A knowledge graph integrating teaching and learning and its construction method

Abstract

The object of the present invention is to provide a knowledge graph for teaching and learning assistance and its construction method, which relates to the technical field of educational data processing. The method includes the steps of: constructing a teaching and learning assistance evaluation matrix according to the learning behavior data, teaching and learning assistance resource data, and learning stage data of users; decomposing the teaching and learning assistance evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix through a non-negative matrix factorization algorithm; and constructing a knowledge graph according to the teaching and learning assistance evaluation matrix, the educational knowledge mastery degree matrix, and the educational knowledge correlation degree matrix. The construction method of the knowledge graph in this application integrates the relationships among educational knowledge nodes, learning stage nodes, and teaching and learning assistance resource nodes, and can, by analyzing the knowledge mastery and resource usage situations, as well as identifying the influence degrees of different teaching and learning assistance resources on educational knowledge points at different learning stages of users, help to efficiently screen teaching and learning assistance resources, help users discover weak links in the learning process, and optimize learning plans and learning methods.

Description

Technical Field

[0001] The present invention relates to the technical field of educational data processing, and particularly relates to a knowledge graph for coordinated teaching and learning aids and a construction method thereof. Background Art

[0002] A 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 a large knowledge system but also help users more intuitively understand the knowledge content through a visual form. The applications of knowledge graphs cover many fields, such as search engine optimization, recommendation systems, and intelligent question-and-answer 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. By linking educational resources with the entities and relationships in the knowledge graph, it realizes the systematic organization and management of knowledge. This connection can not only help students more intuitively understand the associations between knowledge points but also enable students to independently explore relevant content through the knowledge graph, thereby improving the efficiency and depth of learning. In addition, teachers can also use knowledge graphs to more clearly design the curriculum structure, evaluate students' learning effects, identify knowledge weaknesses, and thus adjust teaching strategies targeted. Generally speaking, knowledge graphs show great potential in the field of education and contribute to building a more scientific and efficient learning environment.

[0004] However, there are a wide variety of educational resources on the market currently, with scattered sources, and the associations between educational resources and knowledge points are complex. Building a comprehensive and accurate knowledge graph faces many challenges. Existing technologies and tools have deficiencies in establishing precise relationships between resources, knowledge points, and learning stages, and are difficult to handle large-scale data and complex relationships, resulting in students and teachers being unable to effectively integrate and utilize rich educational resources, thus restricting 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 for coordinated teaching and learning aids and a construction method thereof to efficiently screen learning aids resources, help users discover weak links in the learning process, optimize learning plans and means, and provide comprehensive learning support for users.

[0006] The purpose of the present invention is achieved by the following technical means:

[0007] In a first aspect, the present invention provides a construction method for a knowledge graph for coordinated teaching and learning aids, including the steps:

[0008] Construct a teaching assistant evaluation matrix based on the user's learning behavior data, teaching assistant resource data, and learning stage data; the elements of the teaching assistant evaluation matrix represent the teaching assistant evaluation indicators for a certain teaching assistant resource at a certain user learning stage;

[0009] Decompose the teaching assistant evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix through a non - negative matrix factorization algorithm; the elements of the educational knowledge mastery degree matrix represent the mastery degree indicators of users for a certain educational knowledge at a certain learning stage; the elements of the educational knowledge correlation degree represent the correlation degree between a certain teaching assistant resource and a certain educational knowledge;

[0010] Construct a knowledge graph based on the teaching assistant evaluation matrix, the educational knowledge mastery degree matrix, and the educational knowledge correlation degree matrix; the nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching assistant resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set through the educational knowledge mastery degree matrix; the edges between the teaching assistant resource nodes and the educational knowledge nodes are set through the educational knowledge correlation degree matrix; the edges between the learning stage nodes and the teaching assistant resource nodes are set through the teaching assistant evaluation matrix.

[0011] Preferably, the constructing of the teaching assistant evaluation matrix according to the user's learning behavior data, teaching assistant resource data, and learning stage data includes the steps of:

[0012] Collect the learning behavior data, teaching assistant resource data, and learning stage data involved in the user's learning process;

[0013] Clean the collected learning behavior data, teaching assistant resource data, and learning stage data, and process missing values, noise data, and outliers;

[0014] Construct a teaching assistant evaluation matrix according to the learning behavior data, teaching assistant resource data, and learning stage data; the rows of the teaching assistant evaluation matrix represent the user learning stage, which is obtained through the learning stage data; the columns of the teaching assistant evaluation matrix represent the teaching assistant resource identifiers, which are obtained through the teaching assistant resource data.

[0015] Preferably, the teaching assistant evaluation indicators are calculated by weighted average of the user's concentration, participation, learning duration, and exercise score rate during the use of the teaching assistant resource.

[0016] Preferably, the decomposing of the teaching assistant evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix through a non - negative matrix factorization algorithm includes the steps of:

[0017] Randomly initialize the educational knowledge mastery degree matrix and the educational knowledge correlation degree matrix, and set the sizes of the educational knowledge mastery degree matrix and the educational knowledge correlation degree matrix;

[0018] Set the maximum number of iterations and the error threshold;

[0019] Iteratively update the education knowledge mastery degree matrix and the education knowledge correlation 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.

[0020] Preferably, the mastery degree index is expressed as:

[0021] ;

[0022] The correlation degree is expressed as:

[0023] ;

[0024] Among them, represents the education knowledge mastery degree matrix, represents the mastery degree index of the user for the k-th education knowledge in the i-th learning stage in the current iteration; represents the education knowledge correlation degree matrix, represents the correlation degree between the j-th teaching assistant resource and the k-th education knowledge in the current iteration; represents the teaching assistant evaluation matrix;

[0025] The matrix approximation error is expressed as:

[0026] ;

[0027] Among them, represents the matrix approximation error of the iter-th iteration, and F represents the Frobenius norm.

[0028] Preferably, this method further includes the steps of:

[0029] Updating the knowledge graph through the non-dominated sorting genetic algorithm.

[0030] Preferably, the updating of the knowledge graph through the non-dominated sorting genetic algorithm includes the steps of:

[0031] Randomly initialize and generate a population, and each individual in the population represents an update scheme of the knowledge graph.

[0032] Calculate the fitness parameter group of each individual in the population through a fitness function group; divide the population into several non-dominated levels according to the fitness parameter group, record the non-dominated rank of each individual, and calculate the crowding distance of each individual;

[0033] Perform selection, crossover, and mutation operations on the individuals in the population according to the non-dominated rank and crowding distance of each individual;

[0034] 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;

[0035] Iterate until the stopping condition is met, and output the final Pareto front, denoted as the knowledge graph set;

[0036] Calculate the sum of the fitness parameters of each individual in the knowledge graph set according to the preset weights, and update the knowledge graph according to the individual with the highest sum of fitness parameters.

[0037] Preferably, 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.

[0038] Preferably, the accuracy evaluation function is expressed as:

[0039] ;

[0040] Wherein, represents an update scheme of an individual in a population, that is, a knowledge graph, represents the value of the i-th row and j-th column of the actual teaching assistant evaluation matrix, represents the individual the value of the i-th row and j-th column of the teaching assistant evaluation matrix; m and n are the number of rows and columns of the teaching assistant evaluation matrix, respectively;

[0041] The connectivity evaluation function is expressed as:

[0042] ;

[0043] Where: N is the total number of nodes of individual G, and x is the node number; is the number of nearest neighbor nodes of node x; is the total number of edges between the nearest neighbor nodes of node x;

[0044] The simplicity evaluation parameter is expressed as:

[0045] ;

[0046] Wherein, is the total number of edges in individual G.

[0047] Preferably, the sum of the fitness parameters is expressed as:

[0048] ;

[0049] Wherein, , and They are the preset weights of the accuracy evaluation function, the connectivity evaluation function, and the simplicity evaluation function, respectively.

[0050] In a second aspect, the present invention provides a knowledge graph for teaching and learning assistance. The knowledge graph for teaching and learning assistance is constructed by building an evaluation matrix, a matrix of the degree of mastery of educational knowledge, and a matrix of the degree of association of educational knowledge. The nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching and learning assistance resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set through the matrix of the degree of mastery of educational knowledge; the edges between the teaching and learning assistance resource nodes and the educational knowledge nodes are set through the matrix of the degree of association of educational knowledge; the edges between the learning stage nodes and the teaching and learning assistance resource nodes are set through the teaching and learning assistance evaluation matrix.

[0051] The teaching and learning assistance evaluation matrix is constructed based on the user's learning behavior data, teaching and learning assistance resource data, and learning stage data; the elements of the teaching and learning assistance evaluation matrix represent the teaching and learning assistance evaluation indicators for a certain teaching and learning assistance resource at a certain user learning stage.

[0052] The matrix of the degree of mastery of educational knowledge and the matrix of the degree of association of educational knowledge are obtained by decomposing the teaching and learning assistance evaluation matrix through the non-negative matrix factorization algorithm; the elements of the matrix of the degree of mastery of educational knowledge represent the degree of mastery indicators of the user for a certain educational knowledge at a certain learning stage; the elements of the degree of association of educational knowledge represent the degree of correlation between a certain teaching and learning assistance resource and a certain educational knowledge.

[0053] The beneficial effects of the present invention are as follows:

[0054] This application constructs a teaching and learning assistance evaluation matrix based on the user's learning behavior data, teaching and learning assistance resource data, and learning stage data to evaluate the teaching and learning assistance resources used by the user at different learning stages; decomposes the teaching and learning assistance evaluation matrix into a matrix of the degree of mastery of educational knowledge and a matrix of the degree of association of educational knowledge through the non-negative matrix factorization algorithm to achieve a detailed analysis of the user's degree of mastery of educational knowledge and the degree of association of teaching and learning assistance knowledge; constructs the nodes and edges of the knowledge graph through the teaching and learning assistance evaluation matrix, the matrix of the degree of mastery of educational knowledge, and the matrix of the degree of association of educational knowledge to achieve a graphical representation of the relationship between educational knowledge, learning stages, and teaching and learning assistance resources. The construction method of the knowledge graph in this application integrates the relationship between educational knowledge nodes, learning stage nodes, and teaching and learning assistance resource nodes, and can, by analyzing the knowledge mastery and resource usage situations, and distinguishing the influence degree of different teaching and learning assistance resources on educational knowledge points at different learning stages of the user, help to efficiently screen teaching and learning assistance resources, help the user discover weak links in the learning process, optimize the learning plan and means, and provide comprehensive learning support for the user.

[0055] The embodiments 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 among different objectives, making the update of the knowledge graph more comprehensive and reasonable; moreover, through fast non-dominated sorting, the non-dominated sorting genetic algorithm can efficiently screen and sort the population, improve the operation efficiency, and reduce the computational complexity compared with the traditional genetic algorithm.

[0056] The embodiments of the present application take accuracy, connectivity, and simplicity as the comprehensive evaluation objectives of the total fitness parameter to ensure the balance among different objectives. Since the knowledge graphs in the final Pareto front have different specific characteristics, this embodiment can select the knowledge graph 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

[0057] The accompanying drawings here are incorporated into the specification and form a part of the specification, showing the embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0059] Figure 1 It is a flowchart of the method for constructing a knowledge graph with supplementary teaching and learning advancing side by side according to an embodiment of the present invention;

[0060] Figure 2 It is a schematic flowchart of decomposing a supplementary teaching and learning evaluation matrix into a matrix of educational knowledge mastery degree and a matrix of educational knowledge association degree through a non-negative matrix factorization algorithm according to an embodiment of the present invention;

[0061] Figure 3 It is a schematic flowchart of the method for constructing a knowledge graph with supplementary teaching and learning advancing side by side according to another embodiment of the present invention;

[0062] Figure 4 It is a schematic flowchart of updating the knowledge graph through a non-dominated sorting genetic algorithm according to another embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0064] It should be noted that all the directional indications (such as up, down, left, right, front, back...) in the embodiments of the present invention are only used to explain the relative positional relationship and movement conditions between components in a specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indications will also change accordingly.

[0065] In addition, the descriptions involving "first", "second", etc. in the present invention are only for descriptive purposes, and cannot be understood as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In addition, the technical solutions between various embodiments can be combined with each other, but it must be based on the fact that those of ordinary skill in the art can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0066] The purpose of the present invention is to provide a knowledge graph for teaching and learning assistance and its construction method to efficiently screen teaching and learning assistance resources, help users discover weak links in the learning process, optimize learning plans and means, and provide comprehensive learning support for users.

[0067] Embodiment 1

[0068] Please refer to Figure 1 , a construction method of a knowledge graph for teaching and learning assistance, including the steps of:

[0069] S1. Construct a teaching and learning assistance evaluation matrix according to the user's learning behavior data, teaching and learning assistance resource data, and learning stage data; the rows of the teaching and learning assistance evaluation matrix represent the user's learning stages, the columns represent the teaching and learning assistance resource identifiers, and the elements of the teaching and learning assistance evaluation matrix represent the teaching and learning assistance evaluation indicators for a certain teaching and learning assistance resource at a certain user learning stage.

[0070] Further, the constructing of the teaching and learning assistance evaluation matrix according to the user's learning behavior data, teaching and learning assistance resource data, and learning stage data includes the steps of:

[0071] S11. Collect the learning behavior data, teaching and learning assistance resource data, and learning stage data involved in the user's learning process;

[0072] Among them, the learning behavior data are various behavior data generated by users during the learning process, such as the duration of watching videos, the correct rate of doing questions, the submission status of homework, etc.

[0073] The teaching assistant resource data is the digital representation of the content of teaching assistant materials. The sources of teaching assistant materials include textbook content, after-class exercises, reference books, learning videos, etc. In one embodiment, the teaching assistant resource data is stored through an independent teaching assistant resource ID. Specifically, for a certain chapter in a certain textbook content, its corresponding teaching assistant resource data can be represented in the form of "Resource ID: unique identifier; Resource type: textbook content, after-class exercises, reference book or learning video; Resource name: specific teaching assistant material name; Teaching assistant material identifier: unique identifier for different types of teaching assistant materials; Chapter identifier: identifier for the specific chapter corresponding to the teaching assistant material; Resource content: specific content or link of the teaching assistant material". For example, a teaching assistant resource data is identified as {"Resource ID": "001", "Resource type": "textbook content", "Resource name": "Compulsory Mathematics 1 for High School", "Teaching assistant material identifier": "Textbook - High School Mathematics - Compulsory 1", "Chapter identifier": "Chapter 1 - Sets and Functions", "Resource content": "Concept of sets, operations of sets..."}.

[0074] The learning stage data is used to reflect the current learning stage of the user. The learning stage data can be obtained through user registration information, learning progress, etc.

[0075] S12. Clean the collected learning behavior data, teaching assistant resource data, and learning stage data, and process missing values, noise data, and outliers to ensure the reliability and accuracy of the data.

[0076] S13. Construct a teaching assistant evaluation matrix based on the learning behavior data, teaching assistant resource data, and learning stage data;

[0077] Among them, the rows of the teaching assistant evaluation matrix represent the user's learning stage, which is obtained through the learning stage data; the columns of the teaching assistant evaluation matrix represent the teaching assistant resource identifiers, which are obtained through the teaching assistant resource data; the matrix elements in the teaching assistant evaluation matrix represent the teaching assistant evaluation indicators of a certain user learning stage for a certain teaching assistant resource, which are obtained through comprehensive analysis of the learning behavior data.

[0078] In one embodiment, the teaching assistant evaluation indicators are obtained by weighted average calculation of the user's concentration, participation, learning duration, and exercise score rate during the use of the teaching assistant resource. Among them,

[0079] The methods for obtaining the concentration include:

[0080] Sensor data, using mouse and keyboard activities monitoring or wearable devices (such as smart bracelets) to obtain users' behavioral and physiological data and infer their concentration level; log analysis, analyzing users' operation records on the platform and paying attention to behaviors such as frequent page switching or staying on a specific page for a long time.

[0081] The ways to obtain the engagement include: server logs, analyzing the active time, access times, types and frequencies of activities participated by users on the platform; NLP technology, evaluating the engagement by analyzing the interaction frequency or speech content of users in the discussion area.

[0082] The ways to obtain the learning duration include: client logs, recording the login time and logout time of users on the platform to calculate the learning duration; server logs, analyzing the learning session duration of users and calculating the learning duration through timestamp records; sensor data, using mouse and keyboard activity records to identify the actual learning duration.

[0083] The ways to obtain the exercise score rate include: platform data, directly obtaining the performance data of users in various exercises and tests on each online learning platform; real-time scoring, using a camera or mobile phone camera to take pictures of the exercises completed by the user currently, identifying the exercises and the user's answers through computer vision technologies such as OCR (Optical Character Recognition) technology, and comparing the identified answers with the standard answers to calculate the exercise score rate of the user in real time.

[0084] S2. Decompose the teaching assistant evaluation matrix into an educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix through the non-negative matrix factorization 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 mastery degree indicators of the user for a certain educational knowledge at a certain learning stage; the rows of the educational knowledge correlation degree represent the educational knowledge identifiers, the columns represent the teaching assistant resource identifiers, and the elements of the educational knowledge correlation degree represent the correlation degree between a certain teaching assistant resource and a certain educational knowledge.

[0085] Among them, the non-negative matrix factorization algorithm (Non-negative Matrix Factorization, NMF) is a matrix factorization technology 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 constructing the knowledge graph of teaching assistant advancement in this application is to provide different teaching assistant resources for students at different learning stages to improve learning efficiency and effect. In order to achieve personalized recommendation, it is necessary to understand the students' mastery of various educational knowledge and the correlation between teaching assistant resources and educational knowledge, and this purpose is achieved through the non-negative matrix factorization algorithm.

[0086] It should be noted that educational knowledge represents the educational knowledge points involved in the user's learning process. To distinguish the "knowledge points" in the conventional technical terms of the educational data technology field and the knowledge graph technology field, the educational knowledge points involved in the user's learning process are denoted as "educational knowledge" in this article.

[0087] Further, please refer to Figure 2 , the method of decomposing the teaching assistant evaluation matrix into the educational knowledge mastery degree matrix and the educational knowledge correlation degree matrix by the non-negative matrix factorization algorithm includes the steps:

[0088] S21. Randomly initialize the educational knowledge mastery degree matrix and the educational knowledge correlation degree matrix, and set the sizes of the educational knowledge mastery degree matrix and the educational knowledge correlation degree matrix to m×k and k×n respectively; the size of the teaching assistant evaluation matrix is denoted as m×n. Wherein, m, n, and k are all positive integers.

[0089] S22. Set the maximum number of iterations and the error threshold;

[0090] S23. Iteratively update the educational knowledge mastery degree matrix and the educational knowledge correlation 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;

[0091] During the iteration process, the mastery degree index is expressed as:

[0092] ;

[0093] The correlation degree is expressed as:

[0094] ;

[0095] Among them, represents the educational knowledge mastery degree matrix, represents the mastery degree index of the user for the k-th educational knowledge in the i-th learning stage in the current iteration; represents the educational knowledge correlation degree matrix, represents the correlation degree between the j-th teaching assistant resource and the k-th educational knowledge in the current iteration; represents the teaching assistant evaluation matrix; represents the (i,k)-th item of the product of the teaching assistant evaluation matrix and the transpose of the educational knowledge correlation degree matrix, represents the (i,k)-th item of the result of multiplying the educational knowledge mastery degree matrix, the educational knowledge correlation degree matrix, and the transpose of the educational knowledge correlation degree matrix, represents the (k,j)-th item of the result of multiplying the transpose of the educational knowledge mastery degree matrix and the teaching assistant evaluation matrix, Denote the (k,j)-th term of the result of multiplying the transpose of the matrix representing the educational knowledge mastery degree by the matrix representing the correlation degree of educational knowledge;

[0096] The specific expression of the matrix approximation error is as follows:

[0097] ;

[0098] where denotes the matrix approximation error of the iter-th iteration, and F denotes the Frobenius norm.

[0099] In this embodiment, by decomposing the high-dimensional teaching assistant evaluation matrix into a low-dimensional educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix, the potential educational knowledge mastery degree and educational knowledge correlation degree can be extracted, providing a data basis for intuitively showing the relationship between educational knowledge, the user's learning stage, and teaching assistant resources in the subsequently constructed knowledge graph.

[0100] S3. Construct a knowledge graph according to the teaching assistant evaluation matrix, the educational knowledge mastery degree matrix, and the educational knowledge correlation degree matrix; the nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching assistant resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set through the educational knowledge mastery degree matrix; the edges between the teaching assistant resource nodes and the educational knowledge nodes are set through the educational knowledge correlation degree matrix; the edges between the learning stage nodes and the teaching assistant resource nodes are set through the teaching assistant evaluation matrix.

[0101] This application realizes the evaluation of teaching assistant resources used by users at different learning stages by constructing a teaching assistant evaluation matrix based on the user's learning behavior data, teaching assistant resource data, and learning stage data; through the non-negative matrix factorization algorithm, the teaching assistant evaluation matrix is decomposed into an educational knowledge mastery degree matrix and an educational knowledge correlation degree matrix to realize a detailed analysis of the user's educational knowledge mastery degree and teaching assistant knowledge correlation degree; by constructing the nodes and edges of the knowledge graph through the teaching assistant evaluation matrix, the educational knowledge mastery degree matrix, and the educational knowledge correlation degree matrix, a graphical representation of the relationship between educational knowledge, learning stage, and teaching assistant resources is realized. The construction method of the knowledge graph in this application integrates the relationship between educational knowledge nodes, learning stage nodes, and teaching assistant resource nodes, and can, by analyzing the knowledge mastery and resource usage situations, as well as identifying the influence degree of different teaching assistant resources on educational knowledge points at different learning stages of users, help to efficiently screen teaching assistant resources, help users discover weak links in the learning process, optimize learning plans and means, and provide comprehensive learning support for users.

[0102] To more intuitively illustrate how to construct a knowledge graph according to this embodiment, here an example related to high school mathematics with a relatively small amount of data is used for explanation.

[0103] The key knowledge points, teaching auxiliary resources, and learning stages in this example are as follows:

[0104] Key knowledge points: Definition and properties of functions (K1), Trigonometric functions (K2), Derivatives (K3), Permutations and combinations (K4)

[0105] Teaching auxiliary resources: Lecture notes (T1), Exercise sets (T2), Video explanations (T3), Test papers (T4)

[0106] Learning stages: First semester (S1), Second semester (S2)

[0107] In step S1, a teaching auxiliary evaluation matrix is constructed. Assume that the teaching auxiliary evaluation indicators of students using various teaching auxiliary resources (T1, T2, T3, T4) in different learning stages (S1, S2) are obtained from the user learning behavior data.

[0108] The teaching auxiliary evaluation matrix constructed according to the teaching auxiliary evaluation indicators is as follows:

[0109] | T1 | T2 | T3 | T4 |

[0110] --| --| --| --| --|

[0111] S1 | 0.8| 0.7| 0.6| 0.5|;

[0112] S2 | 0.7| 0.9| 0 | 0.6|

[0113] In step S2, the teaching auxiliary evaluation matrix is decomposed by the non - negative matrix factorization algorithm. After decomposition, we get:

[0114] Educational knowledge mastery degree matrix:

[0115] | K1 | K2 | K3 | K4 |

[0116] -- | --|-- |-- |-- |

[0117] S1 | 0.9| 0.6| 0.2| 0.4|;

[0118] S2 | 0.8| 0.7| 0.5| 0.6|

[0119] Educational knowledge correlation degree matrix:

[0120] | T1 | T2 | T3 | T4 |

[0121] -- |-- |-- |-- |-- |

[0122] K1 | 0.8| 0.7| 0.6| 0.5|

[0123] K2 | 0.6| 0.8| 0.7| 0.4|;

[0124] K3 | 0 | 0.7| 0.9| 0.6|

[0125] K4 | 0.4| 0.6| 0.5| 0.7|

[0126] In step S3, a knowledge graph is constructed based on the teaching assistant evaluation matrix, the educational knowledge mastery degree matrix, and the educational knowledge correlation degree matrix, including:

[0127] 1. Create nodes:

[0128] Create learning stage nodes: S1, S2;

[0129] Create educational knowledge nodes: K1, K2, K3, K4;

[0130] Create teaching assistant resource nodes: T1, T2, T3, T4;

[0131] 2. Create edges:

[0132] Edges between learning stage nodes and educational knowledge nodes:

[0133] S1-K1 (weight 0.9), S1-K2 (weight 0.6), S1-K3 (weight 0.2), S1-K4 (weight 0.4)

[0134] S2-K1 (weight 0.8), S2-K2 (weight 0.7), S2-K3 (weight 0.5), S2-K4 (weight 0.6)

[0135] Edges between educational knowledge nodes and teaching assistant resource nodes:

[0136] K1-T1 (weight 0.8), K1-T2 (weight 0.7), K1-T3 (weight 0.6), K1-T4 (weight 0.5)

[0137] K2-T1 (weight 0.6), K2-T2 (weight 0.8), K2-T3 (weight 0.7), K2-T4 (weight 0.4)

[0138] K3-T1 (weight 0.5), K3-T2 (weight 0.7), K3-T3 (weight 0.9), K3-T4 (weight 0.6)

[0139] K4-T1 (weight 0.4), K4-T2 (weight 0.6), K4-T3 (weight 0.5), K4-T4 (weight 0.7)

[0140] Edges between learning stage nodes and teaching assistant resource nodes:

[0141] S1-T1 (weight 0.8), S1-T2 (weight 0.7), S1-T3 (weight 0.6), S1-T4 (weight 0.5)

[0142] S2-T1 (weight 0.7), S2-T2 (weight 0.9), S2-T3 (weight 0.8), S2-T4 (weight 0.6)

[0143] By merging the above nodes and edges, a knowledge graph representation of the learning process of users using teaching assistant resources T1, T2, T3, and T4 in learning stages S1 and S2 can be constructed.

[0144] As a preferred embodiment, please refer to Figure 3 , the method for constructing the knowledge graph of this application with coordinated teaching assistance further includes the steps:

[0145] S4. Update the knowledge graph through the non-dominated sorting genetic algorithm.

[0146] The non-dominated sorting genetic algorithm (NSGA-II) is an efficient multi-objective optimization evolutionary algorithm. It deals with the trade-off relationships between multiple objectives through non-dominated sorting and crowding distance comparison, and adopts an elitist strategy to improve the algorithm performance. The non-dominated sorting genetic algorithm stratifies the individuals in the population according to their domination relationships based on the concept of Pareto optimality. This process helps the algorithm identify which solutions are optimal (i.e., solutions that are not dominated by any other solutions), and can maintain the population diversity. In each generation, NSGA-II merges the current population and the offspring population, and then performs fast non-dominated sorting, thus effectively reducing the computational complexity.

[0147] In the embodiment of this application, the non-dominated sorting genetic algorithm can optimize multiple objectives simultaneously, 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 operation efficiency, and can improve the operation efficiency and reduce the computational complexity compared with the traditional genetic algorithm.

[0148] Further, please refer to Figure 4 , the step of updating the knowledge graph through the non-dominated sorting genetic algorithm includes the steps:

[0149] S41. Randomly initialize and generate a population, where each individual in the population represents an update scheme for a knowledge graph.

[0150] S42. Calculate the fitness parameter group of each individual in the population through a fitness function group; divide the population into several non-dominated levels according to the fitness parameter group, record the non-dominated rank of each individual, and calculate the crowding distance of each individual; individuals in each non-dominated level are non-dominated with each other, and individuals in lower levels are superior to those in higher levels among different non-dominated levels.

[0151] S43. Perform selection, crossover, and mutation operations on the individuals in the population according to the non-dominated rank and crowding distance of each individual.

[0152] Step S43 specifically includes:

[0153] Perform tournament selection on the individuals in the population according to the non-dominated rank and crowding distance of each individual to obtain a set of winning individuals.

[0154] Perform crossover operations on the individuals in the set of winning individuals to generate offspring individuals; the crossover operations can use single-point crossover, uniform crossover, etc.

[0155] Perform mutation operations on the offspring individuals.

[0156] S44. Incorporate the offspring individuals into the population, recalculate the non-dominated rank and crowding distance of each individual, and screen to obtain a new population according to the non-dominated rank and crowding distance of each individual.

[0157] S45. Iterate until the stop condition is met, and output the final Pareto front as the knowledge graph set; the knowledge graph set includes several individuals.

[0158] Among them, the iteration in this step refers to repeatedly executing steps S42 to S44; the stop conditions include reaching the maximum number of iterations and the population fitness not improving significantly in several generations.

[0159] S46. Calculate the total fitness parameter of each individual in the knowledge graph set according to the preset weight, and update the knowledge graph according to the individual with the highest total fitness parameter.

[0160] 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.

[0161] The accuracy evaluation function is expressed as:

[0162] ;

[0163] Among them, represents an individual in a population, i.e., an update scheme of a knowledge graph, represents the value of the i-th row and j-th column of the actual teaching assistant evaluation matrix, represents an individual the value of the i-th row and j-th column of the teaching assistant evaluation matrix of. Wherein, the actual teaching assistant evaluation matrix is the teaching assistant evaluation matrix obtained in step S1; m and n are the number of rows and columns of the teaching assistant evaluation matrix respectively, represents the total number of elements of the teaching assistant evaluation matrix. It should be noted that the negative sign in this formula is used to convert the minimization of error into a problem of maximizing fitness.

[0164] The connectivity evaluation function is expressed as:

[0165] ;

[0166] Where: N is the total number of nodes of individual G, and 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.

[0167] The simplicity evaluation parameter is expressed as:

[0168] ;

[0169] Where is the total number of edges in individual G.

[0170] Each final knowledge graph performs evenly on different objectives and can be selected according to specific requirements in practical applications.

[0171] Based on the foregoing embodiments, the sum of the fitness parameters is expressed as:

[0172] ;

[0173] Where , and are the preset weights of the accuracy evaluation function, the connectivity evaluation function, and the simplicity evaluation function respectively.

[0174] This embodiment takes accuracy, connectivity, and simplicity as the comprehensive evaluation objectives of the sum of fitness parameters to ensure the balance between different objectives. 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 some other graphs may be better in simplicity and connectivity and are suitable for application scenarios with resource constraints or high-efficiency query requirements; this embodiment can select a knowledge graph suitable for a specific application scenario by adjusting the preset weights, which helps to enhance the applicability of the knowledge graph.

[0175] Based on the foregoing method for constructing a knowledge graph with complementary teaching and learning aids, the present invention also provides a knowledge graph with complementary teaching and learning aids. The knowledge graph with complementary teaching and learning aids is constructed by building an evaluation matrix, a matrix of the degree of mastery of educational knowledge, and a matrix of the degree of association of educational knowledge. The nodes of the knowledge graph include educational knowledge nodes, learning stage nodes, and teaching and learning aid resource nodes; the edges between the educational knowledge nodes and the learning stage nodes are set through the matrix of the degree of mastery of educational knowledge; the edges between the teaching and learning aid resource nodes and the educational knowledge nodes are set through the matrix of the degree of association of educational knowledge; the edges between the learning stage nodes and the teaching and learning aid resource nodes are set through the teaching and learning aid evaluation matrix.

[0176] The teaching and learning aid evaluation matrix is constructed based on the user's learning behavior data, teaching and learning aid resource data, and learning stage data; the elements of the teaching and learning aid evaluation matrix represent the teaching and learning aid evaluation indicators for a certain teaching and learning aid resource at a certain user learning stage;

[0177] The matrix of the degree of mastery of educational knowledge and the matrix of the degree of association of educational knowledge are obtained by decomposing the teaching and learning aid evaluation matrix through the non - negative matrix factorization algorithm; the elements of the matrix of the degree of mastery of educational knowledge represent the degree of mastery indicators of a certain educational knowledge by the user at a certain learning stage; the elements of the degree of association of educational knowledge represent the degree of correlation between a certain teaching and learning aid resource and a certain educational knowledge.

[0178] The above - mentioned are only the specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can 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 these embodiments shown herein, but will conform 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 according to 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; 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; Constructing a teaching aid evaluation matrix according to the learning behavior data, the teaching aid resource data and the 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; 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.

2. 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.

3. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 1, 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.

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

5. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 4 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.

6. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 5, 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.

7. The method for constructing a knowledge graph that combines teaching and supplementing according to claim 6 is 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.

8. The method for constructing a knowledge graph that combines teaching and supplementary learning according to claim 7, 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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