Personalized learning path recommendation method based on knowledge relation mining and graph embedding driving

Abstract

The invention belongs to the technical field of recommendation algorithms, and discloses a personalized learning path recommendation method based on knowledge relation mining and graph embedding driving, and the method comprises the following specific steps: 1, mining a knowledge point dependency relation, constructing a weighted directed graph, carrying out the data analysis on public data sets ASSISTments and Junyi, and carrying out the data analysis on the public data sets ASSISTments and Junyi; the implicit dependency relationship among knowledge points is mined through an improved Apriori algorithm, time dynamics and sequential dependency characteristics in the learning process are fully considered, and a weighted directed graph among the knowledge points is constructed according to the mined dependency relationship and the weight of the mined dependency relationship. According to the method, the implicit dependency relationship between the knowledge points is mined through an innovative method, the weighted directed graph is constructed, and a graph embedding technology is integrated into a recommendation model in combination with a unique self-defined embedding layer, so that compared with an existing recommendation method based on a simple association rule or a shallow network, the method has the advantages that the recommendation efficiency is improved; the mining and expression ability of the complex logic relation between the knowledge points is remarkably improved, and the recommendation omission rate of the sparse knowledge points can be effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of recommendation algorithms, and specifically provides a personalized learning path recommendation method based on knowledge relationship mining and graph embedding drive. Background Art

[0002] In the current research on learning path recommendation algorithms, there are already a variety of technical means to achieve personalized learning path design. Among them, a common method is to generate recommended paths based on knowledge graphs through pre-set constraint rules. This method uses the logical relationship between knowledge points to provide students with a structured learning sequence; another widely used technology is based on students' historical learning sequences, combined with long short-term memory networks (LSTMs) to predict the concepts that students should learn next. This method attempts to dynamically infer students' learning needs by analyzing their learning behavior patterns. In recent years, knowledge tracking technology has gradually been introduced into the field of learning path recommendation. This technology can evaluate students' mastery of the current recommended knowledge points in real time, and adjust subsequent learning paths based on this. Many studies have attempted to combine knowledge tracking with learning path recommendation models in order to more accurately reflect students' learning status and optimize recommendation effects.

[0003] However, the above methods have the following problems: the learning path recommendation method based on knowledge point graphs relies too much on predefined knowledge constraints, making it difficult to flexibly adapt to the learners' personalized needs, limiting its application effect in diverse learning scenarios; deep learning-based methods (such as LSTM and GRU) only consider students' learning preferences, ignore the relationship between knowledge points, and have high computational complexity, which affects large-scale real-time applications; some methods use Transformer to explore the relationship between knowledge points and integrate the DKT knowledge tracking module to predict students' mastery of concepts, but the logical relationship between knowledge points is complex, and it is difficult to reveal its deep cognitive structure by relying solely on native attention mechanisms and neural networks. Therefore, it is necessary to introduce knowledge graphs and graph embedding technologies to enhance the ability to explore the relationship between knowledge points. Summary of the Invention

[0004] The purpose of the present invention is to provide a personalized learning path recommendation method based on knowledge relationship mining and graph embedding drive to solve the problems raised in the above background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a personalized learning path recommendation method based on knowledge relationship mining and graph embedding drive, the specific steps are as follows:

[0006] Step 1: Mining knowledge point dependencies and building a weighted directed graph

[0007] Data analysis is carried out on the public datasets ASSISTments and Junyi. The improved Apriori algorithm is used to mine the implicit dependencies between knowledge points, fully considering the time dynamics and sequential dependence characteristics in the learning process. According to the mined dependencies and their weights, a weighted directed graph between knowledge points is constructed to accurately represent the knowledge structure of the learning field;

[0008] Step 2: Generate knowledge point vector representations based on graph embedding

[0009] Based on the weighted directed graph constructed in the previous step, the DGI algorithm is used for graph embedding processing to generate dense vector representations for each knowledge point. These vector embeddings effectively capture the structural attributes and relationship characteristics of knowledge points in the learning field, laying a foundation for subsequent processing;

[0010] Step 3: Knowledge graph enhanced neural network embedding and Transformer processing

[0011] Using the dense vectors of knowledge points generated in Step 2, a neural network embedding layer is designed to assign a unique integer index to each knowledge point and map it to a low-dimensional vector representation to form a semantic representation. Subsequently, these vectors are input into the Transformer architecture and processed through an optimized attention mechanism to capture the deep semantic associations and cognitive structures between knowledge points, exploring complex knowledge dependence patterns and hierarchical relationships;

[0012] Step 4: Design and generate a personalized learning path recommendation model

[0013] Define the candidate knowledge point set S = [s1, s2, s3, …, sm] (m < n). Map it to the embedding vector set X = [x1, x2, x3, …, xm] through the embedding layer to obtain the low-dimensional semantic representation of knowledge points. Use an improved Transformer architecture to further mine the deep associations between knowledge points, optimize the attention mechanism to enhance the sensitivity to sparse or weakly associated knowledge points. Then design a long short-term memory network (LSTM) to model the student's historical answering sequence and dynamically capture the time dependence of learning behaviors. Input the knowledge point vectors output by the Transformer, the long short-term memory network (LSTM) state vectors, and the predefined learning objectives into a multi-layer perceptron (MLP), and achieve accurate concept selection through joint optimization. Finally, generate a personalized learning path that takes into account both knowledge dependence and individual differences.

[0014] As a preferred technical solution of the present invention, in step one, the Apriori algorithm introduces a minimum confidence threshold as a sequence constraint condition. For the knowledge point pair C1→C2, a directed association is established only when its confidence exceeds the preset threshold, and the directionality of the knowledge point association is ensured to conform to the learning and cognitive laws through confidence constraint; in order to capture temporal proximity and statistical significance in the knowledge point association, a double-weighting method combining a sliding window mechanism and a confidence value is introduced. For a sequence of length n, a fixed window length w (w < n) is defined to analyze local relationships, and at the same time, the confidence score of each valid pair is calculated.

[0015] As a preferred technical solution of the present invention, the final weight of the knowledge point association is determined by two factors:

[0016] Weight based on distance:

[0017]

[0018] where d represents the distance between points within the window length w, and only the point pairs within the window length w are considered;

[0019] Weight based on confidence:

[0020] weight c (C1→C2) = confidence(C1→C2) = P(C2|C1)

[0021] = support(C1∪C2) / support(C1)

[0022] which reflects the statistical strength of the association;

[0023] Then the formula for calculating the final edge weight is:

[0024] weight final (C1→C2) = α * weight d * weight c

[0025] where α is a normalization factor to ensure that the weight falls within the range of [0, 1].

[0026] As a preferred technical solution of the present invention, the DGI algorithm described in step two achieves unsupervised knowledge point learning by maximizing the mutual information between the global graph representation and the local node representation. The purpose of the graph embedding in step two is to ensure that adjacent nodes in the graph have closer representations in the embedding space. During the graph embedding process, the target embedding vector representation is learned by maximizing the objective function:

[0027]

[0028] Among them, N i Represents knowledge point e i The neighborhood node set, σ(·) is the sigmoid function, e vi and e vk It is knowledge point V i and V k The embedding vector of .

[0029] As a preferred technical solution of the present invention, the knowledge graph-enhanced neural network described in step 3 enhances attention to sparse knowledge points by adjusting the weight distribution in the attention mechanism, that is, using relative position encoding to integrate the weights between knowledge points in the knowledge graph into the attention mechanism of the Transformer:

[0030]

[0031] In order to emphasize the importance of knowledge points in the attention mechanism, the weight of the knowledge point graph is introduced into the calculation of the attention score, where R i,j is the relationship embedding between knowledge points i and j in the knowledge point graph:

[0032]

[0033] α i,j =SoftMax(Score i,j )

[0034] Q i =X i W Q , K i =X i W K , V i =X i W V

[0035] W Q , W K , W V is the trainable matrix, d is the embedding layer vector dimension, It is the vector representation of the knowledge point obtained through the attention mechanism layer, which is used for the subsequent task of path recommendation.

[0036] As a preferred technical solution of the present invention, the personalized learning path recommendation model described in step 4 has three main structures: Transformer, long short-term memory network (LSTM) and custom embedding layer. Transformer is used to explore knowledge structure, long short-term memory network (LSTM) is used to memorize students' learning sequences, and the embedding layer is an embedding layer made by all the knowledge point vectors C = [Cv1, Cv2, Cv3, Cv4, ..., Cvn] obtained above. When the long short-term memory network (LSTM) memorizes and updates the state, the initial state is the student's historical learning concept H = [H1, H2, ...Ht], and H is represented by a vector obtained through the embedding layer. stsates0 represents the initial state:

[0037]

[0038] Since the candidate set S is screened and sorted to obtain a suitable path to recommend to the student, the generated path is π={π1,π2,...,πm}. Assuming that the recommendation has reached step i, (i<=m), then π={π1,π2,...,πi-1}, then the current state of the long short-term memory network (LSTM) is:

[0039]

[0040] As a preferred technical solution of the present invention, the predefined learning target input in step 4 is a multi-layer perceptron (MLP) layer. When the learning target T = {t1, t2, ...} is input, the embedding vector of the candidate set knowledge point is And the probability of generating knowledge points after the state of the long short-term memory network (LSTM) is:

[0041]

[0042] out=softmax(prob)

[0043] P(πi)=argmax(out)

[0044] in, It represents the vector representation of the target concept obtained through embedding. w1, W1, and W2 are all learnable matrices. Softmax is the activation function, and argmax selects the one with the highest probability from m probabilities.

[0045] As a preferred technical solution of the present invention, when the personalized learning path recommendation model described in step 4 is used, in order to obtain immediate feedback, the knowledge tracking auxiliary module (KT) is trained as the student's mastery of the concept, and the following definition is defined:

[0046]

[0047] Among them, E e and E b represents the students’ mastery of the target concepts before and after the path π, E sup Represents the upper limit of mastery.

[0048] As a preferred technical solution of the present invention, the E T As a reward in reinforcement learning, the policy gradient loss is defined as:

[0049]

[0050] The beneficial effects of the present invention are as follows:

[0051] 1. This invention uses an innovative method to mine the implicit dependencies between knowledge points and construct a weighted directed graph. It then integrates graph embedding technology into the recommendation model through a unique custom embedding layer. Compared with existing recommendation methods based on simple association rules or shallow networks, this method significantly improves the ability to mine and express complex logical relationships between knowledge points. In particular, in learning scenarios with complex knowledge structures, it can effectively reduce the recommendation omission rate of sparse knowledge points, demonstrating higher applicability and accuracy.

[0052] 2. This invention highly integrates the graph embedding layer with the deep learning network. It generates low-dimensional semantic representations of knowledge points through a custom embedding layer and combines it with the long short-term memory network (LSTM) to accurately capture the temporal dependencies of students' learning sequences. Compared with existing static recommendation models or path planning that relies solely on rules, it can dynamically optimize the priority and content of learning paths, significantly improving the accuracy and adaptability of personalized recommendations, and overcoming the limitations of traditional methods that lack support for the dynamic nature of student behavior.

[0053] 3. The present invention innovatively incorporates knowledge point graph constraints into the Transformer architecture, designs a knowledge graph-enhanced attention module, and embeds the knowledge point relationship weights generated by graph embedding into the attention mechanism. Compared with existing recommendation schemes that lack knowledge structure constraints or dynamic feedback, it can ensure the high consistency between the recommended path and the logical dependencies of the knowledge points in real time, and realize dynamic adjustment of the path through reinforcement learning and knowledge tracking feedback, significantly enhancing the adaptability to changes in students' learning behavior. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a structural diagram of the model of the present invention;

[0055] Figure 2 It is a weighted directed graph of the present invention. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] like Figures 1 to 2 As shown, the embodiment of the present invention provides a personalized learning path recommendation method based on knowledge relationship mining and graph embedding drive, and the specific steps are as follows:

[0058] Step 1: Mining knowledge point dependencies and building a weighted directed graph

[0059] We conducted data analysis on the public datasets ASSISTments and Junyi. We used an improved Apriori algorithm to mine implicit dependencies between knowledge points, fully considering the temporal dynamics and sequential dependency characteristics of the learning process. Based on the mined dependencies and their weights, we constructed a weighted directed graph between knowledge points to accurately represent the knowledge structure of the learning domain.

[0060] Step 2: Generate knowledge point vector representation based on graph embedding

[0061] Based on the weighted directed graph constructed in the previous step, the DGI algorithm is used for graph embedding processing to generate dense vector representations for each knowledge point. These vector embeddings effectively capture the structural attributes and relational characteristics of knowledge points in the learning domain, laying the foundation for subsequent processing;

[0062] Step 3: Knowledge Graph Enhanced Neural Network Embedding and Transformer Processing

[0063] Using the dense vectors of knowledge points generated in step 2, we design a neural network embedding layer that assigns a unique integer index to each knowledge point and maps it to a low-dimensional vector representation to form a semantic representation. These vectors are then fed into the Transformer architecture and processed through an optimized attention mechanism to capture the deep semantic connections and cognitive structures between knowledge points, exploring complex knowledge dependency patterns and hierarchical relationships.

[0064] Step 4: Design and generate a personalized learning path recommendation model

[0065] Define the candidate knowledge point set S = [s1, s2, s3, …, sm] (m < n). Map it to the embedding vector set X = [x1, x2, x3, …, xm] through the embedding layer to obtain the low-dimensional semantic representation of the knowledge points. Adopt an improved Transformer architecture to further explore the deep correlation between knowledge points, optimize the attention mechanism to enhance the sensitivity to sparse or weakly correlated knowledge points. Then design a long short-term memory network (LSTM) to model the student's historical answering sequence, dynamically capture the time dependence of learning behaviors, and input the knowledge point vector output by the Transformer, the long short-term memory network (LSTM) state vector, and the predefined learning objective into a multi-layer perceptron (MLP). Through joint optimization, achieve accurate concept selection, and finally generate a personalized learning path that takes into account both knowledge dependence and individual differences.

[0066] The present invention constructs an accurate personalized learning path recommendation model by integrating the knowledge relationship mining of knowledge graph embedding, the graph-enhanced Transformer structure, the path recommendation of long short-term memory network (LSTM) and reinforcement learning, and the dynamic optimization of the knowledge tracking module. This method can not only effectively capture the cognitive correlation and structural dependence between knowledge points, but also dynamically adjust the recommended path according to the basic differences and real-time feedback of students, thereby significantly improving the personalization accuracy and adaptability of the learning path, and providing more optimized learning support for students with different bases. Figure 1 In the initial candidate set S, the vector representation of knowledge points is formed through a custom embedding layer. The Transformer explores the relationship between knowledge points and finally generates the final vector representation of knowledge points. In the decoder module, H represents the student's historical learning sequence, T represents the target concept to be learned, and the predefined learning objective is input into the multi-layer perceptron (MLP) to generate and rank the learning path π based on the combination of the above information.

[0067] Among them, the Apriori algorithm in step one introduces the minimum confidence threshold as the sequence constraint condition. For the knowledge point pair C1 → C2, a directed association is established only when its confidence exceeds the preset threshold, and the directionality of the knowledge point association is ensured to conform to the learning cognitive law through the confidence constraint. In order to capture the temporal proximity and statistical significance in the knowledge point association, a double-weighting method combining the sliding window mechanism and the confidence value is introduced. For a sequence of length n, a fixed window length w (w < n) is defined to analyze the local relationship, and at the same time, the confidence score of each valid pair is calculated.

[0068] The ordinary Apriori algorithm cannot fully explore the deep logical relationships of knowledge points. However, by introducing the minimum confidence threshold as a sequence constraint and introducing a double-weighted method combining the sliding window mechanism and the confidence value, it can fully explore the deep logical relationships of knowledge points. At the same time, for the generated knowledge points, manual inspection is performed to specifically observe whether they conform to the logical relationships of the knowledge points, thereby ensuring the validity of the knowledge points.

[0069] The final weight of the knowledge point association is determined by two factors:

[0070] Distance-based weighting:

[0071]

[0072] Among them, d represents the distance between points within the window length w, and only point pairs within the window length w are considered;

[0073] Confidence-based weighting:

[0074] weight c (C1→C2)=confidence(C1→C2)=P(C2|C1)

[0075] =support(C1∪C2) / support(C1)

[0076] reflects the statistical strength of the association;

[0077] The final edge weight calculation formula is:

[0078] weight final (C1→C2)=α*weight d *weight c

[0079] Here, α is a normalization factor that ensures the weights fall within the range [0, 1].

[0080] Through the above methods, the logical relationship between knowledge points can be determined. With this logical relationship, a weighted directed graph can be constructed, such as Figure 2 The knowledge point relationship graph G(V,E) in the dataset is shown in Figure 2, where the node set V represents all the knowledge points, the edge set E represents the associations between these knowledge points, and the edge weights reflect the strength of the relationship between them.

[0081] The DGI algorithm in step 2 achieves unsupervised knowledge point learning by maximizing the mutual information between the global graph representation and the local node representation. The purpose of graph embedding in step 2 is to ensure that adjacent nodes in the graph have closer representations in the embedding space. In the process of graph embedding, the target embedding vector representation is learned by maximizing the objective function:

[0082]

[0083] Among them, N i Represents knowledge point e i The neighborhood node set, σ(·) is the sigmoid function, e vi and e vk It is knowledge point V i and V k The embedding vector of .

[0084] The DGI algorithm can effectively capture the topological structure and weight information between knowledge points while maintaining good interpretability. These vectors provide rich representative information for subsequent learning and reasoning tasks. By maximizing the objective function to learn the target embedding vector representation, it ensures that related knowledge points have similar representations in the embedding space, enabling the model to better capture the implicit relationships between knowledge points. After obtaining the vector representations of the knowledge points through the above methodology, these vectors are subsequently embedded in the personalized learning path recommendation model.

[0085] The knowledge graph-enhanced neural network in step 3 enhances attention to sparse knowledge points by adjusting the weight distribution in the attention mechanism. That is, relative position encoding is used to integrate the weights between knowledge points in the knowledge graph into the attention mechanism of the Transformer:

[0086]

[0087] In order to emphasize the importance of knowledge points in the attention mechanism, the weight of the knowledge point graph is introduced into the calculation of the attention score, where R i,j is the relationship embedding between knowledge points i and j in the knowledge point graph:

[0088]

[0089] α i,j =SoftMax(Score i,j )

[0090] Q i =X i W Q , K i =X i W K , V i =X i W V

[0091] W Q , W K , W Vis the trainable matrix, d is the embedding layer vector dimension, It is the vector representation of the knowledge point obtained through the attention mechanism layer, which is used for the subsequent task of path recommendation.

[0092] Figure 2 It can be seen that By visualizing the data in a two-dimensional coordinate system using the T-SNE dimensionality reduction method, we can clearly see that knowledge points with close logical relationships are well clustered together.

[0093] Among them, the personalized learning path recommendation model in step 4 has three main structures: Transformer, Long Short-Term Memory Network (LSTM), and custom embedding layer. Transformer is used to explore knowledge structure, Long Short-Term Memory Network (LSTM) is used to memorize students' learning sequences, and the embedding layer is made by using all the knowledge point vectors C = [Cv1, Cv2, Cv3, Cv4, ..., Cvn] obtained above. When the Long Short-Term Memory Network (LSTM) memorizes and updates the state, the initial state is the student's historical learning concept H = [H1, H2, ...Ht]. H is represented by the vector after the embedding layer. states0 represents the initial state:

[0094]

[0095] Since the candidate set S is screened and sorted to obtain a suitable path to recommend to the student, the generated path is π={π1,π2,...,πm}. Assuming that the recommendation has reached step i, (i<=m), then π={π1,π2,...,πi-1}, then the current state of the long short-term memory network (LSTM) is:

[0096]

[0097] The concept recommended at each step needs to be added to the long short-term memory network (LSTM) network for state update to select the appropriate concept for the next step.

[0098] Among them, the predefined learning target in step 4 is input into the multi-layer perceptron (MLP) layer. When the learning target T = {t1, t2, ...} is input, the embedding vector of the candidate set knowledge point is And the probability of generating knowledge points after the state of the long short-term memory network (LSTM) is:

[0099]

[0100] out=softmax(prob)

[0101] P(πi)=argmax(out)

[0102] in, It represents the vector representation of the target concept obtained through embedding. w1, W1, and W2 are all learnable matrices. Softmax is the activation function, and argmax selects the one with the highest probability from m probabilities.

[0103] The concept recommended above sets the probability to 0 at the corresponding location to avoid path duplication.

[0104] Among them, when the personalized learning path recommendation model in step 4 is used, in order to obtain immediate feedback, the knowledge tracking auxiliary module (KT) is trained as the student's mastery of the concept, and the definition is:

[0105]

[0106] Among them, E e and E b represents the students’ mastery of the target concepts before and after the path π, E sup Represents the upper limit of mastery.

[0107] E e and E b The score is obtained by using the Knowledge Tracking (KT) auxiliary module as the examination environment.

[0108] Among them, E T As a reward in reinforcement learning, the policy gradient loss is defined as:

[0109]

[0110] Through the knowledge tracking auxiliary module (KT), students' feedback on concepts is introduced in real time, and the adaptability and accuracy of the recommended path are dynamically optimized, thereby providing students with different foundations with accurate and personalized learning path recommendations that better meet their individual needs.

[0111] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0112] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A personalized learning path recommendation method based on knowledge relationship mining and graph embedding, characterized by: The specific steps are as follows: Step 1: Mining knowledge point dependency relationships and constructing a weighted directed graph Perform data analysis on the public datasets ASSISTments and Junyi. Use the improved Apriori algorithm to mine the implicit dependency relationships between knowledge points, fully considering the time dynamics and sequential dependency characteristics in the learning process. Based on the mined dependency relationships and their weights, construct a weighted directed graph between knowledge points to accurately represent the knowledge structure of the learning domain; Step 2: Generating knowledge point vector representations based on graph embedding Based on the weighted directed graph constructed in Step 1, use the DGI algorithm for graph embedding processing to generate dense vector representations for each knowledge point. These vector embeddings effectively capture the structural attributes and relationship characteristics of knowledge points in the learning domain, laying a foundation for subsequent processing; Step 3: Knowledge graph enhanced neural network embedding and Transformer processing Utilize the dense vectors of knowledge points generated in Step 2 to design a neural network embedding layer, assign a unique integer index to each knowledge point and map it to a low-dimensional vector representation to form a semantic representation. Subsequently, input these vectors into the Transformer architecture and process them through the optimized attention mechanism to capture the deep semantic associations and cognitive structures between knowledge points, and explore complex knowledge dependency patterns and hierarchical relationships; Step 4: Designing and generating a personalized learning path recommendation model Define the candidate knowledge point set S = [s1, s2, s3, …, sm] (m < n), map it to the embedding vector set X = [x1, x2, x3, …, xm] through the embedding layer to obtain the low-dimensional semantic representation of knowledge points. Use the improved Transformer architecture to further mine the deep correlations between knowledge points, optimize the attention mechanism to enhance the sensitivity to sparse or weakly correlated knowledge points. Then design a long short-term memory network (LSTM) to model the student's historical answering sequence, dynamically capture the time dependence of learning behaviors, and input the knowledge point vectors output by the Transformer, the long short-term memory network (LSTM) state vectors, and the predefined learning goals into a multi-layer perceptron (MLP). Through joint optimization, achieve accurate concept selection, and finally generate a personalized learning path that takes into account both knowledge dependencies and individual differences.

2. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: The Apriori algorithm described in Step 1 introduces a minimum confidence threshold as a sequence constraint condition. For the knowledge point pair C1 → C2, a directed association is established only when its confidence exceeds the preset threshold. Ensure the directionality of knowledge point associations conforms to the learning cognitive law through confidence constraints; To capture temporal proximity and statistical significance in knowledge point associations, introduce a double-weighting method that combines a sliding window mechanism and confidence values. For a sequence of length n, define a fixed window length w (w < n) to analyze local relationships, and calculate the confidence scores for each valid pair at the same time.

3. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 2 is characterized by: The final weight of the knowledge point association is determined by two factors: Distance-based weight: where d represents the distance between points within the window length w, and only consider the point pairs within the window length w; Confidence-based weight: weight c (C1→C2)=confidence(C1→C2)=P(C2|C1) =support(C1∪C2) / support(C1) reflects the statistical strength of the association; The final edge weight calculation formula is: weight final (C1→C2)=α*weight d *weight c Here, α is a normalization factor that ensures the weights fall within the range [0, 1].

4. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: The DGI algorithm described in step 2 achieves unsupervised knowledge point learning by maximizing the mutual information between the global graph representation and the local node representation. The purpose of the graph embedding described in step 2 is to ensure that adjacent nodes in the graph have closer representations in the embedding space. During the graph embedding process, the target embedding vector representation is learned by maximizing the objective function: Among them, N i Represents knowledge point e i The neighborhood node set, σ(·) is the sigmoid function, e vi and e vk It is knowledge point V i and V k The embedding vector of .

5. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: The knowledge graph-enhanced neural network described in step 3 enhances attention to sparse knowledge points by adjusting the weight distribution in the attention mechanism. That is, relative position encoding is used to integrate the weights between knowledge points in the knowledge graph into the attention mechanism of the Transformer: In order to emphasize the importance of knowledge points in the attention mechanism, the weight of the knowledge point graph is introduced into the calculation of the attention score, where R i,j is the relationship embedding between knowledge points i and j in the knowledge point graph: α i,j =Softmax(Score i,j ) Q i =X i W Q ,K i =X i W K ,V i =X i W V W Q , W K , W V is the trainable matrix, d is the embedding layer vector dimension, It is the vector representation of the knowledge point obtained through the attention mechanism layer, which is used for the subsequent task of path recommendation.

6. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: The personalized learning path recommendation model described in step 4 has three main structures: Transformer, Long Short-Term Memory Network (LSTM) and custom embedding layer. Transformer is used to explore knowledge structure, Long Short-Term Memory Network (LSTM) is used to memorize students' learning sequences, and the embedding layer is made by using all the knowledge point vectors C = [Cv1, Cv2, Cv3, Cv4, ..., Cvn] obtained above. When the Long Short-Term Memory Network (LSTM) memorizes and updates the state, the initial state is the student's historical learning concept H = [H1, H2, ...Ht], and H is represented by the vector after the embedding layer. states0 represents the initial state: Since the candidate set S is screened and sorted to obtain a suitable path to recommend to the student, the generated path is π={π1,π2,...,πm}. Assuming that the recommendation has reached step i, (i<=m), then π={π1,π2,...,πi-1}, then the current state of the long short-term memory network (LSTM) is:

7. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: The predefined learning target described in step 4 is input into the multi-layer perceptron (MLP) layer. When the learning target T = {t1, t2, ...} is input, the embedding vector of the candidate set knowledge point And the probability of generating knowledge points after the state of the long short-term memory network (LSTM) is: out=softmax(prob)) P(πi)=argmax(out) in, It represents the vector representation of the target concept obtained through embedding. w1, W1, and W2 are all learnable matrices. Softmax is the activation function, and argmax selects the one with the highest probability from m probabilities.

8. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 1 is characterized by: When using the personalized learning path recommendation model described in step 4, in order to obtain immediate feedback, the knowledge tracking auxiliary module (KT) is trained as the student's mastery of the concept, and the following definition is given: Among them, E e and E b represents the students’ mastery of the target concepts before and after the path π, E sup Represents the upper limit of mastery.

9. The personalized learning path recommendation method based on knowledge relationship mining and graph embedding according to claim 8 is characterized by: The E T As a reward in reinforcement learning, the policy gradient loss is defined as:

Images