A knowledge tracking method based on learning representation of heterogeneous entity multi-association graphs

Abstract

The present invention relates to the field of educational big data mining, and provides a knowledge tracking method based on heterogeneous entity multi-association graph representation learning, comprising the following steps: (1) heterogeneous entity multi-association graph representation learning; (2) knowledge propagation based on association attention mechanism; (3) multi-source knowledge state learning based on dual LSTM. The method of the present invention comprehensively utilizes technical methods such as heterogeneous graph construction and node information aggregation to systematically integrate information on the knowledge association between test questions and concepts, and comprehensively considers multiple associations between heterogeneous entities, including prerequisite associations, similar associations and related associations between test questions and concepts, thereby improving the accuracy of test question representation, further scientifically and comprehensively predicting learners' learning situations, and assisting teachers in precise teaching.

Description

Technical Field

[0001] The present invention relates to the field of educational big data mining, and in particular to a knowledge tracking method based on heterogeneous entity multi-association graph representation learning. Background Art

[0002] With the rise of artificial intelligence and educational big data technology, precision teaching has received strong technical support. To meet the needs of precision teaching, researchers need to study the learning trajectory of learners from their own perspective and predict their performance in future learning. This is the purpose of the knowledge tracking task, which is to model the learner's knowledge mastery status based on time, so as to accurately track the learner's current mastery of the concept and predict his performance in the next learning interaction.

[0003] In recent years, more and more works have noticed the value of complex associations between test questions and concepts, which contain rich knowledge information. For example, GKT uses the prerequisite associations between concepts to redefine knowledge tracking as a time series node-level classification problem; PEBG uses similar associations between concepts to enhance test question representation; SKT uses the prerequisite associations and similar associations between concepts to model influence propagation. Although these methods have significantly improved knowledge tracking, previous studies have not simultaneously considered the existence of heterogeneous entities such as test questions and concepts, as well as the prerequisite associations, similar associations, and related associations between them, resulting in insufficient accuracy in test question representation. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and to provide a knowledge tracking method based on heterogeneous entity multi-association graph representation learning, which comprehensively utilizes technical methods such as heterogeneous graph construction and node information aggregation to systematically integrate information on the knowledge associations between test questions and concepts, and comprehensively consider the multiple associations between heterogeneous entities, including the prerequisite associations, similar associations and related associations between test questions and concepts, thereby improving the accuracy of test question representation, further scientifically and comprehensively predicting learners' learning situation, and assisting teachers in precise teaching.

[0005] The purpose of the present invention is achieved through the following technical measures.

[0006] The present invention provides a knowledge tracking method based on heterogeneous entity multi-association graph representation learning, which comprises the following steps:

[0007] (1) Representation learning of heterogeneous entity multi-association graph: Construct a heterogeneous entity multi-association graph and extract (entity, association, entity) triples and association weight matrices. Entities include test questions and concepts, and associations include relevant associations between test questions and concepts, similar associations and prerequisite associations between test questions, and similar associations and prerequisite associations between concepts. Use the triple representation learning method to obtain dense representations of test questions and concepts.

[0008] (2) Knowledge propagation based on the associative attention mechanism: The associative attention mechanism is used to aggregate the representations of multi-hop entities and solve the problem that different associations should have different aggregation weights, thereby realizing knowledge propagation between different associations;

[0009] (3) Multi-source knowledge state learning based on dual LSTM: Based on dual LSTM, the learner’s knowledge state on the test questions and the knowledge state on the concepts are modeled separately to predict the correctness of the learner’s answer.

[0010] In the above technical solution, the heterogeneous entity multi-association graph representation learning in step (1) is specifically as follows:

[0011] (1-1) Construct a heterogeneous entity multi-association graph to mine the prerequisite associations and similar associations between test questions and concepts from the learners' response data; consider the multiple associations between test questions and concepts: the relevant associations between test questions and concepts, the similar associations and prerequisite associations between test questions, and the similar associations and prerequisite associations between concepts. Among them, the relevant associations between test questions and concepts are usually manually annotated in the dataset, while the similar associations and prerequisite associations between test questions and concepts are mined from the learners' response data.

[0012] (1-2) Extracting triples and association weight matrices,For a heterogeneous entity multi-association graph, each edge in the graph is converted into a triple. In addition, the adjacency matrix of the graph is used with the Laplace algorithm to obtain the association weight matrix of the graph.

[0013] (1-3) Triple representation learning, based on the triple representation learning method, is an effective way to parameterize entities and associations into vector representations and preserve the structure of the graph. In addition, triple representation learning has good scalability, that is, it can expand existing associations to enrich the final test question representation or concept representation. The specific method is: given a triple, first project the entity into a space specific to the association, and then optimize the representation of the entity and association through the loss function.

[0014] In the above technical solution, the knowledge propagation based on the associative attention mechanism in step (2) is specifically as follows:

[0015] (2-1) A question or concept participates in multiple triples. First, for a certain entity, its first-order connectivity self-network representation is calculated to collect information propagated from the first-order neighbor entities. At the same time, for different associations, the attention weight of knowledge propagation on each association should also be different.

[0016] (2-2) The attention weight in knowledge dissemination is calculated through the associative attention mechanism. This weight score depends on the distance between the entity and the neighboring entity in the associative space. The closer entity should spread more knowledge information. Then, the coefficients of the triples involved by all entities are normalized.

[0017] (2-3) Aggregate the entity representation and the entity’s self-network representation as a new representation of the entity. There are three aggregation methods: GCN aggregator, which adds the two representations and applies a nonlinear transformation; GraphSage aggregator, which concatenates the two representations and then applies a nonlinear transformation; and Bi-Interaction aggregator, which considers the two feature interactions between the entity representation and the self-network representation.

[0018] (2-4) By recursively computing the representation of entities, more propagation layers are further stacked to explore high-order connectivity information and collect knowledge propagated from high-level neighbor entities.

[0019] In the above technical solution, the multi-source knowledge state learning based on dual LSTM in step (3) is specifically as follows:

[0020] (3-1) After obtaining the dense representation of the test question and the dense representation of the concept, the two are aggregated to obtain the comprehensive representation of the test question, and then the comprehensive representation of the test question is multiplied by the correctness of the answer and concatenated to obtain the interaction vector.

[0021] (3-2) All learners’ interaction vectors are input into the dual LSTM to model the students’ knowledge status on concepts and test questions. The two LSTMs correspond to each other, and their outputs are added and averaged to obtain the students’ average knowledge status.

[0022] (3-3) Use the student’s average knowledge state through an activation function to predict the student’s response to the next exercise.

[0023] The present invention proposes a knowledge tracking method based on the representation learning of heterogeneous entity multi-association graph. The present invention constructs a heterogeneous entity multi-association graph, taking into account the existence of heterogeneous entities of test questions and concepts, as well as the prerequisite associations, similar associations and related associations between them, to explore the implicit knowledge associations hidden behind the test questions; extract high-order information through knowledge propagation based on the associative attention mechanism to obtain the final dense representation of the test questions; finally, aggregate the test question representation and answer correctness into a dual LSTM module to achieve knowledge tracking for students and learner performance prediction. The present invention can scientifically and comprehensively predict the learning situation of learners, thereby achieving precise teaching assistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 The flowchart of the method of the embodiment of the present invention is shown in FIG.

[0025] Figure 2 This is an example diagram of the structure of test questions and concepts.

[0026] Figure 3 A flowchart for triplet representation learning.

[0027] Figure 4 A flowchart of multi-layer knowledge propagation based on attention mechanism.

[0028] Figure 5 Flowchart of the knowledge propagation computation process based on the associative attention mechanism.

[0029] Figure 6 Schematic diagram of the association weights between concepts and test questions. DETAILED DESCRIPTION

[0030] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0031] like Figure 1 As shown, an embodiment of the present invention provides a knowledge tracking method based on heterogeneous entity multi-association graph representation learning, comprising the following steps:

[0032] (1) Learning representations of heterogeneous entity multi-association graphs

[0033] In order to explore the implicit knowledge associations behind test questions and concepts and enrich the representation of test questions, it is necessary to construct a heterogeneous entity multi-association graph, then extract triples and association weight matrices, and use the representation learning of triples to obtain a dense representation of the test questions.

[0034] (1-1) Constructing a heterogeneous entity multi-association graph

[0035] Mining prerequisite and similarity associations between test items and concepts from learners' response data.

[0036] (1-1-1) Take mining the prerequisite associations and similar associations between concepts as an example:

[0037] First, construct a concept correct matrix U c , U c is a count matrix, calculated as follows:

[0038]

[0039] in It indicates the number of times concept j is answered correctly after concept i is answered correctly.

[0040] In order to calculate whether there is an implicit prerequisite relationship between two concepts, a concept prerequisite matrix T is constructed. c First, calculate the concept transfer matrix where i≠j; otherwise, it is 0. represents the probability of one-way propagation from concept i to concept j. Then, if set up Otherwise it is 0, where the threshold is set to And in order to keep the DAG of the graph, the loop is deleted.

[0041] In order to calculate whether there is an implicit similarity association between two concepts, a concept similarity matrix O is constructed. c . First, calculate the conceptual concurrency matrix Where ε = 0.1 is used to prevent zero division. Then the maximum and minimum scale method is used to Expand and get is the probability of bidirectional communication between concept i and concept j. Finally, if set up Otherwise it is 0, where the threshold is set to The average value of .

[0042] (1-1-2) Use the same method as step (1-1-1) to construct the correct matrix U of the test questions. q , the test question prerequisite matrix T q , and the test similarity matrix O q , to extract the implicit associations between test questions.

[0043] (1-1-3) Through steps (1-1-1) and (1-1-2), a heterogeneous entity multi-association graph is constructed. Example: The structure of the graph is as follows Figure 2 As shown, the types of nodes include concepts and test questions; the edge associations include the relevant associations between test questions and concepts, the prerequisite associations and similar associations between concepts, and the prerequisite associations and similar associations between test questions.

[0044] (1-2) Extracting triples and associated weight matrices

[0045] For a heterogeneous entity multi-association graph, each edge in the graph is converted into a triple (h, r, t), also known as a fact, indicating that two entities are connected by a specific association.

[0046] The association weight matrix is ​​a two-dimensional matrix used to record the association weights between each entity in the graph. In the association weight matrix, each row and column corresponds to an entity, and each element in the matrix represents the strength of the association between two entities.

[0047] First, for each association, construct an (n+m)*(n+m) adjacency matrix Where r represents one of the above relationships. The calculation is as follows:

[0048]

[0049] Next, construct a degree matrix D r , the calculation formula is as follows:

[0050]

[0051] Calculate the normalized Laplace matrix to get the associated weight matrix, and implement the Laplace algorithm in two ways:

[0052] Symmetric Normalized Laplace Algorithm:

[0053]

[0054] Or the random walk normalized Laplace algorithm:

[0055]

[0056] Among them, I is the identity matrix.

[0057] (1-3) Triplet representation learning

[0058] like Figure 3 As shown, by optimizing the conversion principle to learn to embed each entity and association. Here, and are the embeddings of h, r, and t respectively; is the projection representation of and in the associated r space. Given a triple (h, r, t), first project the entity into the association-specific space, that is:

[0059]

[0060] Here M r ∈Rk×d is the projection matrix from the entity space to the association space of r. Then, the likelihood score formula is defined as:

[0061]

[0062] The loss function is designed as follows:

[0063]

[0064] in, (h, r, t′) is a constructed triplet, which is constructed by randomly replacing one entity in a real triplet; σ(·) is the sigmoid activation function.

[0065] (2) Knowledge propagation based on associative attention mechanism

[0066] To further enrich the representation of test questions and concepts, we use the architecture of graph convolutional networks to recursively propagate embeddings along high-order connectivity. In addition, we use the idea of ​​graph attention networks to reveal the importance of this connectivity by using the associated attention matrix to pay attention to weights, so as to aggregate entities with different associations, such as Figure 4 , 6 Here we first describe a single-layer propagation, which consists of three components: knowledge diffusion, knowledge-aware attention, and knowledge aggregation, and then discuss how to generalize it to multi-layer propagation.

[0067] (2-1) Knowledge dissemination

[0068] A question or concept participates in multiple triples, serving as a bridge to connect triples and spread knowledge. Consider an entity h, and use (h, r, t) to represent the set of triples. In order to characterize the first-order connectivity structure of entity h, the self-network representation of h is calculated:

[0069]

[0070] in It controls the weight of propagation on each triple (h, r, t), indicating how much important knowledge should be propagated from t to h under association r.

[0071] (2-2) Knowledge Perception Attention

[0072] This is achieved through the associated attention mechanism The update is as follows:

[0073]

[0074] Among them, tanh is selected as the nonlinear activation function.

[0075] Afterwards, the softmax function is used to normalize the coefficients of all triplets participating in h:

[0076]

[0077] (2-3) Knowledge aggregation

[0078] Finally, the entity representation e h and its ego network representation Aggregate as a new representation of entity h, more specifically: Three types of aggregators are used to implement f(·):

[0079] GCN aggregator: Add the two representations together and apply a non-linear transformation as follows:

[0080]

[0081] Among them, the activation function set is set to LeakyReLU; is a trainable weight matrix to extract useful knowledge information for propagation, and d′ is the transformation size.

[0082] GraphSage Aggregator: concatenates two representations and then applies a non-linear transformation:

[0083]

[0084] Bi-Interaction Aggregator: Consider e h and The two feature interactions between are as follows:

[0085]

[0086] in, is a trainable weight matrix and ⊙ is an element-wise product.

[0087] (2-4) High-order communication

[0088] like Figure 5 As shown in Figure 1, more propagation layers are further stacked to explore high-order connectivity information and collect knowledge propagated from high-level neighbor entities. Specifically, in step l, the representation of an entity is recursively expressed as:

[0089]

[0090] Here, the knowledge propagated in the ego-network representation of entity h is defined as follows:

[0091]

[0092] is the representation of entity t generated by the previous knowledge propagation step, and the memory is passed to this entity from its (l-1)-layer neighbors; during the initial information propagation iteration, Set to e h .

[0093] (3) Multi-source knowledge state learning based on dual LSTM

[0094] Multi-source knowledge state learning based on dual LSTM consists of three parts, including: fusion of knowledge representation and interactive projection, multi-source knowledge state fusion based on dual LSTM, and learner performance prediction.

[0095] (3-1) Fusion of knowledge representation and interactive projection

[0096] Representation of test questions q and conceptual representation c Aggregation is performed to obtain the fused knowledge representation v. Then, in order to distinguish between correct answers and incorrect answers, v is multiplied by the response a and concatenated to obtain the interaction vector x:

[0097]

[0098] Where a∈R d , x∈R 2d .

[0099] (3-2) Multi-source knowledge state fusion based on dual LSTM

[0100] In order to better distinguish the difference between test questions and concepts, dual LSTM is used to model the learner's knowledge state on test questions and knowledge state on concepts respectively. The specific approach is as follows:

[0101] The learner’s hidden knowledge state h at step t t According to the current input and the previous state h t =LSTM(x t ,h t-1 ; θ) is updated as:

[0102] i t =σ(W xi x t +W hi h t-1 +b i ),

[0103] f t =σ(W xf x t +W hf h t-1 +bf ),

[0104] o t =σ(W xo x t +W ho h t-1 +b o ),

[0105] c t =f t c t-1 +i t tanh(W xc x t +W hc h t-1 +b c )

[0106] h t =o t tanh(c t )

[0107] where i t ,f t ,o t are the input, forget and output gates respectively, c t The unit stores the vector, W * and b * etc. are network parameters.

[0108] Dual LSTM Neural Network Output They represent the knowledge state of the test question and the knowledge state of the concept respectively, and then go through a linear layer for dimension conversion, as follows:

[0109]

[0110] Where W * ,b * is a trainable parameter. The dimension is Where m is the number of test questions; The dimension is Where n is the number of concepts.

[0111] According to the students' knowledge status of the test questions and the state of knowledge of concepts Add the two together and take the average to get the multi-source knowledge state of the learner at time step t-1

[0112]

[0113] (3-3) Learner Performance Prediction

[0114] By using to predict the learner's response to the next exercise. After a Sigmoid function, the predicted probability is generated Use binary cross entropy calculation and response a t The loss between them is:

[0115]

[0116] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

[0117] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A knowledge tracking method based on learning representations of heterogeneous entity multi-association graphs, Features The method comprises the following steps: (1) Representation learning of heterogeneous entity multi-association graph: Construct a heterogeneous entity multi-association graph and extract (entity, association, entity) triples and association weight matrices. Entities include test questions and concepts, and associations include relevant associations between test questions and concepts, similar associations and prerequisite associations between test questions, and similar associations and prerequisite associations between concepts. Use the triple representation learning method to obtain dense representations of test questions and concepts. Specifically: (1-1) Construct a heterogeneous entity multi-association graph to mine the prerequisite associations and similar associations between test questions and concepts from the learners' response data; there are multiple associations between test questions and concepts: relevant associations between test questions and concepts, similar associations and prerequisite associations between test questions, and similar associations and prerequisite associations between concepts, where the relevant associations between test questions and concepts are manually annotated in the dataset, and the similar associations and prerequisite associations between test questions and concepts are mined from the learners' response data; (1-1-1) Mining prerequisite and similar relationships between concepts: First, construct a concept correct matrix U c , U c is a count matrix, calculated as follows: in represents the number of correct answers to concept j after the correct answer to concept i; Construct a concept prerequisite matrix T c , represents whether there is an implicit prerequisite relationship between concepts. First, the concept transfer matrix is ​​calculated where i≠j; otherwise, it is 0, represents the probability of one-way propagation from concept i to concept j; then, if set up Otherwise, it is 0, where the threshold is set to The average value of , and in order to maintain the DAG of the graph, the loop is deleted; Construct a concept similarity matrix O c , represents whether there is an implicit similarity between concepts. First, the concept concurrency matrix is ​​calculated Where ε = 0.1, and then use the maximum and minimum scale method to Expand and get is the probability of bidirectional communication between concept i and concept j; finally, if set up Otherwise, it is 0, where the threshold is set to The average value of (1-1-2) Use the same method as step (1-1-1) to construct the correct matrix U of the test questions. q , the test question prerequisite matrix T q , and the test similarity matrix O q , to extract the implicit associations between test questions; (1-1-3) Through steps (1-1-1) and (1-1-2), a heterogeneous entity multi-association graph is constructed; (1-2) Extracting triples and association weight matrices. For a heterogeneous entity multi-association graph, each edge in the graph is converted into a triple (h, r, t); (1-3) Triplet representation learning, by optimizing the transformation principle To learn the representation of each entity and association, h , and They are the representations of h, r, and t respectively; It is a projection representation in the association r space. Given a triple (h, r, t), the entity is first projected into the association-specific space, that is: Here M r ∈R k×d is the projection matrix from the entity space to the association space of r, then the likelihood score formula is defined as: The loss function is as follows: in, (h, r, t′) is a constructed triplet, which is constructed by randomly replacing an entity in a real triplet; σ(·) is the sigmoid activation function; (2) Knowledge propagation based on the associative attention mechanism: The associative attention mechanism is used to aggregate the representations of multi-hop entities and solve the problem that different associations should have different aggregation weights, thereby realizing knowledge propagation between different associations; (3) Multi-source knowledge state learning based on dual LSTM: Based on dual LSTM, the learner’s knowledge state on the test questions and the knowledge state on the concepts are modeled separately to predict the correctness of the learner’s answer.

2. The knowledge tracking method based on heterogeneous entity multi-association graph representation learning according to claim 1, Features Step (1-2) extracts the triples and association weight matrix. For a heterogeneous entity multi-association graph, each edge in the graph is converted into a triple (h, r, t), specifically: The association weight matrix is ​​a two-dimensional matrix used to record the association weights between each entity in the graph. In the association weight matrix, each row and column corresponds to an entity, and each element in the matrix represents the strength of the association between two entities. First, for each association, construct an (n+m)*(n+m) adjacency matrix Where r represents one of the above relationships, calculated as follows: Next, construct a degree matrix D r , the calculation formula is as follows: Calculate the normalized Laplace matrix to get the associated weight matrix A r .

3. The knowledge tracking method based on heterogeneous entity multi-association graph representation learning according to claim 2, Features The Laplace algorithm in step (1-2) includes: Symmetric Normalized Laplace Algorithm: Or the random walk normalized Laplace algorithm: Among them, I is the identity matrix.

4. The knowledge tracking method based on heterogeneous entity multi-association graph representation learning according to claim 1, Features The knowledge propagation based on the associative attention mechanism described in step (2) first implements a single-layer propagation, which consists of three components: knowledge propagation, knowledge-aware attention, and knowledge aggregation, and then generalizes it to multiple layers; specifically: (2-1) Knowledge dissemination, an entity participates in multiple triples, where entities include test questions and concepts; for an entity h, calculate the self-network representation of h: in Controls the weight of propagation on each triple (h, r, t), indicating how much important knowledge should be propagated from t to h under association r; (2-2) Knowledge-aware attention, achieved through associative attention mechanism The update is as follows: Among them, tanh is selected as the nonlinear activation function; After that, the softmax function is used to normalize the coefficients of all triplets involved in h: (2-3) Knowledge aggregation, representing entities h and its ego network representation Aggregate as a new representation of entity h, more specifically: Use an aggregator to implement f(·); (2-4) High-order propagation, further stacking more propagation layers to learn high-order connectivity information and collect knowledge propagated from high-level neighbor entities. Specifically, in step l, the representation of an entity is recursively expressed as: Here, the knowledge propagated in the ego-network representation of entity h is defined as follows: is the representation of entity t generated by the previous knowledge propagation step, and the memory is passed to this entity from its (l-1)-layer neighbors; during the initial information propagation iteration, Set to e h .

5. The knowledge tracking method based on heterogeneous entity multi-association graph representation learning according to claim 4, Features The aggregator in step (2-3) includes: GCN aggregator: Add the two representations together and apply a non-linear transformation as follows: Among them, the activation function set is set to LeakyReLU; is a trainable weight matrix to extract useful knowledge information for dissemination, and d′ is the transformation size; GraphSage Aggregator: concatenates two representations and then applies a non-linear transformation: Bi-Interaction Aggregator: Consider e h and The two feature interactions between are as follows: in, is a trainable weight matrix and ⊙ is an element-wise product.

6. The knowledge tracking method based on heterogeneous entity multi-association graph representation learning according to claim 1, Features The multi-source knowledge state learning module based on dual LSTM in step (3) consists of three parts, including: fusion knowledge representation and interactive projection, multi-source knowledge state fusion based on dual LSTM, and learner performance prediction; specifically: (3-1) Fusion of knowledge representation and interactive projection to represent test questions q and conceptual representation c Perform aggregation to obtain the fused knowledge representation v; Distinguish between correct and incorrect answers, multiply v by the response a and concatenate them to get the interaction vector x: Where a∈R d , x∈R 2d ; (3-2) Multi-source knowledge state fusion based on dual LSTM: Based on dual LSTM, the learner’s knowledge state on the test questions and the knowledge state on the concepts are modeled separately; the details are as follows: The learner’s hidden knowledge state h at step t t According to the current input and the previous state h t =LSTM(x t ,h t-1 ; θ) is updated as: i t =σ(W xi x t +W hi h t-1 +b i ), f t =σ(W xf x t +W hf h t-1 +b f ), o t =σ(W xo x t +W ho h t-1 +b o ), c t =f t c t-1 +i t tanh(W xc x t +W hc h t-1 +b c ) h t =o t fishy t ) where i t ,f t ,o t are the input, forget and output gates respectively, c t The unit stores the vector, W * and b * is the network parameter; Dual LSTM Neural Network Output They represent the knowledge state of the test question and the knowledge state of the concept respectively, and then go through a linear layer for dimension conversion, as follows: Where W * ,b * is a trainable parameter, and the obtained The dimension is Where m is the number of test questions; The dimension is Where n is the number of concepts; According to the learner's knowledge status of the test questions and the state of knowledge of concepts Add the two together and take the average to get the multi-source knowledge state of the learner at time step t-1 (3-3) Learner performance prediction, by using to predict the learner's response to the next exercise, After a Sigmoid function, the predicted probability is generated Use binary cross entropy calculation and response a t The loss between them is:

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