CN115374942A - Knowledge tracking method based on hierarchical knowledge points - Google Patents
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Abstract
The invention provides a knowledge tracking method based on hierarchical knowledge points, which comprises the following specific steps: firstly, constructing a knowledge point concurrency graph according to historical answer information of students, and explicitly mining the sequence relation and the co-occurrence relation among knowledge points; on the basis of a knowledge point concurrent graph, dynamically updating the knowledge point embedding through a graph convolution algorithm, acquiring high-order knowledge point embedding through a graph pooling algorithm, and finally acquiring knowledge point characteristic representation with a hierarchical structure by aggregating knowledge point embedding of different levels; and the answer condition of the student is predicted in real time by inputting the answer characteristics of other questions and the past answer condition of the student into a long-term and short-term memory network together. The method utilizes the graph structure information in the knowledge points to establish the hierarchical association between the knowledge points and mine the potential relation between the questions; and the knowledge tracking network model is combined to more accurately know the mastery degree of the knowledge points of the students, the learning path of the students is planned in real time, and personalized learning is realized.
Description
Technical Field
The invention belongs to the fields of intelligent teaching systems, data mining analysis and knowledge tracking, and particularly relates to a knowledge tracking method based on hierarchical knowledge points.
Background
Knowledge tracking models a student's learning state according to a sequence of the student's learning activities. Knowledge tracking is one of the most challenging tasks to solve in the field of intelligent teaching systems, as these systems need to accurately predict student performance and master the student's knowledge. Knowledge points are used as key features for forming the questions, and the knowledge tracking performance can be effectively improved. The current knowledge tracking model mainly takes knowledge points as common subject feature information, and the knowledge points and other features such as subject difficulty or subject type are sent to a deep neural network together for automatic learning. The method mainly aims to dig out potential associations existing before knowledge points according to sequential answer information of students, but the interpretability of the potential associations in practical application is poor, and the method is not practical. From a data structure perspective, there is natural graph structure information between knowledge point concepts. Therefore, the representation capability of the feature of the knowledge point can be greatly improved by summarizing the graph structure information of the knowledge point as a relationship.
Disclosure of Invention
The invention aims to provide a knowledge tracking method based on hierarchical knowledge points. The method aims to mine high-order hierarchical association among knowledge points so as to enrich characteristic information of problems and effectively improve the accuracy of knowledge tracking task model prediction.
The specific technical scheme for realizing the purpose of the invention is as follows:
a knowledge tracking method based on hierarchical knowledge points comprises the following specific steps:
step 1: extracting question-knowledge point bipartite graph G according to historical answer data information of students bi And student's sequential answer information;
step 2: topic-knowledge point bipartite graph G according to step 1 bi Construction of implicit knowledge point graph G sim Then, a knowledge point transfer graph G is constructed through the sequential answer information of the students cor And combining the knowledge point implicit map G sim And knowledge point transfer graph G cor Automatic mechanismEstablishing a new knowledge point concurrent graph G con ；
And step 3: acquiring initial knowledge point embedding by a knowledge point id through an embedding layer, and then constructing a knowledge point concurrency graph G based on the step 2 con And obtaining the correlation degree between the initial knowledge points, and inputting the correlation degree into a multi-layer graph neural network architecture together, wherein each layer of the architecture consists of three operations of aggregation, pooling and reading: the aggregation operation updates the embedding of the knowledge points by using a graph convolution algorithm according to the association degree between the knowledge points; performing pooling operation to calculate and generate high-order knowledge point embedding and association degree information through a graph pooling algorithm; the reading operation is used for calculating the characteristic representation of the knowledge point representing the layer after the embedding average of all the knowledge points generated by the pooling operation is normalized;
and 4, step 4: splicing the knowledge point feature representations of different levels obtained by calculation in the step 3, and inputting the knowledge point feature representations into a feedforward neural network to construct a knowledge point feature representation with a hierarchical structure;
and 5: the information is input into the long-term and short-term memory network together with other subject characteristics such as subject difficulty and subject types and the past answering conditions of students, so as to predict the answering conditions of the students in real time.
In step 2, the method constructs a knowledge point concurrency graph G con The method specifically comprises the following steps:
firstly, according to the question-knowledge point bipartite graph G bi Construction of implicit knowledge point graph G sim ＝(S,A sim ) Knowledge points s i And s j On the topic-knowledge point bipartite graph G bi Has a common neighbor topic node q k Then knowledge point s i And s j Implicit map G at knowledge point sim Degree of association of
Calculating according to formula (1):
wherein N is bi (i) Representing knowledge points s i On the topic-knowledge point bipartite graph G bi A neighbor topic node in (1);
s i and s j Is transferred to the matrix
Constructing knowledge point transfer graph G according to student answer sequence cor ＝(S,A cor ) (ii) a First, the transfer matrix is used to count the knowledge points s i And s j Transfer correlation, n ij Represents s i Appearing in student answer sequence at s j The number of previous answer states; calculating the transition graph G at the knowledge point according to the formula (2) cor Middle knowledge point s i To s j The degree of association of (a):
knowledge point concurrency graph G con ＝(S,A con ) Combines the implicit map G of knowledge points sim And transition diagram G cor Associations between calculated knowledge points, knowledge points s thereof i And knowledge points s j Degree of association
Expressed as:
where θ is the degree of sparseness of the control knowledge point concurrency graph.
In step 3, each layer of the architecture consists of three operations, namely aggregation, pooling and reading, and specifically comprises the following steps:
the aggregation operation is based on the relevance A between knowledge points of the l-th layer (l) Updating the embedded X of knowledge points using a graph convolution algorithm (l) Generating the first layer aggregate map
The graph convolution algorithm is expressed as:
wherein,
as a point of knowledge s i N (i) denotes a knowledge point s i All the nodes that are neighbors of the node,
and
is a parameter matrix which can be learnt in the network; a. The (l) The adjacency matrix of the l layer represents the degree of association between knowledge points, wherein G (0) ＝G con (ii) a Sigma (-) represents an activation function, and ReLU is selected as the activation function;
pooling operation is based on layer I aggregation maps
Generating a high-order knowledge point relation graph G (l+1) ＝(X (l+1) ,A (l+1) ,W (l+1) ) Expressed mathematically as follows:
A (l+1) ＝(S (l) ) T A (l) S (l) (5)
wherein A is (l+1) An adjacency matrix which is a relation graph of knowledge points of the l +1 th layer;
representing knowledge point embedding obtained by aggregation operation of the l-th layer, MLP (-) is a multi-layer perceptron function with Softmax, embedded according to knowledge points of the l-layer aggregation diagram
Obtaining an allocation matrix S (l) And using an allocation matrix S (l) Further generation of high-order knowledge point embedding X (l+1) And association degree information A (l+1) (ii) a Combining a min-cut problem clustering method, two loss functions are utilized:
and
to minimize the allocation matrix S (l) Hierarchical assignment of (2):
wherein Tr (·) and | · | F Respectively represent adjacent matrixes A of the knowledge point relational graph (l) Trace and Frobenius norm, D (l) Represents A (l) A degree matrix of (c); c (l) The number of knowledge point nodes in the knowledge relationship graph representing the l layer, k is equal to (0, 1)]Representing the pooling rate;
the read operation is performed by embedding X in all knowledge point nodes of the l-th layer (l) Carrying out an averaging operation for capturing the knowledge point feature representation of the ith layer:
the invention can objectively and effectively excavate the association between the layers existing among knowledge points according to the historical answer data of students, help educators and practitioners to automatically excavate the association between the knowledge points, assist in constructing knowledge maps, improve the accuracy of models in the knowledge tracking field, accurately know the mastering degree of the knowledge points of the students, recommend teaching contents suitable for the students through an intelligent teaching system, plan the learning path of the students in real time and realize personalized learning.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the construction of a knowledge point concurrency graph in the present invention;
fig. 3 is a flowchart of the construction of hierarchical knowledge points in the present invention.
Detailed Description
The present invention is described in detail below with reference to the attached drawings and embodiments so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention can be clearly and clearly defined.
The invention provides a knowledge tracking method based on hierarchical knowledge points. The method aims to mine high-order hierarchical association among knowledge points so as to enrich the characteristic information of the problem. The specific flow chart is shown in fig. 1, which includes two methods: and (4) constructing a knowledge point concurrent graph and expressing a knowledge point in a hierarchy mode. The method comprises the steps of constructing a new knowledge point concurrency graph through the knowledge point concurrency graph, constructing knowledge point characteristic representation with a hierarchical structure according to the hierarchical knowledge point representation, and inputting other subject characteristics such as subject difficulty and subject type and the answer condition of students into a long-term and short-term memory network together to predict the answer condition of the students in real time. The related specific implementation method is as follows:
1. knowledge point concurrent graph construction
The knowledge point relation graph is represented as G = (S, A), wherein
Each vertex s in the figure i Corresponding to the ith knowledge point, N = | S | represents the total number of knowledge points involved in the student answering process, and A ∈ R N×N The adjacency matrix which is a knowledge point relational graph represents the correlation degree between the knowledge points. Knowledge point concurrencyThe specific diagram construction process is shown in fig. 2, and is composed of a knowledge point implicit diagram and a knowledge point transition diagram, and the construction methods of the two diagrams will be described below respectively.
Generally, a topic contains a plurality of knowledge points, and one knowledge point can be in a plurality of topics, so that a topic-knowledge point bipartite graph G can be constructed naturally bi ＝(Q,S,A bi ) Wherein
q i Representing the ith question, and M = | Q | represents the total number of questions involved in the student answering process; a. The bi ∈{0,1} M×N Is a binary adjacency matrix, wherein if the topic q k Contains the ith knowledge point s i Then q k And s i Has an edge
Otherwise then
Implicit knowledge point map G sim ＝(S,A sim ) By topic-knowledge point bipartite graph G bi To mine co-occurrence between knowledge points. In particular if at two knowledge points s i And s j With common neighbor topic node q k Then knowledge point implicit map G sim Knowledge point s in i And s j Degree of association of (2)
Expressed as:
wherein N is bi (i) Representing knowledge points s i On the topic-knowledge point bipartite graph G bi Is selected.
TABLE 1 s i And s j Is transferred to the matrix
Knowledge point transfer graph G cor ＝(S,A cor ) For mining s in student answer sequences i And s j Are associated with each other. As shown in Table 1, the points of knowledge s are first counted using a transition matrix i And s j Transfer of associations, n ij Represents s i Appearing in student answer sequence at s j The number of previous answer states; calculating the transition graph G at the knowledge point according to the formula (2) cor Chinese knowledge point s i To s j The degree of association of (a):
knowledge point concurrency graph G con ＝(S,A con ) Combines the implicit map G of knowledge points sim And knowledge point transfer graph G cor Associations between calculated knowledge points, knowledge points s thereof i And knowledge points s j Degree of association
Expressed as:
where θ is the degree of sparseness of the control knowledge point concurrency graph. The step provides a method for automatically constructing knowledge point association, which helps educates educators and practitioners to automatically mine the association between knowledge points from the historical answer data of students and assists in completing the work of constructing knowledge maps and the like.
2. Hierarchical knowledge point representation
The hierarchical knowledge point representation is mainly used for constructing hierarchical knowledge point embedding, and the initial knowledge point embedding X is obtained by a knowledge point id through an embedding layer (0) And then constructing a knowledge point concurrency graph G based on the step 2 con Obtain an initialDegree of association a between knowledge points of (1) (0) And the data are input into a multi-layer graph neural network architecture together, and finally, a hierarchical knowledge point representation is obtained, wherein each layer of the architecture is composed of three operations of aggregation, pooling and reading, and is shown in a figure 3.
The aggregation operation is based on the association degree A between knowledge points of the l layer (l) Updating the embedded X of knowledge points using a graph convolution algorithm (l) Generating the first layer aggregate map
The graph convolution algorithm is expressed as:
wherein,
as a point of knowledge s i N (i) denotes a knowledge point s i All the nodes that are neighbors of the node,
and
is a parameter matrix which can be learnt in the network; a. The (l) The adjacency matrix of the l layer represents the degree of association between knowledge points, wherein G (0) ＝G con (ii) a σ (-) represents the activation function, and ReLU is selected as the activation function in the invention.
Pooling operations are based on a l-layer aggregation map
Generating high-order knowledge point relationships G (l+1) ＝(X (l+1) ,A (l+1) ,W (l +1) ) The mathematical formula is as follows:
A (l+1) ＝(S (l) ) T A (l) S (l) (5)
MLP (-) is a multi-layer perceptron function with Softmax according to l layers
Obtain an allocation matrix S (l) And use the allocation matrix S (l) And further updating the high-order knowledge point embedding and relevance information. The parameter matrix used in MLP is learnable, combines the method of min-cut problem clustering, and utilizes two loss functions:
and
to minimize the allocation matrix S (l) Hierarchical allocation of (2):
wherein Tr (·), | · | | non-woven phosphor F Adjacency matrixes A respectively representing knowledge point relation graphs (l) Trace and Frobenius norm, D (l) Represents A (l) A degree matrix of (c); c (l) The number of knowledge point nodes in the knowledge relationship graph representing the l layer, k ∈ (0, 1)]Representing the pooling rate.
The read operation is performed by embedding X in all knowledge point nodes of the l-th layer (l) Carrying out an averaging operation for capturing the knowledge point feature representation of the ith layer:
finally, the knowledge points of different levels are characterized by s (l) Spliced and input into a feedforward neural network (Linear) to output a final hierarchical knowledge point feature representation
The method can dig out the natural hierarchical knowledge point structure in the knowledge point, and provides a new topic feature information: hierarchical knowledge points
The method can be used as key knowledge point characteristic information to acquire the hierarchical relationship among knowledge points, assist in the construction of questions, and mine the potential relation among the questions, thereby improving the prediction of the model on the student answer accuracy.
3. Student learning state prediction
The obtained hierarchical knowledge points
And splicing with other topic characteristics, such as topic difficulty k and topic type t, inputting into a feedforward neural network to obtain characteristic representation q of the topic:
and the answer condition r of the current question by the student is input into a long-term short-term memory network (LSTM) together:
h t ＝LSTM([q；r]) (12)
wherein h is t The vector of LSTM hidden layer represents the mastery condition of student on knowledge point at t moment, and the knowledge point and the feature representation q of other questions are input into the classification network, so that the question aimed at by student at t moment can be obtainedq answer status:
a t ＝Softmax(Linear([h t ；q])) (13)
through model training, the mastering condition of the students on the knowledge points can be accurately acquired, the teaching content suitable for the students is recommended through the intelligent teaching system according to the answering conditions of the students, the learning path of the students is planned in real time, and personalized learning is achieved.
Claims (3)
1. A knowledge tracking method based on hierarchical knowledge points is characterized by comprising the following specific steps:
step 1: extracting question-knowledge point bipartite graph G according to historical answer data information of students bi And student's sequential answer information;
step 2: topic-knowledge point bipartite graph G according to step 1 bi Construction of implicit knowledge point graph G sim Then, a knowledge point transfer graph G is constructed through the sequential answer information of the students cor And combining the knowledge point implicit map G sim And knowledge point transfer graph G cor Automatically constructing a knowledge point concurrency graph G con ；
And step 3: the knowledge point id is embedded into the initial knowledge point through an embedding layer, and then a knowledge point concurrency graph G is constructed based on the step 2 con Obtaining the correlation degree between initial knowledge points, and inputting the correlation degree into a multi-layer graph neural network architecture together to construct hierarchical knowledge points, wherein each layer of the architecture consists of three operations of aggregation, pooling and reading: the aggregation operation updates the embedding of the knowledge points by using a graph convolution algorithm according to the association degree between the knowledge points; performing pooling operation to calculate and generate high-order knowledge point embedding and association degree information through a graph pooling algorithm; the reading operation is used for calculating the characteristic representation of the knowledge point representing the layer after the embedding average of all the knowledge points generated by the pooling operation is normalized;
and 4, step 4: splicing the knowledge point feature representations of different levels obtained by calculation in the step 3, and inputting the knowledge point feature representations into a feedforward neural network to construct a knowledge point feature representation with a hierarchical structure;
and 5: the student answer condition is input into the long-term and short-term memory network together with other question characteristics and the past answer condition of the student to predict the student answer condition in real time.
2. The knowledge tracking method based on hierarchical knowledge points as claimed in claim 1, wherein in step 2, the knowledge point concurrent graph G is constructed con The method specifically comprises the following steps:
firstly, according to the question-knowledge point bipartite graph G bi Construction of implicit knowledge point graph G sim ＝(S,A sim ) Knowledge points s i And s j On the topic-knowledge point bipartite graph G bi Has a common neighbor topic node q therein k Then knowledge point s i And s j Implicit map G at knowledge point sim Degree of association of (2)
Calculating according to formula (1):
wherein N is bi (i) Representing points of knowledge s i Dichotomy graph G at topic-knowledge point bi A neighbor topic node in (1);
s i and s j Is transferred to the matrix
Constructing knowledge point transfer graph G according to student answer sequence cor ＝(S,A cor ) (ii) a First, the transfer matrix is used to count the knowledge points s i And s j Transfer of associations, n ij Represents s i In student answering sequencesAppears at s j Number of previous answers; calculating the transition graph G at the knowledge point according to the formula (2) cor Middle knowledge point s i To s j The degree of association of (a):
knowledge point concurrency graph G con ＝(S,A con ) Combines the implicit map G of knowledge points sim And transition diagram G cor Associations between calculated knowledge points, knowledge points s thereof i And knowledge points s j Degree of association
Expressed as:
where θ is the degree of sparseness of the control knowledge point concurrency graph.
3. The knowledge tracking method based on hierarchical knowledge points as claimed in claim 1, wherein in step 3, each layer of the architecture is composed of three operations of aggregation, pooling and reading, specifically:
the aggregation operation is based on the relevance A between knowledge points of the l-th layer (l) Updating the embedded X of knowledge points using a graph convolution algorithm (l) Generating the first layer aggregate map
The graph convolution algorithm is expressed as:
wherein,
as a point of knowledge s i N (i) denotes a knowledge point s i All of the nodes that are neighbors of the node,
and
is a parameter matrix which can be learnt in the network; a. The (l) The adjacency matrix of the l layer represents the degree of association between knowledge points, wherein G (0) ＝G con (ii) a Sigma (·) represents an activation function, and ReLU is selected as the activation function;
pooling operation is based on layer I aggregation maps
Generating a high-order knowledge point relation graph G (l+1) ＝(X (l+1) ,A (l+1) ,W (l+1) ) Expressed mathematically as follows:
A (l+1) ＝(S (l) ) T A (l) S (l) (5)
wherein, A (l+1) An adjacency matrix of the l +1 layer knowledge point relation graph;
representing knowledge point embedding obtained by aggregation operation at the l-th layer, MLP (-) is a multi-layer perceptron function with Softmax, embedded according to knowledge points of the l-layer aggregation diagram
Obtain an allocation matrix S (l) And use the allocation matrix S (l) Further generation of high-order knowledge point embedding X (l+1) And association degree information A (l+1) (ii) a Combining a min-cut problem clustering method, two loss functions are utilized:
and
to minimize S (l) Hierarchical assignment of (2):
wherein Tr (·) and | · | F Respectively represent an adjacency matrix A of a knowledge point relation graph (l) Trace and Frobenius norm, D (l) Represents A (l) A degree matrix of (d); c (l) The number of knowledge point nodes in the knowledge relationship graph representing the l layer, k is equal to (0, 1)]Representing the pooling rate;
the read operation is performed by embedding X in all knowledge point nodes of the l-th layer (l) Carrying out an averaging operation for capturing the knowledge point feature representation of the ith layer:
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