A knowledge tracking method based on hierarchical knowledge points

Abstract

The application provides a knowledge tracking method based on hierarchical knowledge points, and the specific steps are as follows: firstly, a knowledge point concurrent graph is constructed according to historical answering information of students, which explicitly mines the order relationship and co-occurrence relationship between knowledge points; on the basis of the knowledge point concurrent graph, the knowledge point embedding is dynamically updated through a graph convolution algorithm, and a high-order knowledge point embedding is obtained through a graph pooling algorithm; finally, the knowledge point feature representation with a hierarchical structure is obtained by aggregating knowledge point embeddings at different levels; and other question features and past answering conditions of students are jointly input into a long short-term memory network to predict the answering conditions of students in real time. The application utilizes the graph structure information in the knowledge points, establishes the hierarchical association between the knowledge points, mines the potential connection between the questions, and combines the knowledge tracking network model to more accurately understand the mastery degree of the knowledge points of the students, plan the learning path of the students in real time, and realize personalized learning.

Description

Technical Field

[0001] This invention belongs to the fields of intelligent teaching systems, data mining and analysis, and knowledge tracing, specifically a knowledge tracing method based on hierarchical knowledge points. Background Technology

[0002] Knowledge tracing models students' learning states based on the sequence of their learning activities. In the field of intelligent teaching systems, knowledge tracing is one of the most challenging tasks, as these systems need to accurately predict student performance and grasp their knowledge mastery. Knowledge points, as key features constituting questions, can effectively improve the performance of knowledge tracing. Current knowledge tracing models primarily treat knowledge points as ordinary question features, feeding them along with other features such as question difficulty or question type into a deep neural network for automatic learning. This method mainly relies on students' sequential answer information to uncover potential relationships between knowledge points; however, its interpretability in practical applications is poor, making this approach impractical. From a data structure perspective, knowledge point concepts naturally possess graph structure information. Therefore, using the graph structure information of knowledge points as a relational induction can greatly improve the representational power of this feature. Summary of the Invention

[0003] The purpose of this invention is to provide a knowledge tracing method based on hierarchical knowledge points. Its aim is to uncover high-level relationships between knowledge points to enrich the feature information of the problem and effectively improve the prediction accuracy of the knowledge tracing task model.

[0004] The specific technical solution for achieving the objective of this invention is as follows:

[0005] A knowledge tracing method based on hierarchical knowledge points, comprising the following specific steps:

[0006] Step 1: Extract the question-knowledge point bipartite graph G based on students' historical answer data. bi And the students' order of answering questions;

[0007] Step 2: Based on the question from Step 1 - the bipartite graph G of the knowledge point bi Constructing an implicit graph G of knowledge points sim Then, a knowledge point transfer graph G is constructed based on the students' sequential answer information. cor And in conjunction with the aforementioned knowledge points, implicit graph G sim and knowledge point transfer graph G cor Automatically construct a new concurrent graph G of knowledge points con ;

[0008] Step 3: Obtain the initial knowledge point embedding by embedding the knowledge point ID through the embedding layer, and then build the knowledge point concurrency graph G based on the knowledge point ID constructed in Step 2.con The initial correlation between knowledge points is obtained and fed into a multi-layer graph neural network architecture. Each layer of this architecture consists of three operations: aggregation, pooling, and readout. The aggregation operation updates the embeddings of knowledge points based on their correlation with each other using a graph convolution algorithm. The pooling operation calculates and generates higher-order knowledge point embeddings and correlation information using a graph pooling algorithm. The readout operation averages and normalizes the embeddings of all knowledge points generated by the pooling operation to calculate the feature representation of the knowledge points representing this layer.

[0009] Step 4: Concatenate the knowledge point feature representations at different levels calculated in Step 3, and input them into the feedforward neural network to construct a hierarchical knowledge point feature representation;

[0010] Step 5: Combine other question characteristics, such as question difficulty and question type, with the student's past answering performance and input them into the Long Short-Term Memory Network to make real-time predictions about the student's answering performance.

[0011] In step 2, the construction of the knowledge point concurrent graph G... con Specifically:

[0012] First, based on the bipartite graph G of the question and knowledge points... bi Constructing an implicit graph G of knowledge points sim =(S,A sim ), knowledge point s i and s j In the bipartite graph G of the question and knowledge point bi The problem involves nodes q that share a common neighbor. k So, knowledge point s i and s j In the implicit graph G of knowledge points sim correlation Calculate according to formula (1):

[0013]

[0014] Where N bi (i) represents knowledge point s i In the bipartite graph G of the question and knowledge point bi The neighboring question node in the;

[0015] s i and s j Transition matrix

[0016]

[0017] Construct a knowledge point transfer diagram G based on the students' answer sequence. cor =(S,A cor First, we use the statistical knowledge point s of the transition matrix.i and s j Transfer association, n ij Represents s i The s appearing in the student's answer sequence j Previous answer counts; calculate the knowledge point transfer graph G according to formula (2). cor Chinese knowledge points i to s j Relevance:

[0018]

[0019] Knowledge Point Concurrency Graph G con =(S,A con This incorporates implicit graph G, which combines knowledge points. sim and transition graph G cor The calculated relationships between knowledge points, and the knowledge point s i and knowledge points s j correlation Represented as:

[0020]

[0021] Where θ controls the sparsity of the concurrent graph of knowledge points.

[0022] In step 3, each layer of the architecture consists of three operations: aggregation, pooling, and reading, specifically:

[0023] Aggregation operations are based on the degree of association A between knowledge points at level l. (l) Using graph convolution algorithms, the embedding X of knowledge points is updated. (l) Generate the l-th layer aggregation graph Its graph convolution algorithm is represented as:

[0024]

[0025] in, For knowledge point s i The node embedding, where N(i) represents knowledge point s i All neighboring nodes of a node, and A is the learnable parameter matrix in the network; (l) Let G be the adjacency matrix of the l-th layer, representing the degree of association between various knowledge points. (0) =G con σ(·) represents the activation function, and ReLU is selected as the activation function in this invention;

[0026] Pooling operations are based on the l-th layer aggregation graph. To generate a high-order knowledge point relationship graph G (l+1)= (X (l+1) ,A (l+1) ,W (l+1) ), which can be expressed by mathematical formula as follows:

[0027] A (l+1) = (S (l) ) T A (l) S (l) (5)

[0028]

[0029]

[0030] wherein A (l+1) is the adjacency matrix of the (l+1)th layer knowledge point relationship graph; represents the knowledge point embedding obtained by the aggregation operation of the lth layer, and MLP(·) is a multilayer perceptron function with Softmax, and the knowledge point embedding of the lth layer aggregation graph is used as the input of the function to obtain the knowledge point embedding of the (l+1)th layer: obtains the allocation matrix S (l) , and uses the allocation matrix S (l) to further generate high-order knowledge point embedding X (l+1) and correlation degree information A (l+1) ; in combination with the method of clustering the min-cut problem, two loss functions: and are used to minimize the hierarchical allocation of the allocation matrix S (l) :

[0031]

[0032] wherein Tr(·), ||·|| F respectively represent the trace and Frobenius norm of the knowledge point relationship graph adjacency matrix A (l) , and D (l) represents the degree matrix of A (l) ; C (l) represents the number of knowledge point nodes in the lth layer knowledge relationship graph, and k∈(0,1] represents the pooling rate;

[0033] The read operation is performed by averaging all the knowledge point node embeddings X (l) of the lth layer to capture the knowledge point feature representation of the lth layer:

[0034]

[0035] The application can objectively and effectively mine the correlation between the levels existing between knowledge points according to historical answering data of students, help educators and practitioners automatically mine the correlation between knowledge points, assist in constructing a knowledge graph, improve the accuracy of a knowledge tracking field model, accurately understand the knowledge point mastery of students, and then recommend teaching content suitable for students through an intelligent teaching system, plan a student learning path in real time, and realize personalized learning. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A flowchart of the application;

[0037] Figure 2 A schematic diagram of knowledge point concurrent graph construction in the application;

[0038] Figure 3 A flowchart of level knowledge point construction in the application. DETAILED DESCRIPTION

[0039] The application will be described in detail below in combination with the drawings and embodiments, so that the advantages and features of the application can be more easily understood by those skilled in the art, and the protection scope of the application can be more clearly and explicitly defined.

[0040] The application proposes a knowledge tracking method based on hierarchical knowledge points. The purpose is to mine high-order level correlation between knowledge points to enrich the feature information of the question. The specific flowchart is as shown in Figure 1 , which includes two methods: knowledge point concurrent graph construction and hierarchical knowledge point representation. A new knowledge point concurrent graph is obtained through knowledge point concurrent graph construction, and then a knowledge point feature representation with a hierarchical structure is constructed according to the hierarchical knowledge point representation, and other question features such as question difficulty and question type, and the answering status of students are combined and input into a long short-term memory network to predict the answering status of students in real time. The related specific implementation method is as follows:

[0041] 1. Knowledge point concurrent graph construction

[0042] The knowledge point relationship graph is represented as G=(S,A), wherein Each vertex s i in the graph corresponds to the ith knowledge point, N=|S| represents the total number of knowledge points involved in the answering process of the student, A∈R N×N is the adjacency matrix of the knowledge point relationship graph, representing the correlation degree between the knowledge points. The specific construction process of the knowledge point concurrent graph is as shown in Figure 2 , which is composed of a knowledge point implicit graph and a knowledge point transition graph. The construction methods of the two graphs will be introduced next.

[0043] Generally speaking, a question contains multiple knowledge points, and a knowledge point can be in multiple questions, so it can be naturally constructed into a question-knowledge point bipartite graph G bi =(Q, S, A bi ), where q i represents the ith question, M = |Q| represents the total number of questions involved in the student's answering process; A bi ∈{0, 1} M×N is a binary adjacency matrix, where if the ith knowledge point s k is contained in the question q i , then there is an edge between q k and s i . Conversely The knowledge point implicit graph G sim =(S, A sim ) mines the co-occurrence between knowledge points through the question-knowledge point bipartite graph G bi . Specifically, if two knowledge points s i and s j have common neighbor question nodes q k , then the association degree sim between knowledge points s i and s j in the knowledge point implicit graph G bi is represented as:

[0044]

[0045] where N bi (i) represents the neighbor question node of the knowledge point s i in the question-knowledge point bipartite graph G bi .

[0046] Table 1 Transition matrix of s i and s j

[0047]

[0048] The knowledge point transition graph G cor =(S, A cor ) is used to mine the sequential association of s i and s j in the student's answering sequence. As shown in Table 1, the transition matrix is first used to count the transition association of knowledge points s i and s j , and n ij represents the occurrence of s i in the student's answering sequence s jPrevious answer counts; calculate the knowledge point transfer graph G according to formula (2). cor Chinese knowledge points i to s j Relevance:

[0049]

[0050] Knowledge Point Concurrency Graph G con =(S,A con This incorporates implicit graph G, which combines knowledge points. sim and knowledge point transfer graph G cor The calculated relationships between knowledge points, and the knowledge point s i and knowledge points s j correlation Represented as:

[0051]

[0052] Here, θ controls the sparsity of the concurrent knowledge graph. This step proposes a method for automatically constructing knowledge point associations, helping educators and practitioners to automatically mine the relationships between knowledge points from students' historical answer data, and assisting in the construction of knowledge graphs and other tasks.

[0053] 2. Hierarchical Representation of Knowledge Points

[0054] Hierarchical knowledge point representation is mainly used to construct hierarchical knowledge point embeddings. First, the knowledge point ID is passed through the embedding layer to obtain the initial knowledge point embedding X. (0) Then, based on the knowledge point concurrency graph G constructed in step 2 con The initial correlation A between knowledge points is obtained. (0) These are then fed into a multi-layered graph neural network architecture, ultimately yielding hierarchical knowledge point representations. Each layer of this architecture consists of three operations: aggregation, pooling, and readout. Figure 3 As shown.

[0055] Aggregation operations are based on the degree of association A between knowledge points at level l. (l) Using graph convolution algorithms, the embedding X of knowledge points is updated. (l) Generate the l-th layer aggregation graph Its graph convolution algorithm is represented as:

[0056]

[0057] in, For knowledge point s i The node embedding, where N(i) represents knowledge point s. i All neighboring nodes of a node, and A is the learnable parameter matrix in the network;(l) is the adjacency matrix of the l-th layer, representing the correlation degree between each knowledge point, where G (0) con ; σ(·) represents the activation function, and ReLU is selected as the activation function in the present application.

[0058] The pooling operation is based on the l-th layer aggregation graph to generate high-order knowledge point relationship G (l+1) = (X (l+1) , A (l+1) , W (l +1) , which is mathematically expressed as follows:

[0059] A (l+1) = (S (l) ) T A (l) S (l) (5)

[0060]

[0061]

[0062] MLP(·) is a multi-layer perceptron function with Softmax, according to the l-th layer to obtain the allocation matrix S (l) , and further update the high-order knowledge point embedding and correlation degree information using the allocation matrix S (l) . The parameter matrix used in MLP is learnable, which combines the method of min-cut clustering and uses two loss functions: and to minimize the hierarchical allocation of the allocation matrix S (l) :

[0063]

[0064] where Tr(·), ||·|| F represent the trace and Frobenius norm of the adjacency matrix A (l) of the knowledge point relationship graph, respectively, D (l) represents the degree matrix of A (l) ; C (l) represents the number of knowledge point nodes in the l-th layer knowledge relationship graph, and k ∈ (0, 1] represents the pooling rate.

[0065] The read operation is performed by averaging all knowledge point node embeddings X (l) of the l-th layer to capture the knowledge point feature representation of the l-th layer:

[0066] ​

[0067] Finally, the different levels of knowledge point feature representation s (l) are spliced into the feedforward neural network (Linear) to output the final hierarchical knowledge point feature representation

[0068]

[0069] This method can mine the natural hierarchical knowledge point structure inside the knowledge point, and proposes a new question feature information: hierarchical knowledge point It can be used as a key knowledge point feature information to obtain the hierarchical relationship between knowledge points, assist in question construction, mine the potential relationship between questions, and further improve the prediction of the student's answer accuracy.

[0070] 3. Student learning state prediction

[0071] The above obtained hierarchical knowledge point is spliced with other question features such as question difficulty k and question type t, and input into the feedforward neural network to obtain the question feature representation q:

[0072]

[0073] And combined with the student's answer status r to the current question, it is input into the long short-term memory network (LSTM):

[0074] h t = LSTM([q; r]) (12)

[0075] Where h t is the vector of the LSTM hidden layer, representing the student's mastery of the knowledge point at time t. Input it and other question feature representations q into the classification network to get the student's answer status for question q at time t:

[0076] a t = Softmax(Linear([h t ; q])) (13)

[0077] Through model training, the student's mastery of the knowledge point can be accurately obtained, and then the student's answer status is recommended through the intelligent teaching system. The teaching content suitable for the student is recommended, the student's learning path is planned in real time, and personalized learning is realized.

Claims

1.A knowledge tracking method based on hierarchical knowledge points, characterized in that, The method comprises the following specific steps: Step 1: Extract the question-knowledge point bipartite graph G according to the historical answering data information of the student bi and the sequential answering information of the student; Step 2: Construct a knowledge point implicit graph G according to the topic-knowledge point bipartite graph G of step 1 bi Construct a knowledge point implicit graph G sim , and further construct a knowledge point transition graph G through the student's sequential answering information cor , and combine the knowledge point implicit graph G sim and the knowledge point transition graph G cor to automatically construct a knowledge point concurrent graph G con ; Step 3: Obtain the initial knowledge point embedding through the embedding layer based on the knowledge point id, and then construct the knowledge point concurrent graph G based on the knowledge point concurrent graph G constructed in step 2 con Obtain the initial correlation between knowledge points, and input into the multi-layer graph neural network architecture to construct hierarchical knowledge points. The architecture of each layer is composed of three operations: aggregation, pooling and reading. The aggregation operation updates the embedding of the knowledge point by using the graph convolution algorithm according to the correlation between the knowledge points; the pooling operation calculates the high-order knowledge point embedding and correlation information through the graph pooling algorithm; the reading operation calculates the knowledge point feature representation representing this layer by averaging and normalizing the embedding of all knowledge points generated by the pooling operation. Step 4: the knowledge point feature representations at different levels calculated according to step 3 are spliced and input into a feedforward neural network to construct the knowledge point feature representation with a hierarchical structure; Step 5: other question features and past answering conditions of the student are jointly input into a long short-term memory network to perform real-time prediction on the answering condition of the student. 2.The knowledge tracking method based on hierarchical knowledge points according to claim 1, wherein, In step 2, the constructing knowledge point and the concurrent graph G con , specifically: First according to the question-knowledge point bipartite graph G bi Construct knowledge point implicit graph G sim =(S, A sim ), knowledge point s i and s j In the question-knowledge point bipartite graph G bi There is a common neighbor question node q k , then knowledge point s i and s j In the knowledge point implicit graph G sim The correlation degree According to formula (1): where N bi (i) denotes a knowledge point s i In the topic-knowledge bipartite graph G bi a neighboring topic node; s i and s j transfer matrix According to the student answer sequence, a knowledge point transition graph G is constructed cor = (S, A cor ); first, the transition matrix is used to count the knowledge point s i and s j transition association, n ij represents the number of times s i appears before s j in the student answer sequence; The relevance of a knowledge point s cor to s i to s j is calculated according to formula (2): knowledge point concurrent graph G con = (S, A con ) combines the knowledge point implicit graph G sim and the transition graph G cor The association between the calculated knowledge points, the knowledge point s i and the knowledge point s j Association degree is represented as: Wherein θ is the sparse degree of controlling the knowledge point concurrent graph. 3.The knowledge tracking method based on hierarchical knowledge points according to claim 1, characterized in that, In step 3, each layer of the architecture is composed of three operations of aggregation, pooling and readout, specifically: The aggregation operation is according to the correlation degree A between the knowledge points of the lth layer (l) , the embedding X of the knowledge point is updated by using the graph convolution algorithm (l) , the lth layer aggregation graph is generated The graph convolution algorithm is represented as: wherein, is the node embedding of knowledge point s i N(i) represents all the neighbor nodes of knowledge point s i and is a learnable parameter matrix in the network; A (l) is the adjacency matrix of the l-th layer, representing the degree of association between knowledge points, wherein G (0) = G con ; σ(·) represents an activation function, and ReLU is selected as the activation function;​ The pooling operation is based on the l-th layer aggregated graph to generate a high-order knowledge point relationship graph G (l+1) = (X (l+1) , A (l+1) , W (l+1) ), which is mathematically expressed as follows: A (l+1) = (S (l) ) T A (l) S (l) (5) where A (l+1) is the adjacency matrix of the (l+1)-th layer knowledge point relation graph; represents the knowledge point embedding obtained by the aggregation operation of the l-th layer, and MLP(·) is a multi-layer perception function with Softmax, and the obtains the allocation matrix S (l) , and uses the allocation matrix S (l) to further generate high-order knowledge point embedding X (l+1) and correlation information A (l+1) ; in combination with the min-cut problem clustering method, two loss functions are used: and to minimize the hierarchical allocation of S (l) : where Tr(·),||·|| F F represent the trace and Frobenius norm of the knowledge point relationship graph adjacency matrix A (l) , respectively, D (l) represents the degree matrix of A (l) ; C (l) represents the number of knowledge point nodes in the knowledge relationship graph of the l-th layer, and k e (0, 1] represents the pooling rate; The read operation is performed by embedding X into all knowledge point nodes of the l-th layer (l) An average operation is performed to capture the knowledge point feature representation of the l-th layer:

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