Multi-dimensional feature fused graph convolutional network knowledge tracking model

Abstract

The invention relates to the technical field of knowledge tracking, in particular to a multi-dimensional feature fused graph convolutional network knowledge tracking model, which comprises a feature embedding module, an embedding propagation module, a state updating module and a prediction optimization module, the feature embedding module optimizes side information among various nodes through a full-connection network by using answer records of students, performs low-dimensional embedding on node features by using the side information, and finally constructs a comprehensive knowledge tracking network through correlation and similarity relationships among all the nodes; and the embedding propagation module is used for extracting neighbor information on two paths of'problem-knowledge-problem 'and'problem-student-problem' by utilizing a GCN (Generic Core Network), and generating high-order embedding of the problem. The problems that the model ignores student nodes in a graph structure, effective fusion of node features and edge features is not fully considered, and the prediction precision is reduced due to data sparsity are solved.

Description

Technical Field

[0001] The present invention relates to the field of knowledge tracking technology, and specifically to a graph convolutional network knowledge tracking model that integrates multi-dimensional features. Background Art

[0002] In recent years, the trend of digitalization in education is steadily promoting profound changes in the modern education system, and has achieved efficient and accurate analysis and personalization of teaching data. In this process, knowledge tracking technology, with its unique advantages and importance, has gradually become the core strategy for achieving personalized education goals, and has established its mainstream position in the field of education. As an educational technology, knowledge tracking combines educational psychology, learning theory and data analysis methods. By analyzing the interaction data between students and learning materials, it dynamically evaluates and predicts students' mastery of each knowledge point, so as to achieve personalized teaching and learning path recommendations, thereby improving learning efficiency and teaching effectiveness. At present, the mainstream algorithms in the field of knowledge tracking can be roughly divided into two camps: traditional methods and deep learning.

[0003] However, the existing network knowledge tracking model still has shortcomings. Specifically, it does not fully utilize the characteristics of student nodes, ignores the correlation characteristics between students and problems and knowledge, and the data is sparse, which directly leads to the model's inability to accurately grasp the students' personalized knowledge status.

[0004] Therefore, a graph convolutional network knowledge tracking model that integrates multi-dimensional features is needed to solve the problems raised in the above background technology. Summary of the invention

[0005] The purpose of the present invention is to provide a graph convolutional network knowledge tracking model that integrates multi-dimensional features to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A graph convolutional network knowledge tracking model that integrates multi-dimensional features includes a feature embedding module, an embedding propagation module, a state updating module, and a prediction optimization module. The feature embedding module uses student answer records and optimizes the side information between various nodes through a fully connected network, and then uses the side information to perform low-dimensional embedding of node features. Finally, a comprehensive knowledge tracking network is constructed through the correlation and similarity relationships between all nodes. The embedding propagation module uses GCN to extract neighbor information on the two paths of "question-knowledge-question" and "question-student-question", generates a high-order embedding of the question, and embeds it with the student's answer result to obtain the exercise embedding. The state updating module is used to update the state of the problem. The new module uses LSTM to train exercise embeddings and update students' knowledge status to predict students' answers in the future. The prediction optimization module selects historical questions with similar knowledge points to help with predictions, and improves the prediction accuracy and performance of the model through back-propagation training to achieve the goal of optimizing the model. After the model is built, the AUC value is first used to evaluate the model's prediction performance, and then five classic pioneering models in the field of knowledge tracking are selected for comparison to evaluate the overall performance of the model. Finally, in order to verify the advantages of the MFGKT model, ablation experiments are performed on pre-training, student neighbor associations, etc. to verify the effectiveness of the MFGKT design.

[0008] As a preferred solution of the present invention, the specific analysis steps of the feature embedding module are: representing knowledge and problems as a bipartite graph G = (U, Q, S, R), dividing the relationship between students, problems and knowledge into correlation and similarity, where the relationship between nodes of different types is correlation, and the relationship between nodes of the same type is similarity, using the fully connected network FCN to capture and effectively fuse global features, extracting and optimizing node relationships through pre-training, that is, edge features, including correlation and similarity between nodes, and then obtaining rich potential node relationships of students, problems and knowledge, using them as weights, encoding and embedding node features, using the Random function, generating a fixed-dimensional, dense random value vector to represent each node feature, and obtaining the initial value matrix U of student, problem and knowledge node features. init , Q init , S init , the calculation formula is: Where Dim represents the fixed dimension of the embedding space, Nim u 、Nim q 、Nim s are the number of students, questions, and knowledge respectively. The node feature initial value matrix first passes through the fully connected network, and then uses the Sigmoid function to estimate the local proximity between different nodes in the embedding space, converts their relationship values ​​into probability values, and uses matrix dot multiplication to estimate the problem-knowledge correlation embedding vector in the embedding space. Student-question correlation embedding vector Question Similarity Embedding Vector Student similarity embedding vector Knowledge Similarity Embedding Vector The correlation and similarity between them are then optimized and trained by minimizing the loss entropy to obtain the edge information, that is, the node relationship matrix, including the correlation matrix and the similarity matrix between nodes. The node relationship in the embedding space is optimized to be as close as possible to the correlation and similarity in the real graph structure. The obtained node relationship matrix is ​​used as the weight, and the student node feature u, the problem node feature q, and the knowledge node feature s are encoded as embeddings to obtain the student node embedding Eu, the problem node embedding Eq, and the knowledge node embedding Es as the initial embeddings of various types of nodes. The answers are obtained from the data set and encoded to obtain the answer embedding En, whose two rows represent the wrong and correct answers respectively.

[0009] As a preferred solution of the present invention, the specific analysis steps of the embedding propagation module are: using knowledge or students to update problem information, setting the path for updating the problem to 3 hops, the first hop neighbors of the problem are multiple knowledge or students corresponding to the problem, the second hop neighbors are other problems corresponding to each of these knowledge or students, and the third hop neighbors are other knowledge or students corresponding to each of these problems. A fixed number of student neighbors Nu, problem neighbors Nq, and knowledge neighbors Ns are sampled for each batch. In the graph convolution layer of the graph convolutional neural network, the embeddings of the neighbor nodes are averaged and added to the node's own embedding to update the node's representation. After the embedding propagation of GCN, the problem embedding based on the knowledge neighbor and the problem embedding based on the student neighbor are spliced ​​to obtain the final problem embedding.

[0010] As a preferred solution of the present invention, the specific analysis steps of the state update module are: putting the exercise embedding into LSTM, learning the complex relationship between different knowledge and the change pattern of the students' mastery of these knowledge from the input exercise representation through the input gate, forget gate and output gate, and obtaining the student's knowledge mastery state embedding Em,

[0011] As a preferred solution of the present invention, the specific analysis steps of the prediction optimization module are: constructing a prediction probability expression Where P t represents the predicted probability of correctly answering a new question at time t, f i and f j and represents the forget gate, ⊙ represents the inner product, h t represents the hidden state, I eIndicates the selection of the k most relevant exercises between the target problem and the historical state, Softmax is a normalization function. The Adam optimization method is selected to minimize the cross entropy loss function. to update the parameters in the model.

[0012] As a preferred solution of the present invention, the vertices of the bipartite graph G = (U, Q, S, R) are the student set U, the problem set Q, the knowledge set S and the edge information R between each node, R is a binary adjacency matrix, and its expression is R = [qs, uq, qq, uu, ss] ∈ {0, 1}, qs, uq, qq, uu, ss respectively represent the problem-knowledge correlation, student-problem correlation, problem-problem similarity, student-student similarity, knowledge-knowledge similarity. The student node feature initial value matrix U init The calculation formula is U init =Random(Dim,Num u ), the problem node feature initial value matrix Q init The calculation formula is Q init =Random(Dim,Num q ), knowledge node feature initial value matrix S init The calculation formula is S init =Random(Dim,Num s ), where Dim represents the fixed dimension of the embedding space, and Num u 、Num q 、Num s are the number of students, questions, and knowledge, respectively.

[0013] As a preferred solution of the present invention, the problem-knowledge correlation embedding vector The calculation formula is Student-question correlation embedding vector The calculation formula is Question Similarity Embedding Vector The calculation formula for is Student similarity embedding vector The calculation formula is Knowledge Similarity Embedding Vector The calculation formula is Where σ is the Sigmoid activation function, f represents the fully connected network f=max(0,w1x+b1), that is, each node x is first linearly transformed and then activated, and forward propagation and back propagation are used for pre-training updates.

[0014] As a preferred solution of the present invention, the calculation formula for averaging the embeddings of neighboring nodes and adding them to the node's own embedding to update the representation of the node is: in are the feature embeddings of student nodes, question nodes and knowledge node i at the l+1 layer, Nu i 、Nq i 、Ns i Represents all neighbors of student nodes, question nodes, and knowledge node i, including the node itself. In the lth graph convolution layer, w l is the weight of the lth layer, b l is the bias of the lth layer, and σ is a nonlinear transformation.

[0015] As a preferred solution of the present invention, the AUC value represents the area under the ROC curve. The AUC value is mainly used to measure the classification efficiency of the model. Its value is usually between 0.5 and 1. The closer the value is to 1, the higher the accuracy of the model is, indicating that the model has a more significant predictive value. The calculation formula is: Among them, m i Represents the positive sample prediction score, n j represents the negative sample prediction score, M represents the number of positive samples, and N represents the number of negative samples.

[0016] As the preferred scheme of the present invention, the specific conditions of the four classic pioneering models are as follows: BKT: Bayesian network is used to infer students' knowledge mastery, and students' knowledge status is represented by binary variables; DKT: Deep learning is used for the first time in the field of knowledge tracking, and LSTM is used to model students' knowledge status, which has better prediction performance than traditional methods; DKVMN: Memory network is used to dynamically track changes in students' knowledge status, which has good interpretability; GKT: For the first time, the complex relationship between knowledge points is represented by graph structure, and the dynamic and correlation of knowledge tracking is realized by aggregating adjacent nodes; GIKT: GCN and RNN are used to model students' knowledge status, and various factors such as student status and historical exercises are comprehensively considered. The four models of the ablation experiment are: MFGKT-pu means no pre-training and no student neighbors are added; MFGKT-p means pre-training and no student neighbors are added; MFGKT-u means no pre-training and student neighbors are added; MFGKT means pre-training and student neighbors are added.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] 1. In the present invention, by adopting a bipartite graph model, students, problems and knowledge are taken as nodes, and it is considered that there are two association paths between problems, namely "problem-knowledge-problem" and "problem-student-problem", and a graph convolutional network is used to extract deep features in high-order relationships. The representation of problem nodes is aggregated and updated in combination with the dual association information of students and knowledge to form a new problem embedding, thereby enhancing the learning of node features. A fully connected network is then used for pre-training, combined with local proximity and cross entropy loss, to further optimize edge features, namely the correlation and similarity between nodes, and use them as weights for node embedding transformation, thereby promoting the learning of node features based on the knowledge obtained from edge features, so that nodes can obtain more accurate and comprehensive Information, enhance the representation of edge features, and finally build a comprehensive knowledge tracking network through the correlation and similarity relationships between all nodes. Then use all useful side information to learn the low-dimensional embedding of each question, maximize the extraction and utilization of rich potential information in students, questions and knowledge, and use low-dimensional embedding to alleviate the data sparsity problem. By extracting deep node features and combining dual correlation information, the problem node representation is updated to form a new problem embedding, which improves the accuracy and comprehensiveness of node feature learning. Pre-training is used to optimize side information, including its correlation and similarity, and use this as weight to perform low-dimensional encoding and embedding of node features. This process not only helps node learning based on edge features, but also alleviates the data sparsity problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a schematic diagram of the MFGKT knowledge tracking model framework of the present invention;

[0020] Figure 2 This is a diagram that defines the main symbols of the present invention;

[0021] Figure 3 The student-problem-knowledge relationship diagram of the present invention;

[0022] Figure 4 This is a block diagram of the fully connected network pre-training of the present invention;

[0023] Figure 5 Embedding propagation diagram for the present invention;

[0024] Figure 6 It is a statistical graph of the data set of the present invention;

[0025] Figure 7 This is a graph showing the experimental results of the AUC value predicted by the model of the present invention;

[0026] Figure 8 This is a diagram of the ablation experiment results of the present invention. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0028] To facilitate understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Several embodiments of the present invention are given. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0029] It should be noted that when an element is referred to as being "fixed on" another element, it may be directly on the other element or there may also be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may also be a central element. The terms "vertical", "horizontal", "left", "right" and similar expressions used in this article are for illustrative purposes only.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by technicians in the technical field to which the present invention belongs. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0031] For examples, see Figure 1-8 , the present invention provides a technical solution:

[0032] A graph convolutional network knowledge tracking model that integrates multi-dimensional features includes a feature embedding module, an embedding propagation module, a state updating module, and a prediction optimization module. The features are as follows: the feature embedding module uses student answer records and optimizes the edge information between various nodes through a fully connected network, and then uses the edge information to perform low-dimensional embedding of node features. Finally, a comprehensive knowledge tracking network is constructed through the correlation and similarity relationships between all nodes. The embedding propagation module uses GCN to extract neighbor information on the two paths of "question-knowledge-question" and "question-student-question", generates a high-order embedding of the question, and embeds it with the student's answer result to obtain the exercise embedding, state updating module, and prediction optimization module. The state update module uses LSTM to train exercise embeddings and update the students' knowledge status to predict students' future answers. The prediction optimization module selects historical questions with similar knowledge points to help with predictions, and improves the prediction accuracy and performance of the model through back-propagation training to achieve the goal of optimizing the model. After the model is built, the AUC value is first used to evaluate the model's prediction performance, and then five classic pioneering models in the field of knowledge tracking are selected for comparison to evaluate the overall performance of the model. Finally, in order to verify the advantages of the MFGKT model, ablation experiments are conducted on pre-training, student neighbor associations and other contents to verify the effectiveness of the MFGKT design.

[0033] Furthermore, the specific analysis steps of the feature embedding module are as follows: students, questions and knowledge are represented as a bipartite graph G = (U, Q, S, R), the relationship between students, questions and knowledge is divided into correlation and similarity, where the relationship between nodes of different types is correlation, and the relationship between nodes of the same type is similarity, the fully connected network FCN is used to capture and effectively fuse global features, and the node relationship, that is, the edge feature, is extracted and optimized through pre-training, including the correlation and similarity between nodes, and then the rich potential node relationships of students, questions and knowledge are obtained and used as weights to encode and embed the node features, and the Random function is used to generate a fixed-dimensional, dense random value vector to represent each node feature, and the initial value matrix U of the student, question and knowledge node features is obtained. init , Q init , S init , the calculation formula is: Where Dim represents the fixed dimension of the embedding space, Nim u 、Nim q 、Nim s are the number of students, questions, and knowledge respectively. The node feature initial value matrix first passes through the fully connected network, and then uses the Sigmoid function to estimate the local proximity between different nodes in the embedding space, converts their relationship values ​​into probability values, and uses matrix dot multiplication to estimate the problem-knowledge correlation embedding vector in the embedding space. Student-question correlation embedding vector Question Similarity Embedding Vector Student similarity embedding vector Knowledge Similarity Embedding Vector The correlation and similarity between them are then optimized and trained by minimizing the loss entropy to obtain the edge information, that is, the node relationship matrix, including the correlation matrix and the similarity matrix between nodes. The node relationship in the embedding space is optimized to be as close as possible to the correlation and similarity in the real graph structure. The obtained node relationship matrix is ​​used as the weight, and the student node feature u, the problem node feature q, and the knowledge node feature s are encoded as embeddings to obtain the student node embedding Eu, the problem node embedding Eq, and the knowledge node embedding Es as the initial embeddings of various types of nodes. The answers are obtained from the data set and encoded to obtain the answer embedding En, whose two rows represent the wrong and correct answers respectively.

[0034] Furthermore, the specific analysis steps of the embedding propagation module are: using knowledge or students to update problem information, setting the path for updating the problem to 3 hops, the first hop neighbors of the problem are multiple knowledge or students corresponding to the problem, the second hop neighbors are other problems corresponding to each of these knowledge or students, and the third hop neighbors are other knowledge or students corresponding to each of these problems. A fixed number of student neighbors, problem neighbors, and knowledge neighbors are sampled for each batch. In the graph convolution layer of the graph convolutional neural network, the embeddings of the neighbor nodes are averaged and added to the node's own embedding to update the node's representation. After the embedding propagation of GCN, the problem embedding based on knowledge neighbors and the problem embedding based on student neighbors are spliced ​​to obtain the final problem embedding.

[0035] Furthermore, the specific analysis steps of the state update module are as follows: put the exercise embedding into LSTM, and learn the complex relationship between different knowledge and the change pattern of students' mastery of these knowledge from the input exercise representation through the input gate, forget gate and output gate, and obtain the student's knowledge mastery state embedding Em,

[0036] Furthermore, the specific analysis steps of the prediction optimization module are as follows: Construct the prediction probability expression Where P t represents the predicted probability of correctly answering a new question at time t, f i and f j and represents the forget gate, ⊙ represents the inner product, h t represents the hidden state, I e Indicates the selection of the k most relevant exercises between the target problem and the historical state. Softmax is the normalization function. The Adam optimization method is selected to minimize the cross entropy loss function. to update the parameters in the model.

[0037] Furthermore, the vertices of the bipartite graph G = (U, Q, S, R) are the student set U, the problem set Q, the knowledge set S, and the edge information R between each node. R is a binary adjacency matrix, which is expressed as R = [qs,uq,qq,uu,ss]∈{0,1}, qs,uq,qq,uu,ss represent the problem-knowledge relevance, student-problem relevance, problem-problem similarity, student-student similarity, knowledge-knowledge similarity, respectively. The student node feature initial value matrix U init The calculation formula is U init =Random(Dim,Num u ), the problem node feature initial value matrix Q init The calculation formula is Q init =Random(Dim,Num q ), knowledge node feature initial value matrix S init The calculation formula is S init =Random(Dim,Num s ), where Dim represents the fixed dimension of the embedding space, and Num u 、Num q 、Num s are the number of students, questions, and knowledge, respectively.

[0038] Furthermore, the question-knowledge relevance embedding vector The calculation formula is Student-question correlation embedding vector The calculation formula is Question Similarity Embedding Vector The calculation formula for is Student similarity embedding vector The calculation formula is Knowledge Similarity Embedding Vector The calculation formula is Where σ is the Sigmoid activation function, f represents the fully connected network f=max(0,w1x+b1), that is, each node x is first linearly transformed and then activated, and forward propagation and back propagation are used for pre-training updates.

[0039] Furthermore, the embeddings of neighboring nodes are averaged and added to the node's own embedding to update the representation of the node. The calculation formula is: in are the feature embeddings of student nodes, question nodes and knowledge node i at the l+1 layer, Nu i 、Nq i 、Ns iRepresents all neighbors of student nodes, question nodes, and knowledge node i, including the node itself. In the lth graph convolution layer, w l is the weight of the lth layer, b l is the bias of the lth layer, and σ is a nonlinear transformation.

[0040] Furthermore, the AUC value represents the area under the ROC curve. The AUC value is mainly used to measure the classification efficiency of the model. Its value is usually between 0.5 and 1. The closer the value is to 1, the higher the accuracy of the model, indicating that the model has a more significant predictive value. The calculation formula is Among them, m i Represents the positive sample prediction score, n j represents the negative sample prediction score, M represents the number of positive samples, and N represents the number of negative samples.

[0041] Furthermore, the specific situations of the five classic pioneering models are as follows: BKT: Use Bayesian networks to infer students' knowledge mastery, and represent students' knowledge status with binary variables; DKT: Use deep learning for the first time in the field of knowledge tracking, and use LSTM to model students' knowledge status, which has better prediction performance than traditional methods; DKVMN: Use memory networks to dynamically track changes in students' knowledge status, which has good interpretability; GKT: For the first time, use graph structures to represent the complex relationship between knowledge points, and use aggregated adjacent nodes to achieve the dynamic and correlation of knowledge tracking; GIKT: Use GCN and RNN to model students' knowledge status, and comprehensively consider multiple factors such as student status and historical exercises. The four models of the ablation experiment are: MFGKT-pu means no pre-training and no student neighbors are added; MFGKT-p means pre-training and no student neighbors are added; MFGKT-u means no pre-training and only student neighbors are added; MFGKT means pre-training and only student neighbors are added.

[0042] Specific implementation cases

[0043] Configure the experimental environment, the operating system is Ubuntu 20.04.5LTS (GNU / Linux 5.4.0-172-genericx86_64), the CPU is Intel(R)Xeon(R)CPU E5-2698 v4, the number of cores is 9 cores, the memory is 32GB, the graphics card is NVIDIA-SMI 535.129.03[Tesla V100-SXM2-32GB], the video memory is 32GB, and the experimental analysis of the model is implemented under the PyTorch1.13.1 framework;

[0044] The dimension Dim of the embedding vector is set to 100 dimensions, the batch size is set to 32, the Adam optimizer is selected, and the learning rate is set to 0.001. The neighbor update association in the graph structure is set to 3 hops, the number of student neighbors and knowledge neighbors is set to 10, and the number of student-based question neighbors and the number of knowledge-based question neighbors are set to 4. In the experiment, a 5-fold cross-validation method is used, and the number of training rounds for each fold is 10. 80% of the data set is divided into a training set, and the remaining 20% ​​is used as a test set.

[0045] The ASSIST09 dataset was preprocessed, and the practice records with less than 3 answers were deleted, and useless data such as empty knowledge were removed. After preprocessing, the dataset contained 3852 students, 123 knowledge items, 17737 questions, and 282619 practice records. The statistical data of the dataset are as follows Figure 6 ;

[0046] Students, questions and knowledge are represented as a bipartite graph G = (U, Q, S, R). The vertices of the bipartite graph G = (U, Q, S, R) are the student set U, the question set Q, the knowledge set S and the edge information R between each node. R is a binary adjacency matrix, which is expressed as R = [qs, uq, qq, uu, ss] ∈ {0, 1}. qs, uq, qq, uu, ss represent question-knowledge correlation, student-question correlation, question-question similarity, student-student similarity and knowledge-knowledge similarity respectively. The student node feature initial value matrix U init The calculation formula is U init =Random(Dim,Num u ), the problem node feature initial value matrix Q init The calculation formula is Q init =Random(Dim,Num q ), knowledge node feature initial value matrix S init The calculation formula is S init =Random(Dim,Num s ), where Dim represents the fixed dimension of the embedding space, and Num u 、Num q 、Num s are the number of students, questions, and knowledge, respectively;

[0047] The student-question-knowledge relationship is divided into correlation and similarity, where the relationship between nodes of different types is correlation, and the relationship between nodes of the same type is similarity. The fully connected network FCN is used to capture and effectively fuse global features. The node relationship, that is, the edge feature, is extracted and optimized through pre-training, including the correlation and similarity between nodes. Then, the rich potential node relationships of students, questions, and knowledge are obtained and used as weights to encode and embed the node features. The Random function is used to generate a fixed-dimensional, dense random value vector to represent each node feature, and the initial value matrix U of the student, question, and knowledge node features is obtained. init , Q init , S init , the calculation formula is: Where Dim represents the fixed dimension of the embedding space, Nim u 、Nim q 、Nim s are the number of students, questions, and knowledge, respectively;

[0048] The node feature initial value matrix first passes through the fully connected network, and then uses the Sigmoid function to estimate the local proximity between different nodes in the embedding space, converts their relationship values ​​into probability values, and uses matrix dot multiplication to estimate the problem-knowledge correlation embedding vector in the embedding space. Student-question correlation embedding vector Question Similarity Embedding Vector Student similarity embedding vector Knowledge Similarity Embedding Vector The correlation and similarity between The calculation formula is The calculation formula is The calculation formula is The calculation formula is The calculation formula is Where σ is the Sigmoid activation function, f represents the fully connected network f=max(0,w1x+b1), that is, each node x is first linearly transformed and then activated, and forward propagation and back propagation are used for pre-training and updating;

[0049] Then, by using the minimization of loss entropy for optimization training, we get the edge information, that is, the node relationship matrix, including the correlation matrix and similarity matrix between nodes. Through optimization, the node relationship in the embedding space can be as close as possible to the correlation and similarity in the real graph structure. The obtained node relationship matrix is ​​used as the weight, and the student node feature u, the problem node feature q, and the knowledge node feature s are encoded as embeddings to obtain the student node embedding Eu, the problem node embedding Eq, and the knowledge node embedding Es as the initial embeddings of various nodes. The answers are obtained from the data set and encoded to obtain the answer embedding En, whose two rows represent the wrong and correct answers respectively.

[0050] Use knowledge or students to update the problem information, set the path of updating the problem to 3 hops, the first hop neighbor of the problem is the multiple knowledge or students corresponding to the problem, the second hop neighbor is the other problems corresponding to each of these knowledge or students, and the third hop neighbor is the other knowledge or students corresponding to each of these problems. For each batch, a fixed number of students’ neighbors, problem neighbors, and knowledge neighbors are sampled. In the graph convolution layer of the graph convolutional neural network, the embedding of the neighbor nodes is averaged and added to the node’s own embedding to update the node’s representation. The calculation formula is: in are the feature embeddings of student nodes, question nodes and knowledge node i at the l+1 layer, Nu i 、Nq i 、Ns i Represents all neighbors of student nodes, question nodes, and knowledge node i, including the node itself. In the lth graph convolution layer, w l is the weight of the lth layer, b l is the bias of the lth layer, σ is the nonlinear transformation;

[0051] After the embedding propagation of GCN, the question embedding based on knowledge neighbors and the question embedding based on student neighbors are concatenated to obtain the final question embedding;

[0052] The exercise embedding is placed in LSTM, and through the input gate, forget gate, and output gate, the complex relationship between different knowledge and the changing pattern of students’ mastery of these knowledge are learned from the input exercise representation to obtain the embedding Em of the students’ mastery of knowledge status.

[0053] Constructing the predicted probability expression Where P t represents the predicted probability of correctly answering a new question at time t, f i and f j and represents the forget gate, ⊙ represents the inner product, h t represents the hidden state, I eIndicates the selection of the k most relevant exercises between the target problem and the historical state. Softmax is the normalization function. The Adam optimization method is selected to minimize the cross entropy loss function. To update the parameters in the model;

[0054] The AUC value is used as an indicator to evaluate the model. The AUC value represents the area under the ROC curve. The AUC value is mainly used to measure the classification efficiency of the model. Its value is usually between 0.5 and 1. The closer the value is to 1, the higher the accuracy of the model is, indicating that the model has a more significant predictive value. The calculation formula is: Among them, m i Represents the positive sample prediction score, n j Represents the negative sample prediction score, M represents the number of positive samples, and N represents the number of negative samples;

[0055] To evaluate the performance of the MFGKT model, this paper selected five classic pioneering models in the field of knowledge tracking for comparison:

[0056] BKT: Use Bayesian networks to infer students’ knowledge and represent students’ knowledge status with binary variables;

[0057] DKT: The first use of deep learning in the field of knowledge tracking, using LSTM to model the student's knowledge status, which has better prediction performance than traditional methods;

[0058] DKVMN: It uses memory networks to dynamically track changes in students’ knowledge status, which has good interpretability.

[0059] GKT: For the first time, it uses graph structure to represent the complex relationship between knowledge points and realizes the dynamic and associative nature of knowledge tracking by aggregating adjacent nodes.

[0060] GIKT: Use GCN and RNN to model the student's knowledge status, and comprehensively consider multiple factors such as student status and historical practice;

[0061] Record the AUC performance of all KT models involved in the comparison and get Figure 7 ,like Figure 7 As shown in the figure, MFGKT achieves the best performance on the ASSIST2009 benchmark dataset in predicting students' future knowledge status. First, all deep KT models outperform BKT. Second, the latest deep KT methods show greater improvements than DKT. Third, the proposed MFGKT improves performance by about 4% compared with GIKT.

[0062] In order to verify the advantages of the MFGKT model, this section conducts ablation experiments on pre-training, student neighbor association and other contents to verify the effectiveness of the MFGKT design. The specific contents of the four models are as follows: MFGKT-pu means no pre-training and no student neighbors are added; MFGKT-p means pre-training and no student neighbors are added; MFGKT-u means no pre-training and student neighbors are added; MFGKT means pre-training and student neighbors are added. The ablation experiment data of the dataset are shown in Figure 8 ,The experimental results on the real dataset of ASSIST2009 dataset show that the MFGKT model achieves the best performance after pre-training and comprehensive consideration of the association between students and questions, and questions and knowledge. MFGKT-p shows greater improvement than MFGKT-pu, which verifies that pre-training promotes model performance. In addition, with MFGKT-pu as a reference, the AUC performance of MFGKT is improved by 5% in the dataset, which indicates that the student node has a greater impact on the current knowledge state. In summary, it is effective to introduce pre-training and student nodes in embedding propagation for knowledge tracking.

[0063] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A graph convolutional network knowledge tracking model integrating multi-dimensional features, including a feature embedding module, an embedding propagation module, a state updating module and a prediction optimization module, characterized in that: The feature embedding module uses the student answer records and optimizes the side information between various nodes through a fully connected network, and then uses the side information to embed the node features in a low-dimensional manner. Finally, a comprehensive knowledge tracking network is constructed through the correlation and similarity relationships between all nodes. The embedding propagation module uses GCN to extract the neighbor information on the two paths of "question-knowledge-question" and "question-student-question", generates a high-order embedding of the question, and embeds it with the student's answer results to obtain the exercise embedding. The state update module uses LSTM to train the exercise embedding and update the student's knowledge mastering status to predict the student's answering questions in the future. The prediction optimization module selects historical questions with similar knowledge points to help predict, and improves the prediction accuracy and performance of the model through back-propagation training to achieve the goal of optimizing the model. After the model is built, the AUC value is first used to evaluate the model prediction performance, and then five classic pioneering models in the field of knowledge tracking are selected for comparison to evaluate the overall performance of the model. Finally, in order to verify the advantages of the MFGKT model, an ablation experiment analysis is carried out on pre-training, student neighbor association and other contents to verify the effectiveness of the MFGKT design.

2. According to claim 1, a graph convolutional network knowledge tracking model integrating multi-dimensional features is characterized by: The specific analysis steps of the feature embedding module are as follows: students, questions and knowledge are represented as a bipartite graph G = (U, Q, S, R), the relationship between students, questions and knowledge is divided into correlation and similarity, where the relationship between nodes of different types is correlation, and the relationship between nodes of the same type is similarity, the fully connected network FCN is used to capture and effectively fuse global features, and the node relationship, i.e., edge features, including the correlation and similarity between nodes, is extracted and optimized through pre-training, and then the rich potential node relationships of students, questions and knowledge are obtained and used as weights to encode and embed the node features, and a fixed-dimensional, dense random value vector is generated using the Random function to represent each node feature, and the initial value matrix U of the student, question and knowledge node features is obtained. init , Q init , S init , the calculation formula is: Where Dim represents the fixed dimension of the embedding space, Nim u 、Nim q 、Nim s are the number of students, questions, and knowledge respectively. The node feature initial value matrix first passes through the fully connected network, and then uses the Sigmoid function to estimate the local proximity between different nodes in the embedding space, converts their relationship values ​​into probability values, and uses matrix dot multiplication to estimate the problem-knowledge correlation embedding vector in the embedding space. Student-question correlation embedding vector Question Similarity Embedding Vector Student similarity embedding vector Knowledge Similarity Embedding Vector The correlation and similarity between them are then optimized and trained by minimizing the loss entropy to obtain the edge information, that is, the node relationship matrix, including the correlation matrix and the similarity matrix between nodes. The node relationship in the embedding space is optimized to be as close as possible to the correlation and similarity in the real graph structure. The obtained node relationship matrix is ​​used as the weight, and the student node feature u, the problem node feature q, and the knowledge node feature s are encoded as embeddings to obtain the student node embedding Eu, the problem node embedding Eq, and the knowledge node embedding Es as the initial embeddings of various types of nodes. The answers are obtained from the data set and encoded to obtain the answer embedding En, whose two rows represent the wrong and correct answers respectively.

3. According to claim 1, a graph convolutional network knowledge tracking model integrating multi-dimensional features is characterized by: The specific analysis steps of the embedding propagation module are as follows: using knowledge or students to update the problem information, setting the path of updating the problem to 3 hops, the first hop neighbor of the problem is the multiple knowledge or students corresponding to the problem, the second hop neighbor is the other problems corresponding to each of these knowledge or students, and the third hop neighbor is the other knowledge or students corresponding to each of these problems. For each batch, a fixed number of students' neighbors Nu, problem neighbors Nq, and knowledge neighbors Ns are sampled. In the graph convolution layer of the graph convolutional neural network, the embedding of the neighbor nodes is averaged and added to the node's own embedding to update the node's representation. After the embedding propagation of GCN, the problem embedding based on the knowledge neighbor and the problem embedding based on the student neighbor are spliced ​​to obtain the final problem embedding.

4. According to claim 1, a graph convolutional network knowledge tracking model integrating multi-dimensional features is characterized by: The specific analysis steps of the state update module are: putting the exercise embedding into LSTM, learning the complex relationship between different knowledge and the change pattern of students' mastery of these knowledge from the input exercise representation through the input gate, forget gate and output gate, and obtaining the student's knowledge mastery state embedding Em, 5. According to claim 1, a graph convolutional network knowledge tracking model integrating multi-dimensional features is characterized by: The specific analysis steps of the prediction optimization module are: select the top k similar knowledge points with the highest scores from the historical questions, and construct the prediction probability expression Where P t represents the predicted probability of correctly answering a new question at time t, f i and f j and represents the forget gate, ⊙ represents the inner product, h t represents the hidden state, I e Indicates the selection of the k most relevant exercises between the target problem and the historical state, Softmax is a normalization function. The Adam optimization method is selected to minimize the cross entropy loss function. to update the parameters in the model.

6. According to claim 2, a graph convolutional network knowledge tracking model integrating multi-dimensional features is characterized by: The vertices of the bipartite graph G = (U, Q, S, R) are the student set U, the problem set Q, the knowledge set S and the edge information R between each node. R is a binary adjacency matrix, which is expressed as R = [qs,uq,qq,uu,ss]∈{0,1}, where qs,uq,qq,uu,ss represent problem-knowledge relevance, student-problem relevance, problem-problem similarity, student-student similarity and knowledge-knowledge similarity respectively. student Node feature initial value matrix U init The calculation formula is U init =Random(Dim,Num u ), the problem node feature initial value matrix Q init The calculation formula is Q init =Random(Dim,Num q ), knowledge node feature initial value matrix S init The calculation formula is S init =Random(Dim,Num s ), where Dim represents the fixed dimension of the embedding space, and Num u 、Num q 、Num s are the number of students, questions, and knowledge, respectively.

7. The graph convolutional network knowledge tracking model integrating multi-dimensional features according to claim 2 is characterized in that: The question-knowledge relevance embedding vector The calculation formula is Student-question correlation embedding vector The calculation formula is Question Similarity Embedding Vector The calculation formula for is Student similarity embedding vector The calculation formula is Knowledge Similarity Embedding Vector The calculation formula is Where σ is the Sigmoid activation function, f represents the fully connected network f=max(0,w1x+b1), that is, each node x is first linearly transformed and then activated, and forward propagation and back propagation are used for pre-training updates.

8. The graph convolutional network knowledge tracking model integrating multi-dimensional features according to claim 3 is characterized by: The calculation formula for updating the representation of a node by averaging the embeddings of neighboring nodes and adding them to the embedding of the node itself is: in are the feature embeddings of student nodes, question nodes and knowledge node i at the l+1 layer, Nu i 、Nq i 、Ns i Represents all neighbors of student nodes, question nodes, and knowledge node i, including the node itself. In the lth graph convolution layer, w l is the weight of the lth layer, b l is the bias of the lth layer, and σ is a nonlinear transformation.

9. The graph convolutional network knowledge tracking model integrating multi-dimensional features according to claim 1, characterized in that: The AUC value represents the area under the ROC curve. The AUC value is mainly used to measure the classification efficiency of the model. Its value is usually between 0.5 and 1. The closer the value is to 1, the higher the accuracy of the model is, indicating that the model has a more significant predictive value. The calculation formula is Among them, m i Represents the positive sample prediction score, n j represents the negative sample prediction score, M represents the number of positive samples, and N represents the number of negative samples.

10. The graph convolutional network knowledge tracking model integrating multi-dimensional features according to claim 1, characterized in that: The specific details of the five classic pioneering models are as follows: BKT: Use Bayesian networks to infer students' knowledge mastery, and represent students' knowledge status with binary variables; DKT: Use deep learning for the first time in the field of knowledge tracking, and use LSTM to model students' knowledge status, which has better prediction performance than traditional methods; DKVMN: Use memory networks to dynamically track changes in students' knowledge status, which has good interpretability; GKT: Use graph structures to represent for the first time; GIKT: Use GCN and RNN to model students' knowledge status, and comprehensively consider multiple factors such as student status and historical exercises. The four models of the ablation experiment are: MFGKT-pu means no pre-training and no student neighbors are added; MFGKT-p means pre-training and no student neighbors are added; MFGKT-u means no pre-training and student neighbors are added; MFGKT means pre-training and student neighbors are added.

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