-K4 (weight 0.4) S2-K1 (weight 0.8), S2-K2 (weight 0.7), S2-K3 (weight 0.5), S2-K4 (weight 0.6) Edges between educational knowledge nodes and teaching resources nodes: K1-T1 (weight 0.8), K1-T2 (weight 0.7), K1-T3 (weight 0.6), K1-T4 (weight 0.5) K2-T1 (weight 0.6), K2-T2 (weight 0.8), K2-T3 (weight 0.7), K2-T4 (weight 0.4) K3-T1 (weight 0.5), K3-T2 (weight 0.7), K3-T3 (weight 0.9), K3-T4 (weight 0.6) K4-T1 (weight 0.4), K4-T2 (weight 0.6), K4-T3 (weight 0.5), K4-T4 (weight 0.7) Edges between learning stage nodes and supplementary teaching resource nodes: S1-T1 (weight 0.8), S1-T2 (weight 0.7), S1-T3 (weight 0.6), S1-T4 (weight 0.5) S2-T1 (weight 0.7), S2-T2 (weight 0.9), S2-T3 (weight 0.8), S2-T4 (weight 0.6) By merging the above nodes and edges, a knowledge graph representation of the user's learning process using teaching resources T1, T2, T3 and T4 in learning stages S1 and S2 can be constructed.

[0050] As a preferred embodiment, please refer to Figure 3 The method for constructing a knowledge graph for teaching and supplementing in this application also includes the following steps: S4. Update the knowledge graph through a non-dominated sorting genetic algorithm.

[0051] The non-dominated sorting genetic algorithm (NSGA-II) is an efficient multi-objective optimization evolutionary algorithm that handles the trade-offs between multiple objectives through non-dominated sorting and crowding comparison, and uses an elite strategy to improve algorithm performance. Based on the concept of Pareto optimality, the non-dominated sorting genetic algorithm stratifies individuals in the population according to the dominance relationship between them. This process helps the algorithm identify which solutions are optimal (i.e., solutions that are not dominated by any other solution) and can maintain population diversity. In each generation, NSGA-II merges the current population and the offspring population, and then performs a fast non-dominated sort, thereby effectively reducing computational complexity.

[0052] In the embodiment of the present application, the non-dominated sorting genetic algorithm can simultaneously optimize multiple objectives, such as accuracy, connectivity, and simplicity. Specifically, through the Pareto optimal solution set, the non-dominated sorting genetic algorithm finds the best balance between different objectives, making the knowledge graph update more comprehensive and reasonable; and through fast non-dominated sorting, the non-dominated sorting genetic algorithm can efficiently screen and sort the population, improve the computational efficiency, and can improve the computational efficiency and reduce the computational complexity compared to the traditional genetic algorithm.

[0053] For further information, see Figure 4 , the updating of the knowledge graph by a non-dominated sorting genetic algorithm comprises the steps of: S41. Randomly initialize and generate a population, where each individual in the population represents an update plan for a knowledge graph.

[0054] S42, calculating the fitness parameter group of each individual in the population through the fitness function group; dividing the population into several non-dominated levels according to the fitness parameter group, recording the non-dominated level of each individual and calculating the crowding distance of each individual; the individuals in each non-dominated level are mutually non-dominated, and the individuals at the lower level in different non-dominated levels are superior to the individuals at the higher level; S43, performing selection, crossover and mutation operations on individuals in the population according to the non-dominated rank and crowding distance of each individual; Step S43 specifically includes: According to the non-dominated level and crowding distance of each individual, the individuals in the population are selected in a tournament to obtain the set of winning individuals; Perform crossover operation on individuals in the winning individual set to generate offspring individuals; the crossover operation can be single-point crossover, uniform crossover, etc.

[0055] Perform mutation operations on offspring individuals.

[0056] S44, merging the offspring individuals into the population, recalculating the non-dominated rank and crowding distance of each individual, and obtaining a new population based on the non-dominated rank and crowding distance of each individual; S45, iterating until a stop condition is met, outputting a final Pareto frontier recorded as a knowledge graph set; the knowledge graph set includes a number of individuals; The iteration of this step refers to the cyclic execution of steps S42 to S44; the stopping conditions include reaching the maximum number of iterations and the population fitness not being significantly improved in several generations.

[0057] S46. Calculate the sum of fitness parameters of each individual in the knowledge graph set according to preset weights, and update the knowledge graph according to the individual with the highest sum of fitness parameters.

[0058] In one embodiment, the fitness function group includes an accuracy evaluation function, a connectivity evaluation function and a simplicity evaluation function; the fitness parameter group includes an accuracy evaluation parameter, a connectivity evaluation parameter and a simplicity evaluation parameter; The accuracy evaluation function is expressed as: ; in, Represents an update scheme for an individual in a population, i.e. a knowledge graph, represents the value of the i-th row and j-th column of the actual teaching aid evaluation matrix, Represents an individual The value of the i-th row and j-th column of the teaching aid evaluation matrix. The actual teaching aid evaluation matrix is ​​the teaching aid evaluation matrix obtained in step S1; m and n are the number of rows and columns of the teaching aid evaluation matrix, respectively. It should be noted that the negative sign in this formula is used to transform the error minimization into the fitness maximization problem.

[0059] The connectivity evaluation function is expressed as: ; Where: N is the total number of nodes of individual G, x is the node number; is the number of nearest neighbors of node x; is the total number of edges between the nearest neighbors of node x.

[0060] The simplicity evaluation parameter is expressed as: ; in, is the total number of edges in individual G.

[0061] Each final knowledge graph has balanced performance on different objectives and can be selected according to specific needs in practical applications.

[0062] Based on the above embodiment, the sum of the fitness parameters is expressed as: ; in, , and They are the preset weights for the accuracy evaluation function, connectivity evaluation function, and simplicity evaluation function respectively.

[0063] This embodiment uses accuracy, connectivity and simplicity as comprehensive evaluation targets of the sum of fitness parameters to ensure a balance between different targets. Since the knowledge graphs in the final Pareto front have different specific characteristics, for example, some graphs are outstanding in accuracy and are suitable for application scenarios with high accuracy requirements, while other graphs may be better in simplicity and connectivity, suitable for application scenarios with limited resources or requiring efficient queries; this embodiment can select knowledge graphs that are suitable for specific application scenarios by adjusting preset weights, which helps to enhance the applicability of knowledge graphs.

[0064] Based on the aforementioned method for constructing a knowledge graph of teaching and auxiliary, the present invention also provides a knowledge graph of teaching and auxiliary, wherein the knowledge graph teaching and auxiliary is constructed by constructing an evaluation matrix, an educational knowledge mastery degree matrix, and an educational knowledge association degree matrix. The nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching and auxiliary resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set by the educational knowledge mastery degree matrix; the edges between the teaching and auxiliary resource nodes and the educational knowledge nodes are set by the educational knowledge association degree matrix; the edges between the learning stage nodes and the teaching and auxiliary resource nodes are set by the teaching and auxiliary evaluation matrix.

[0065] The teaching aid evaluation matrix is ​​constructed based on the user's learning behavior data, teaching aid resource data and learning stage data; the elements of the teaching aid evaluation matrix represent the teaching aid evaluation index of a certain teaching aid resource at a certain user learning stage; The educational knowledge mastery degree matrix and the educational knowledge association degree matrix are obtained by decomposing the teaching aid evaluation matrix through a non-negative matrix decomposition algorithm; the elements of the educational knowledge mastery degree matrix represent the user's mastery degree index of a certain educational knowledge at a certain learning stage; the elements of the educational knowledge association degree represent the correlation degree between a certain teaching aid resource and a certain educational knowledge.

[0066] The foregoing is merely a specific embodiment of the present invention, which enables those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for constructing a knowledge graph that combines teaching and supplementary learning, characterized in that: Includes steps: Constructing a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data, and learning stage data; the elements of the teaching aid evaluation matrix represent the teaching aid evaluation index of a certain teaching aid resource at a certain user learning stage; The teaching aid evaluation matrix is ​​decomposed into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm; the elements of the educational knowledge mastery degree matrix represent the mastery degree index of a certain educational knowledge by the user at a certain learning stage; the elements of the educational knowledge association degree represent the correlation degree between a certain teaching aid resource and a certain educational knowledge; A knowledge graph is constructed based on a teaching aid evaluation matrix, an educational knowledge mastery degree matrix and an educational knowledge association degree matrix; the nodes of the knowledge graph include educational knowledge nodes, learning stage nodes and teaching aid resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set by the educational knowledge mastery degree matrix; the edges between the teaching aid resource nodes and the educational knowledge nodes are set by the educational knowledge association degree matrix; the edges between the learning stage nodes and the teaching aid resource nodes are set by the teaching aid evaluation matrix.

2. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 1, characterized in that: The method of constructing a teaching aid evaluation matrix based on the user's learning behavior data, teaching aid resource data, and learning stage data includes the following steps: Collect learning behavior data, teaching resources data and learning stage data involved in the user's learning process; Clean the collected learning behavior data, teaching resource data, and learning stage data, and process missing values, noise data, and outliers; A teaching aid evaluation matrix is ​​constructed based on learning behavior data, teaching aid resource data and learning stage data; the rows of the teaching aid evaluation matrix represent the user learning stage, which is obtained through the learning stage data; the columns of the teaching aid evaluation matrix represent the teaching aid resource identifier, which is obtained through the teaching aid resource data.

3. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 1, characterized in that: The teaching aid evaluation index is calculated by weighted average of the user's concentration, participation, learning time and exercise score rate in the process of using the teaching aid resources.

4. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 1, characterized in that: The method of decomposing the teaching aid evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge association degree matrix by a non-negative matrix decomposition algorithm comprises the following steps: Randomly initialize the educational knowledge mastery degree matrix and the educational knowledge association degree matrix, and set the sizes of the educational knowledge mastery degree matrix and the educational knowledge association degree matrix; Set the maximum number of iterations and error threshold; Iteratively update the educational knowledge mastery degree matrix and the educational knowledge association degree matrix and calculate the matrix approximation error until the maximum number of iterations is reached or the matrix approximation error is less than the error threshold.

5. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 4 is characterized in that: The mastery index is expressed as: ； The degree of correlation is expressed as: ； in, Represents the educational knowledge mastery matrix, It represents the user's mastery of the kth educational knowledge in the i-th learning stage in the current iteration; represents the educational knowledge correlation matrix, Indicates the degree of relevance between the j-th teaching resource and the k-th educational knowledge in the current iteration; represents the teaching aid evaluation matrix; The matrix approximation error is expressed as: ； in, It represents the matrix approximation error of the iter-th iteration, and F represents the Frobenius norm.

6. The method for constructing a knowledge graph that combines teaching and supplementing according to claim 1, characterized in that: Also includes the steps: The knowledge graph is updated by a non-dominated sorting genetic algorithm.

7. The method for constructing a knowledge graph that combines teaching and supplementing according to claim 6 is characterized in that: The updating of the knowledge graph by a non-dominated sorting genetic algorithm comprises the steps of: The population is generated by random initialization, and each individual in the population represents an update plan for the knowledge graph; The fitness parameter group of each individual in the population is calculated through the fitness function group; the population is divided into several non-dominated levels according to the fitness parameter group, the non-dominated level of each individual is recorded and the crowding distance of each individual is calculated; Perform selection, crossover and mutation operations on individuals in the population according to the non-dominated rank and crowding distance of each individual; Merge the offspring individuals into the population, recalculate the non-dominated rank and crowding distance of each individual, and select a new population based on the non-dominated rank and crowding distance of each individual; Iterate until the stopping condition is met, and output the final Pareto frontier as a knowledge graph set; The sum of the fitness parameters of each individual in the knowledge graph set is calculated according to the preset weights, and the knowledge graph is updated according to the individual with the highest sum of fitness parameters.

8. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 7, characterized in that: The fitness function group includes an accuracy evaluation function, a connectivity evaluation function and a simplicity evaluation function; the fitness parameter group includes an accuracy evaluation parameter, a connectivity evaluation parameter and a simplicity evaluation parameter.

9. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 8, characterized in that: The accuracy evaluation function is expressed as: ； in, Represents an update scheme for an individual in a population, i.e. a knowledge graph, represents the value of the i-th row and j-th column of the actual teaching aid evaluation matrix, Represents an individual The value of the i-th row and j-th column of the teaching aid evaluation matrix; m and n are the number of rows and columns of the teaching aid evaluation matrix respectively; The connectivity evaluation function is expressed as: ； Where: N is the total number of nodes of individual G, x is the node number; is the number of nearest neighbors of node x; is the total number of edges between the nearest nodes of node x; The simplicity evaluation parameter is expressed as: ； in, is the total number of edges in individual G.

10. The method for constructing a knowledge graph that combines teaching and supplementing according to claim 9 is characterized in that: The sum of the fitness parameters is expressed as: ； in, , and They are the preset weights for the accuracy evaluation function, connectivity evaluation function, and simplicity evaluation function respectively.

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