Knowledge Tracing Modeling Method and System Based on Dual Graph Neural Network

Abstract

The present invention discloses a knowledge tracing modeling method and system based on a dual graph neural network, mainly related to the fields of intelligent education and educational big data mining. It includes a question-answering interaction node: based on the question information, adding the possible answering situation of the student to this question (i.e., answering correctly or wrongly), and fusing it into the student's question-answering interaction, which serves as the node for constructing a graph; a concept association graph: constructing a hypergraph between the question-answering interaction nodes, and using a hypergraph convolutional network to obtain the representation of each question-answering interaction node, which incorporates the association information between the questions and knowledge concepts; a directed transfer graph: constructing a directed graph between the question-answering interaction nodes, and using a directed graph neural network to obtain the representation of each question-answering interaction node, which incorporates the transfer information between the question-answering interaction nodes. The beneficial effects of the present invention are as follows: it can improve the quality of teaching work and achieve personalized teaching.

Description

Technical Field

[0001] The present invention relates to the fields of intelligent education and educational big data mining, and specifically to a knowledge tracing modeling method and system based on a dual-graph neural network. Background Art

[0002] Looking around the world, education has been found to have a close and positive relationship with economic, political, and cultural development. Governments of various countries have been constantly working hard to adjust their education policies to promote the growth and development of their adolescents.

[0003] At the same time, formulating a learning plan according to the actual situation of each student can efficiently utilize educational resources and improve learning efficiency and educational output. This educational method of "teaching students in accordance with their aptitude" has always received much attention from educators. In the traditional educational achievement evaluation mechanism, simply relying on the final exam scores to evaluate students' knowledge mastery level cannot reflect the mastery of each knowledge concept by students. For example, even if two students, A and B, get the same score in the same test paper, it cannot be simply considered that the two students have the same level of knowledge mastery, because there may be situations where the questions that student A answers wrongly are answered correctly by student B. Even if two students make mistakes in the same question, it may be that they make mistakes in different knowledge concepts examined in this question. Being able to model the mastery level of each knowledge concept by students is the basic premise for implementing teaching students in accordance with their aptitude, implementing personalized teaching, and improving the quality of teaching work.

[0004] Knowledge Tracing (KT) is to model the knowledge mastery of students based on their past answering situations, so that we can accurately predict the degree of students' mastery of knowledge concepts. The knowledge tracing problem can be formalized as in a student answering interaction, there is a set of students S and a set of exercises E, where different students are required to answer different exercises to achieve the mastery of relevant knowledge. Each exercise is related to a specific knowledge concept. The learning order of students is represented as I = {(e1, a1), (e2, a2),..., (e N , a N )}, where e t represents the t-th exercise answered by the student, a t represents the correct / incorrect label (i.e., 1 represents the correct answer, 0 represents the wrong answer), and N represents the length of the learning interaction sequence. The research content of knowledge tracing is to model the answering sequence of students to obtain the knowledge state of students at each moment (the degree of students' mastery of each knowledge concept), so that before the student does the next question, the probability of the student answering this question correctly can be predicted based on the student's knowledge state.

[0005] Most of the methods based on deep neural networks use the "one-hot representation" method to encode information such as questions, knowledge concepts, and answer performances. This encoding method is simple and easy to understand, but it cannot utilize the relationships between test questions, between knowledge concepts, and between test questions and knowledge concepts, which greatly limits the further improvement of model performance. Moreover, in traditional deep knowledge tracing methods, most methods use knowledge concept s as the input of the model and do not consider the question number q of the actual answer. That is, if q1 and q2 belong to the same knowledge concept s1, it is considered that these two questions belong to the same question. However, in fact, if a question has two or more knowledge concepts, this method cannot well reflect the differences and correlations between questions. Summary of the Invention

[0006] To solve the above problems and improve the quality of teaching work and achieve personalized teaching, the present invention discloses a knowledge tracing modeling method and system based on a dual graph neural network. The present invention uses a dual graph neural network to encode the answering interactions of students, fuses the two obtained representations, and finally inputs them into a gated recurrent unit (GRU) for modeling to predict the answering performances of students, thereby improving the accuracy of model prediction.

[0007] To achieve the above object, the present invention is realized through the following technical solutions:

[0008] Answering interaction node: Based on the question information, add the possible answering situation (i.e., correct or wrong) of the student for this question, and fuse it into the student answering interaction as the node for constructing the graph;

[0009] Concept association hypergraph: Construct a hypergraph between answering interaction nodes. In this hypergraph, each knowledge concept is decomposed into two hyperedges, corresponding to mastering and not mastering this knowledge concept respectively. According to the knowledge concepts associated with a question, add the interaction nodes of the correctly answered questions to the hyperedge corresponding to the mastered knowledge concept, and add the interaction nodes of the wrongly answered questions to the hyperedge corresponding to the not mastered knowledge concept. Use a hypergraph convolutional network to obtain the representation of each answering interaction node, which fuses the association information between the question and the knowledge concept;

[0010] Directed transition graph: Construct a directed graph between answering interaction nodes. According to the historical answering interaction sequences of all students, in this directed graph, use directed edges to connect the nodes corresponding to any two consecutive interactions in the sequence, so as to reflect the transition situation between answering interactions. Use a directed graph neural network to obtain the representation of each answering interaction node, which fuses the transition information between answering interaction nodes;

[0011] It further includes the following steps:

[0012] (1) Problem definition and data preprocessing;

[0013] (2) Fusion of dual-graph neural network encoding;

[0014] (3) Gated unit GRU modeling;

[0015] (4) Prediction, loss calculation, and optimization function.

[0016] Preferably, in the problem definition and data preprocessing, i.e., in the dataset, there are often short sequences (the number of answers is less than 2) and missing values (the test questions lack knowledge concepts or there are no corresponding test questions for the knowledge concepts) in the actual student answer interaction sequence. For student sample data with short sequences and incomplete information, they need to be removed in the preprocessing stage.

[0017] Preferably, the fusion of the dual-graph neural network encoding includes the fusion of the concept association hypergraph encoding and the directed transfer graph encoding.

[0018] Preferably, the gated unit GRU modeling includes:

[0019] z t = σ(W z x t + U z h t-1 )

[0020] r t = σ(W r x t + U r h t-1 )

[0021]

[0022]

[0023] Preferably, the prediction, loss calculation, and optimization function include:

[0024] (1) The obtained in GRU is operated with the weight matrix y and the bias b, and after passing through the sigmoid function σ, y t is obtained. y t is a matrix containing 2N questions (including both correct and incorrect answers), and the probability of answering each question correctly (between 0 and 1):

[0025] yt = σ(W yh ht + b y )

[0026] (2) Those with the predicted value of y t greater than or equal to 0.5 are considered to answer the next question correctly (i.e., q t+1= 1), those less than 0.5 are considered as wrong answers (q t+1 = 0). Compared with the true (q t+1 , a t+1 ), calculate the loss Loss and optimize it with the Adam optimization function:

[0027]

[0028] A knowledge tracing modeling system based on a dual graph neural network, including a terminal device, including a server, the server includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor implements all the above methods when executing the program.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] 1. Different from the traditional method of representing questions and answering situations separately, the present invention integrates them into a unified representation of answering interaction nodes, avoiding the incompatibility problems that may occur when representing them separately.

[0031] 2. Construct a concept association hypergraph and use a hypergraph neural network to learn the embedding representation vectors of answering interaction nodes. Compared with the traditional one-hot encoding representation method, the method of the present invention can make full use of the association information between questions and knowledge concepts.

[0032] 3. Construct a directed transfer graph and use a directed graph neural network to learn the embedding representation vectors of answering interaction nodes. Compared with the traditional one-hot encoding representation method, the method of the present invention can make full use of the interaction transfer information in the student's historical answering interaction sequence.

[0033] 4. Fuse the node representations of the two graph neural networks and then input them into a gated recurrent unit GRU to learn the student's knowledge state, comprehensively using the association relationship between questions and knowledge concepts and the interaction transfer relationship in the student's historical answering records. Compared with the existing methods, the accuracy of the knowledge tracing model can be significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Attached Figure 1 is the AUC index value of each method of the present invention.

[0035] Attached Figure 2 is the schematic diagram of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0036] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by this application.

[0037] Embodiment 1: Knowledge Tracing Modeling Method Based on Dual Graph Neural Network

[0038] The specific implementation steps are as follows:

[0039] (1) Problem Definition and Data Preprocessing

[0040] The present invention mainly conducts experiments on three publicly available datasets commonly used for knowledge tracing problems. In the two datasets ASSIST2009 and ASSIST2017, there are often situations such as short answer sequences (the number of answers is less than 2) and missing values (the test questions lack knowledge concepts or there are no corresponding test questions for knowledge concepts) in the actual student answer sequences. For student sample data with short sequences and incomplete information, they need to be removed during the preprocessing stage. For the EdNet dataset, since its original data is too large (about 780,000 student data), 5000 students are randomly selected from it, and then the processing method is the same as that of the above two datasets. In order to intuitively reflect the student's answer sequence, the answer sequence of each student in the dataset is represented by four lines: the first line is the number of answers in the answer sequence; the second line is the question number of the answer sequence; the third line is the knowledge concept corresponding to the question number; the fourth line is whether the student answers correctly (1 for correct, 0 for wrong).

[0041] (2) Dual Graph Neural Network Encoding

[0042] In previous studies on knowledge tracing, whether encoding question information or knowledge concepts, the combination of question information and answer situations has not been fully considered. In fact, the impact of answering a question correctly or wrongly on the entire model is very different. To eliminate the necessity of separately representing question information and answer situations in traditional knowledge tracing, the answer interaction, which includes both question information and the student's answer situation (correct or wrong) to this question, is used as the answer interaction node for constructing the graph. Suppose there are N questions, and each question has two possibilities: correct and wrong, so it is regarded as having 2N questions. For all 2N questions, a d-dimensional feature is randomly initialized to obtain Then are successively input into the Concept Association Hypergraph (CAHG) and the Directed Transition Graph (DTG) to obtain the encoded representations of the two types of questions and After fusion, a new representation of the question is obtained

[0043] Concept Association Hypergraph Encoding

[0044] In practical problems, each question corresponds to at least one knowledge concept, and questions with the same knowledge concept have potential relationships. The present invention uses a hypergraph structure to represent the association relationship between answering interactions and knowledge concepts. A hypergraph is an extension of a simple graph. Different from a simple Figure 1 edge connecting two nodes, a hyperedge of a hypergraph can connect any number of nodes, and a hyperedge is defined as a subset of nodes. Let G c =(V, E) be the association hypergraph CAHG, where E={H 1+ , H 1- , H 2+ , H 2- ,..., H m+ , H m-} represents the set of hyperedges. Since the nodes represent the answering interactions of students' correct or wrong answers, each knowledge concept is also decomposed into two hyperedges H j+ and H j- , corresponding to mastering and not mastering the knowledge concept respectively. Therefore, the number of hyperedges E is also twice the number of knowledge concepts. The association relationship between answering interactions and knowledge concepts can be represented by the association relationship between hyperedges and their nodes. Note that there is a many-to-many correspondence between nodes and hyperedges, which is due to these correspondence relationships between answering interactions and knowledge concepts.

[0045] Input the association matrix H of the knowledge concepts included in the exercise and the initialized X with d-dimensional features into the hypergraph convolutional neural network to obtain the question encoding of the relationship between questions and knowledge concepts. The network includes two layers of hyperedge convolution HGNN_conv - , and the activation function Relu. For a hypergraph, where V={V1, v2,..., V N} is the set of student nodes, and E={e1, e2,..., e M} is the set of hyperedges. A hypergraph can be represented by the association matrix H. A hyperedge can connect multiple nodes. If the node V i is connected by e j , then

[0046] Next, use the concept association hypergraph to construct the relationship between questions and knowledge concepts for training. The composition of the network is: HGNNconv1→Relu→HGNNconv2→Relu

[0047] The composition of the concept association hypergraph is:

[0048] G = Dv -1 / 2 *H*W*DE -1 *H T *DV -1 / 2

[0049] X1 = Relu(HGNNconv1(X, G))

[0050] X2 = Relu(HGNNconv2(X1, G))

[0051] Where DV and DE are the degree matrices of nodes and hyperedges respectively, and W represents the weight matrix of each point (default is 1). After two layers of hypergraph convolutional network, the finally obtained x2 is the representation of the question.

[0052] Directed transition graph encoding

[0053] In addition to the association between answering questions and knowledge concepts, the sequential path of answering questions is also an important factor in knowledge tracing, but it has not been fully explored in previous studies. Intuitively, the interaction between a student's two consecutive times is more likely to be triggered in a knowledge state with little change. Based on this, the present invention uses a directed transition graph DTG to model the transition path between answering questions. In any student's answering sequence, if the student's answering sequence is {v1, v2}, that is, answering the second question after answering the first question, it is reflected in the adjacency matrix as

[0054] A(v1, v2) = 1. Let Gt = (V, E) represent the DTG, and its adjacency matrix is:

[0055]

[0056] For each question, it is both the future answering sequence of the previous question and the nearest historical answering sequence of the next question. Therefore, both its out-degree and in-degree situations should be considered, that is:

[0057]

[0058] The directed transition graph takes the interaction nodes on all answering paths as the nodes of a directed graph, and the transition information between answering interaction nodes can be obtained. Similar to ①, the directed transition graph consists of two layers of convolution

[0059] Graph_Conv1 and Graph_Conv2, and the adjacency matrix adj representing the answering sequence.

[0060] The composition of this network is:

[0061]

[0062] The graph neural network is also a neural network layer, and the propagation method between its layers is:

[0063] H (l+1) = σ(DV -1 / 2*adj*DV -1 / 2 *H (l) *W (l) )

[0064] Among them, DV is the degree matrix of the nodes, and W represents the weight matrix of each point (default is 1). Finally, x2, that is, the representation of the problem, is obtained.

[0065] Two coding representations of the problems are obtained. and After that, the two obtained coding representations are concatenated side by side through the torCh.cat() function to obtain a new coding representation. As the input of the next-step model, its specific concatenation method is (where [] represents the concatenation operation):

[0066]

[0067] (3) Gated Recurrent Unit (GRU) Modeling

[0068] To solve the problem that the number of questions answered by each student varies in length, set the step size to 50 (pad with zeros for those less than 50). Every 50 questions form a group, take the inner product with the problem representation obtained by "one-hot encoding", and the double-graph neural network encoded representation of the current 50 questions can be obtained. Input it into the Gated Recurrent Unit (GRU), and map the obtained output to a 2N-dimensional representation to get the probability of answering each question correctly.

[0069]

[0070] (4) Prediction, Loss Calculation, and Optimization Function

[0071] Obtained in the GRU and the weight matrix bias b y Perform operations, and after passing through the sigmoid function σ, y is obtained. t , y t is a matrix containing 2N questions (including both correct and incorrect cases), and each question corresponds to the probability of answering correctly (between 0 and 1).

[0072]

[0073] For y t , those with predicted values greater than or equal to 0.5 are considered to answer the next question correctly (i.e., q t+1 = 1), and those less than 0.5 are considered to answer incorrectly (q t+1 = 0). Compare with the true (q t+1 , a t+1 ), calculate the loss Loss and optimize it using the Adam optimization function.

[0074]

[0075] The simulation verification of this implementation method is carried out. Figure 1 The performance of the present invention on the public datasets ASSIST2009, ASSIST2017 and EdNet is presented, and it is compared with 4 existing deep knowledge tracing modeling methods (denoted as DKT, DKVMN, SAKT, AKT respectively). It can be seen that the method of the present invention has better performance. The present invention uses the AUC index to measure the performance of each method. Among them, AUC (Area Under Curve) is a commonly used index to measure the performance of model methods, and its meaning is the area of the region enclosed by the ROC curve and the coordinate axes.

[0076] Example 2: Knowledge Tracing Modeling System Based on Dual Graph Neural Network

[0077] In one or more embodiments, a terminal device is disclosed, including a server. The server includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the knowledge tracing modeling method based on the dual graph neural network in the first embodiment. For the sake of brevity, it will not be elaborated here. It should be understood that in this embodiment, the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type. In the implementation process, each step of the above method may be completed by the integrated logic circuit in the hardware of the processor or the instructions in the form of software. The knowledge tracing modeling method based on the dual graph neural network in the first embodiment may be directly embodied as being executed by the hardware processor, or completed by the combination of the hardware and software modules in the processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here. Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with this embodiment can be implemented by electronic hardware or the combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but this implementation should not be considered to exceed the scope of this application. Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that based on the technical solution of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

Claims

1. A knowledge tracing modeling method based on a dual graph neural network, characterized in that Including: Answer interaction node: Based on the question information, add the student's answer situation to this question, that is, correct or wrong answer, and integrate it into the student answer interaction as the node for constructing the graph; Concept association hypergraph: Construct a hypergraph between answer interaction nodes. In this hypergraph, each knowledge concept is decomposed into two hyperedges, corresponding to mastering and not mastering this knowledge concept respectively. According to the knowledge concepts associated with a question, add the interaction nodes of the correct answers to the hyperedge corresponding to the mastered knowledge concept, and add the interaction nodes of the wrong answers to the hyperedge corresponding to the not-mastered knowledge concept. Use a hypergraph convolutional network to obtain the representation of each answer interaction node, and this representation integrates the association information between the question and the knowledge concept; Directed transition graph: Construct a directed graph between answer interaction nodes. According to the historical answer interaction sequences of all students, in this directed graph, use directed edges to connect the nodes corresponding to any two consecutive interactions in the sequence, so as to reflect the transition situation between answer interactions. Use a directed graph neural network to obtain the representation of each answer interaction node, and this representation integrates the transition information between answer interaction nodes; It also includes the following steps: (1) Problem definition and data preprocessing; (2) Fusion of dual-graph neural network encoding; (3) Gated unit GRU modeling; (4) Prediction, loss calculation and optimization function.

2. The knowledge tracing modeling method based on a dual graph neural network according to claim 1, wherein The problem definition and data preprocessing means that in the dataset, in the actual student answer interaction sequences, there are often short sequences, the number of answers is less than 2, missing values, the test questions lack knowledge concepts or there are no corresponding test questions for the knowledge concepts. For the student sample data with short sequences and the incomplete information, they need to be removed in the preprocessing stage.

3. A knowledge tracing modeling method based on a dual graph neural network according to claim 1, characterized in that, The fusion of the dual-graph neural network encoding includes the fusion of the concept association hypergraph encoding and the directed transition graph encoding.

4. A knowledge tracing modeling method based on a dual graph neural network according to claim 1, characterized in that The gated unit GRU modeling includes: z t = σ(W z x t + U z h t-1 ) r t = σ(W r x t + U r h t-1 ) 。 5. The knowledge tracing modeling method based on a dual graph neural network according to claim 1, wherein The prediction, loss calculation and optimization function includes: (1) The h obtained in the GRU t is operated with the weight matrix W yh and the bias b y After passing through the sigmoid function σ, y is obtained t y t is a matrix containing 2N questions, including the two cases of correct and incorrect answers. The probability of answering each question correctly is between 0 and 1: y t = σ(W yh h_t + b y ) (2) Take y t Those with predicted values greater than or equal to 0.5 are considered to answer the next question correctly, that is, q t+1 = 1, and those less than 0.5 are considered to answer q wrongly t+1 = 0, and compare with the true q t+1 , a t+1 Make a comparison, calculate the loss Loss and optimize it using the Adam optimization function: 。 6. A knowledge tracing modeling system based on a dual graph neural network, characterized in that, It includes a terminal device, including a server. The server includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the method described in any one of claims 1-5 above.

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