A learning path recommendation method based on deep heterogeneous learning and topology perception

Abstract

The application belongs to the technical field of learning path recommendation, and discloses a learning path recommendation method based on deep heterogeneous learning and topology perception. First, a prerequisite concept map is constructed to learn a concept prerequisite representation containing prerequisite dependency relationships. On this basis, a heterogeneous graph integrating three types of entities, namely students, questions and concepts, is constructed, and the concept prerequisite representation is taken as an initial representation of a concept node in the graph. In order to fully mine long-range dependency relationships in the heterogeneous graph, effectively extract interaction information and avoid over-smoothing and information squeezing problems in representation learning, a Graph Transformer module for heterogeneous graph representation learning is designed to obtain a comprehensive representation of the concept node. In the path generation stage, a candidate concept set is screened based on a maximum-minimum greedy strategy, and the sampled path is optimized as a whole from the perspective of sequence modeling, so that the search efficiency is effectively improved while the semantic integrity of the knowledge structure is maintained.

Description

Technical Field

[0001] This invention belongs to the field of learning path recommendation technology, and specifically relates to a learning path recommendation method based on deep heterogeneous learning and topology awareness. Background Technology

[0002] As smart education gradually becomes a hot topic of concern across all sectors of society, online learning platforms and educational resources are becoming increasingly abundant. How to plan personalized learning paths that align with learners' cognitive states and developmental needs from this vast pool of resources has become an important research direction in the field of smart education. The goal of learning path recommendation is to generate a sequence of concept learning tailored to individual needs through collaborative modeling of knowledge concept dependencies, learner ability evolution, and historical learning trajectories, thereby improving learning efficiency and knowledge acquisition. Traditional learning path recommendation paradigms generally employ a step-by-step recommendation strategy, requiring students to respond to recommended concepts in real time and dynamically plan paths based on immediate feedback. However, this method lacks a holistic consideration of long-term learning benefits and fails to uncover the overall knowledge structure, easily leading to local convergence and making it difficult to guarantee students' overall benefits. Concepts generally exhibit prerequisite dependencies, commonalities, or other implicit associations. Effective modeling in concept representation, enhancing the model's perception of knowledge structures, will significantly improve model performance. Therefore, existing research attempts to model the intrinsic relationships between concepts when generating learning paths and combines knowledge tracing technology to dynamically simulate students' cognitive states, generating a complete learning path in an end-to-end manner. These methods can not only guide students' cognitive development process in a reasonable way, but also respond to the dynamic evolution of students' abilities in real time. Compared with traditional recommendation strategies, they have obvious advantages in terms of modeling depth and adaptability.

[0003] Learning path recommendation tasks demand a high degree of sophistication in knowledge concept representation. Both accurate assessment of student abilities and generation of personalized paths following knowledge logic require high-quality semantic representations of concepts. Therefore, improving the accuracy of knowledge concept modeling has gained increasing attention. Due to the sequential nature of learning path recommendation tasks, some studies employ Transformer structures to capture complex dependencies between concepts. Furthermore, given the inherent advantages of graph structures in constructing knowledge structures, some works have introduced graph neural networks to mine diverse semantic associations between concepts. While these methods have achieved good results, they still have limitations. In real-world scenarios, the associations between students, questions, and concepts exhibit a significantly sparse distribution, with students and concepts only indirectly connected through questions. The connections between concepts are even more complex, including short-range paths linked by questions (e.g., concept-question-concept) and long-range paths where students and questions alternate (e.g., concept-question-student-question-concept). If the semantic coverage of the learning representation is insufficient, the concept representation will only be effective within a local context, and the recommendation effect will be significantly weakened for students or concepts with sparse interaction records. While Transformers can effectively capture long-range dependencies in a sequence of concepts, they are prone to diluting the semantics of the concepts themselves during contextual interactions. Graph neural networks can preserve the semantic features of nodes during message passing, but they struggle to effectively model long-range dependencies in graphs.

[0004] Therefore, to improve the model's ability to characterize concepts during the encoding stage, and to accurately reflect whether a concept truly meets the needs of students, thereby effectively improving the overall learning benefits of the path, current research still faces two challenges: (1) How to make concept representation learning based on comprehensive and accurate association mining, so that the model can naturally consider the existing knowledge structure when generating learning paths. Concepts do not exist in isolation. In the learning process, there are often collaborative signals between different concepts, which increases the complexity of representation learning. Existing methods have failed to effectively and naturally integrate the association information between concepts into the representation learning process, making it difficult for the final representation to take into account the semantic features between concepts and the semantic features of the concepts themselves. (2) How to effectively integrate the feature information of students and questions into the concept modeling process, so that the model can perceive the students' answering patterns and their interactive semantics with questions from the concept level, thereby enhancing the personalized ability of learning path recommendation. In particular, there are significant differences in the association between different students and questions with the same concept. Therefore, in the representation learning process, it is necessary to adaptively distinguish the role and importance of the above associations. Existing methods model the three entities of students, questions, and concepts in a decentralized manner, lacking attention to the collaborative relationship between heterogeneous entities. The two challenges mentioned above essentially point to a core issue: how to maximize the absorption of effective information from interactive data during representation learning in order to meet the requirements of sufficient concept representation for learning path recommendation.

[0005] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art. Summary of the Invention

[0006] The purpose of this invention is to propose a learning path recommendation method based on deep heterogeneous learning and topology awareness. By constructing a prerequisite concept graph, it learns the prerequisite representation of concepts that contain prerequisite dependencies, and performs representation learning through Graph Transformer to obtain a more semantically rich comprehensive representation of concept nodes. On this basis, it designs a screening method for candidate concept sets by combining students' answer history and comprehensive representation of concept nodes, and recommends a more suitable learning path that conforms to students' cognitive growth.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A learning path recommendation method based on deep heterogeneous learning and topology awareness includes the following steps: Step 1. Construct a directed prior relation graph to generate conceptual prior representations that imply prior dependencies; Step 2. Construct a heterogeneous graph that integrates three types of entities: students, questions, and concepts. ; in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories; The obtained concept pre-modification representation is used as a graph. The initial representation of the conceptual nodes; For the graph For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question. Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set; The Graph Transformer module HCGT, designed for heterogeneous graph representation learning, has the following processing flow: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node. Step 3. Based on the comprehensive representation of all concept nodes obtained in Step 2, design a candidate path generation method to select a set of candidate concepts that are both representative and have broad knowledge coverage; Based on the student's answer history and the comprehensive representation of concept nodes, the system infers the student's real-time status, thereby further filtering concepts from the candidate concept set and generating the final learning path.

[0008] Furthermore, based on the aforementioned learning path recommendation method, this invention also proposes a corresponding learning path recommendation system based on deep heterogeneous learning and topology awareness, which adopts the following technical solution: A learning path recommendation system based on deep heterogeneous learning and topology awareness includes the following modules: The concept prerequisite relation mining module is used to construct a directed prerequisite relation graph and generate a concept prerequisite representation that contains prerequisite dependencies. The concept node comprehensive representation learning module is used to construct a heterogeneous graph that integrates three types of entities: students, questions, and concepts. ; in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories; The obtained concept pre-modification representation is used as a graph. The initial representation of the conceptual nodes; For the graph For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question. Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set; The Graph Transformer module HCGT, designed for heterogeneous graph representation learning, has the following processing flow: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node. And a learning path recommendation module, which is used to design a candidate path generation method based on the comprehensive representation of all concept nodes obtained, so as to select a set of candidate concepts that are both representative and have broad knowledge coverage; Based on the student's answer history and the comprehensive representation of concept nodes, the system infers the student's real-time status, thereby further filtering concepts from the candidate concept set and generating the final learning path.

[0009] The present invention has the following advantages: As described above, this invention discloses a learning path recommendation method based on deep heterogeneous learning and topology awareness. This method first constructs a prerequisite concept graph and learns the concept prerequisite representations containing prerequisite dependencies. Based on this, a heterogeneous graph integrating three types of entities—students, questions, and concepts—is constructed, and the concept prerequisite representations are used as the initial representations of concept nodes in the heterogeneous graph. To fully explore long-range dependencies in the heterogeneous graph and effectively extract interaction information, while avoiding oversmoothing and information compression problems in representation learning, this invention also designs a GraphTransformer module (HCGT) for heterogeneous graph representation learning. The comprehensive representation of concept nodes learned through HCGT not only naturally integrates prerequisite and collaborative relationships between concepts but also preserves the semantic features of the concepts themselves. In the path generation stage, this invention uses a max-min greedy strategy to filter the candidate concept set and optimizes the sampled paths from a sequence modeling perspective, effectively improving search efficiency while maintaining the semantic integrity of the knowledge structure. The three steps in this invention work together to improve the learning path recommendation effect. First, the prerequisite concept graph learns concept representations containing knowledge dependencies, providing a foundation for path generation that conforms to the knowledge structure. Secondly, by integrating student, question, and concept information using heterogeneous graphs and the HCGT module, the concept representation simultaneously incorporates knowledge relationships and learning interaction features, enhancing the personalization of recommendations. Finally, learning paths are generated through candidate concept selection and sequence optimization, further ensuring the coherence and progression of the paths. Therefore, these three steps collectively realize a complete process from knowledge structure modeling and learning state perception to path optimization and generation, making the recommendation results more aligned with knowledge organization principles and students' cognitive needs. Attached Figure Description

[0010] Figure 1 A diagram illustrating the recommended learning path; Figure 2 This is a network architecture diagram of the learning path recommendation method based on deep heterogeneous learning and topology awareness in an embodiment of the present invention. Figure 3 This is a performance comparison chart of all methods in the experiment of this invention regarding path length; where Figure 3 (a), (b), and (c) in the figure represent the comparisons on the Assist09 dataset, the Assist12 dataset, and the SLP dataset, respectively. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 like Figure 1 As shown, this invention describes a learning path recommendation method based on deep heterogeneous learning and topology awareness, which aims to generate high-quality learning paths through concept representation learning and path optimization mechanisms.

[0012] Learning path recommendation typically comprises three core components: knowledge representation, used to encode the semantic features of concepts; ability assessment, used to model the learner's initial cognitive state; and path generation, used to construct personalized learning sequences.

[0013] In the learning path recommendation task, it is necessary not only to model the complex relationships between concepts, but also to pay attention to the role of the two types of entities, students and questions, in shaping the semantics of concepts, so that this information can be naturally integrated into the learning path recommendation process.

[0014] This invention not only captures the local features of nodes but also mines long-range dependencies in sparse graphs, thereby generating learning paths for internalized knowledge structures. Before introducing the method of this invention, a formulaic definition of learning path recommendation is first given.

[0015] For a student His historical learning sequence can be represented as .in, Including the student in Knowledge concepts to learn constantly and the degree of mastery of it. .

[0016] The goal of the learning path recommendation task is: In a given containment A set of candidate knowledge concepts In the middle, for students Recommend and generate a line of length. learning path To make it in the target Maximize learning ability.

[0017] Due to the learning gain metric It can reflect the degree of standardized improvement in students' cognitive level, and is therefore widely used to quantify the effectiveness of learning paths, as shown in the following formula: .

[0018] in, and They represent students respectively. In the learning path Before and after, the level of understanding of the target concept, This represents the theoretical upper limit of cognitive level. and All were obtained through simulation using the Knowledge Tracking Model (DKT). It was set to 1.0.

[0019] Given a student's historical learning sequence Target concept set and collection of knowledge concepts .

[0020] The specific task is to... Select These are different knowledge concepts, arranged into a learning path. Used to improve students' abilities The cognitive level above. Based on the above, the learning path recommendation task can be formally represented as: .

[0021] like Figure 2 As shown, the learning path recommendation method based on deep heterogeneous learning and topology awareness proposed in this invention consists of two parts: encoding and decoding. Its overall network architecture is as follows: Figure 2 As shown.

[0022] The encoding part mainly includes concept prior relationship mining and concept node comprehensive representation learning. The learned concept node comprehensive representation is fed into the decoding part to generate candidate paths and make the final learning path recommendation.

[0023] like Figure 2 As shown, the learning path recommendation method based on deep heterogeneous learning and topology awareness includes the following steps: Step 1. Construct a directed prior relation graph to generate conceptual prior representations that imply prior dependencies.

[0024] Discovering the connections between knowledge concepts can not only reveal the micro-logical relationships within the knowledge system, but also help to capture the macro-evolution of students' abilities, which is a key link in portraying students' cognitive structure in personalized learning.

[0025] Given that there are often significant hierarchical dependencies between different concepts within a knowledge system, and that the learning process usually needs to follow a cognitive pattern of gradual progression from simple to complex.

[0026] First, a prerequisite relation graph is constructed, and then a representation learning of knowledge concepts containing prerequisite relations is achieved through GCN.

[0027] The prerequisite relationship between concepts is defined as: if one has prior knowledge of a concept... You must first understand the concepts. Then it is called for The prerequisite concepts.

[0028] Step 1.1. Construction of the directed prior relationship graph.

[0029] The prerequisite relationships between knowledge concepts have a clear directionality and are naturally suitable for directed graph representation.

[0030] Construct a prerequisite relationship graph by using knowledge concepts as nodes and the prerequisite relationships between concepts as edges. , means as follows: ;in For a set of concept nodes, This is the set of edges to be trimmed first.

[0031] The transition probability of adjacent concepts is used as the basis for constructing the pre-trimmed edges. The process is as follows: First, construct a counting matrix based on the students' answer records. ;definition For this matrix The Middle line, number The elements of the column represent the concepts that students answered correctly. Then immediately answer the question correctly. The number of times; For the quantity of concepts.

[0032] Next, the counting matrix Perform a normalization operation to obtain the probabilistic transition matrix. .

[0033] definition Transition matrix The Middle line, number Column elements, Used to quantify student responses Then immediately answer correctly For counting matrix The Middle The sum of the elements in a row, representing The total number of times a question was answered correctly.

[0034] Then, the final transition matrix is ​​obtained through Min-Max normalization. .

[0035] definition For the final transition matrix The Middle line, number The elements of the column have the following formulas: ; in and Represents the transition matrix The maximum and minimum values ​​in the range.

[0036] Set threshold Used to filter interactions with sufficient signal strength to construct a binarized transition matrix. ;in Binary transition matrix The Middle line, number The elements of the column.

[0037] like Greater than but =1, otherwise =0; This represents the sum of all elements in the final transition matrix.

[0038] Furthermore, the prerequisites between concepts should be unidirectional; therefore, an asymmetric rule is designed to further filter the prerequisite relationships between concepts: for any pair of concepts... If and only if and Only then can As The prerequisite concepts.

[0039] Based on this, we finally obtained adjacency matrix .

[0040] definition Adjacency matrix Elements; when and hour, Otherwise Adding self-loop connections yields a matrix. Afterwards, statistics The degree matrix is ​​obtained by calculating the degree of all nodes in the matrix. .

[0041] in Represents the identity matrix. , representing the degree matrix The diagonal elements in the text.

[0042] Next, we will examine the prerequisite relationship diagram. Symmetric normalization is performed to avoid the influence of degree distribution imbalance, resulting in a symmetric normalized adjacency matrix. As shown in equation (1): (1).

[0043] Step 1.2. Directed pre-edited graph representation learning.

[0044] The goal of this section is to learn concept representations with directional semantics from an existing directed prior relationship graph between concepts. Therefore, we assign two representations to each concept node: a source representation and a target representation.

[0045] Each concept in the same representation space can simultaneously encode two types of role information in the prior relation: one is the source representation indicating which concepts it tends to point to, and the other is the target representation indicating which preceding concepts it tends to be supported by.

[0046] Specifically, the process of learning the conceptual prior representations that imply prior dependencies is as follows: Two representations are assigned to each concept node: a source representation and a target representation. A pre-graph convolutional neural network, PreGCN, is designed to learn the source and target representations respectively. The process is as follows: First, use trainable representations and The concept representation is encoded to obtain the initial source and target representations for each concept node; whereby... For source and target representation dimensions.

[0047] Then, based on the symmetric normalized adjacency matrix To conduct layered information dissemination and integration: (2) (3) in, and They are respectively Layered knowledge concepts: source representation, target representation, and feature matrix. For activation functions; and is a trainable weight matrix.

[0048] and They are respectively The knowledge concepts of the layer are represented by source representation, target representation, and feature matrix.

[0049] Used to aggregate neighborhood information that is reachable in the direction of the edge. This is used to aggregate the pre-conditioning dependency information in the direction of incoming edges, so that the source and target representations can each learn a structural context consistent with their semantics.

[0050] go through After layer propagation, the source representation matrix is ​​obtained. and target representation matrix ;right and Perform a join operation to obtain the concept prerequisite representation of the concept node containing the prerequisite relation. : (4) The concept prior is represented as It is used to comprehensively characterize the feature information of knowledge concepts by combining the roles of source representation and target representation, and can be used as a prior initialization feature for downstream heterogeneous graph learning.

[0051] Step 2. Based on the practice relationship between students and questions, and the examination relationship between questions and concepts, construct a heterogeneous graph that integrates the three types of entities: students, questions, and concepts. .

[0052] in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories.

[0053] Topological awareness refers to the use of the relationships between students, questions, and concepts, rather than focusing on the characteristics of each entity itself, to capture the dependencies and interaction patterns between different entities, providing structural information for learning path generation.

[0054] The concept prior representation obtained in step 1 As a heterogeneous graph The initial representation of the concept nodes in the graph. For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question.

[0055] Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set.

[0056] The Graph Transformer module HCGT, designed for heterogeneous graph representation learning, has the following processing flow: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node.

[0057] The comprehensive representation of concept nodes integrates the prerequisite and collaborative relationships between concepts while retaining the semantic features of the concepts themselves.

[0058] There are not only explicit prerequisite relationships between concepts, but also implicit collaborative relationships. These relationships are not direct logical dependencies and need to be mined from student response data, reflecting, to some extent, the relevance at the cognitive or behavioral level of students.

[0059] For example, two concepts mastered (or not mastered) by the same group of students in similar patterns may have a certain cognitive connection. A complete student-topic-concept heterogeneous graph is constructed, and a hierarchical concept graph Transformer (HCGT) is specifically designed for graph representation learning, integrating explicit and implicit connections between concepts to ultimately obtain a comprehensive representation of concept nodes.

[0060] By using Graph Transformer to perform the learning path recommendation task, the above-mentioned problems can be avoided from interfering with the recommendation results.

[0061] As a powerful graph representation learning method, the core idea of ​​Graph Transformer is to combine the multi-head self-attention mechanism in Transformer with the inductive bias unique to graph structures to effectively handle non-Euclidean data.

[0062] To fully integrate the shaping influence of both student and question entities on the semantics of concepts, thereby obtaining semantically rich concept node representations, HCGT improves upon the general heterogeneous graph Transformer in the following two aspects: (1) Distinguish the semantic information carried by the target node's neighbors at different distances; (2) Distinguish the semantic roles carried by different types of neighbors around the target node.

[0063] Based on the above concepts, when performing heterogeneous graph representation learning, HCGT can effectively integrate long-range dependency information and the interaction semantics of heterogeneous neighbors while preserving the semantic features of the concept nodes themselves, thus obtaining more expressive concept node representations.

[0064] The HCGT module mainly includes hierarchical Transformer and type-level Transformer.

[0065] Both the hierarchical Transformer and the type-based Transformer network structures consist of a multi-head self-attention module and a feedforward neural network module. The feedforward neural network module includes linear layers and non-linear activation functions.

[0066] Heterogeneous graph The initial representations of student nodes and question nodes, as well as the concept prerequisite representations, serve as the inputs to the HCGT module.

[0067] For a concept node, its predefined concept representation and the representations of its neighboring nodes are first fed into a type-level Transformer. Following the neighbor node extraction and classification mechanism in step 2, type-level attention aggregation is performed through a multi-head self-attention module to obtain the set representation of each level. Then, all level set representations are fed into a hierarchical Transformer, and hierarchical attention aggregation is performed through a multi-head self-attention module to obtain the comprehensive representation of the concept node.

[0068] Step 2.1. Neighborhood node partitioning.

[0069] The process of extracting and classifying neighboring nodes is as follows: Define heterogeneous graph The concept nodes that need to be represented in the model are designated as target nodes; the target nodes are then... Jump neighbor division There are three non-overlapping rings, and the neighboring nodes in each ring are equidistant from the target node.

[0070] Based on this, different features are extracted for each concept node. Ring neighborhood; Given concept nodes ,definition for of The set of neighboring nodes in the ring, where express and In heterogeneous graphs The shortest structural distance on is .

[0071] express The set of zero-ring neighborhood nodes is the node itself. hour, .

[0072] Based on this, The neighborhood nodes are further divided into the following three subsets: ; ; ; in , , They represent The set of student, question, and concept nodes in the neighborhood. , , They are respectively , , The nodes in , , express , , The types of the three nodes.

[0073] For each set The features of all nodes are aggregated through average pooling to obtain a dimension of The representation of is, represented as That is, extracting a length of 3. of Ring neighborhood represents sequence ; .in . , and They represent The representation of student, question, and concept node features in the neighborhood after average pooling.

[0074] Appendix Figure 2 middle, , , , Concept nodes Ring 0, Ring 1, Ring 2, A ring represents a sequence. Step 2.1 is to... of First, divide the skip neighbor nodes into There are 10 layers, where layer 0 is... itself.

[0075] Due to heterogeneous diagrams There are three types of nodes in the middle, so the student nodes, question nodes, and concept nodes in each ring are further divided according to their categories. Finally, Neighborhood nodes are assigned to different levels and types. In the collection.

[0076] Step 2.2. After classifying the neighboring nodes, HCGT performs attention aggregation in the type dimension.

[0077] Design a type-level Transformer and define type-level attention, as shown in the following formula: (5) in For attention weights, For dot product operation, The node obtained in step 1 The concept of prerequisite representation. After 3 layers of Transformer encoding The overall representation of the nodes.

[0078] final, Representation of ring neighborhood The calculation is as follows: (6) in , , express Information about students, questions, and concept nodes in a ring is crucial for representation learning. Contributions; , , After 3 layers of Transformer encoding A hierarchical set representation of students, questions, and concept nodes within a layer.

[0079] According to the above formulas (5) and (6), for the set of neighboring nodes in each ring, the type-level Transformer encodes them and learns attention weights, and then performs weighted aggregation to obtain the hierarchical set representation of the neighboring nodes in that layer.

[0080] For ease of explanation, the following text will use the term "information". It can be simplified to Ultimately, the maximum length is obtained as follows: The ring neighborhood nodes are represented by , denoted as . ; They are respectively 0 rings - The neighboring nodes of the ring are represented.

[0081] Through category-level attention, the model can learn dynamic weights along the type dimension, weightedly fusing information from multiple types of neighborhoods to obtain an intermediate representation that is sensitive to heterogeneous semantic differences and can explicitly model cross-type interactions. This stage can be viewed as a structured aggregation of heterogeneous neighborhoods within the same hop, mapping the representation from a dispersed subspace to a unified space.

[0082] Step 2.3. HCGT performs aggregation on the hierarchical dimension to characterize multi-scale information of different structural distances.

[0083] The hierarchical Transformer is designed to enable HCGT to adaptively emphasize the most relevant ring neighborhood for the target node during representation learning. The specific form of the hierarchical attention is as follows: (7) in For attention weights, for , for That is, the result obtained after type-level Transformer encoding. Overall representation, Let be the projection matrix. For connection operations.

[0084] For concept nodes The hierarchical Transformer input is .

[0085] Obtaining attention weights Then, calculate the concept nodes. Comprehensive representation : (8).

[0086] The HCGT-generated concept node comprehensive representation can integrate multi-source information and achieve structure awareness, providing a more structured inductive bias representation basis for candidate concept selection and path decoding in the subsequent learning path generation stage.

[0087] Step 3. Based on the comprehensive representation of all concept nodes obtained in Step 2, design a candidate path generation method to screen a set of candidate concepts that are both representative and have broad knowledge coverage; and based on the student's answer history and the comprehensive representation of concept nodes, infer the student's real-time status to further screen concepts from the candidate concept set and generate the final learning path.

[0088] Step 3.1. Candidate path generation.

[0089] In a policy-based learning path recommendation framework, the decoder needs to progressively select concepts for recommendation. Making decisions directly across the entire concept space would lead to excessively high computational costs and weaken the model's robustness. Therefore, a candidate path generation method is designed to iteratively select the concept least similar to the currently selected concept, maximizing the minimum distance across the entire candidate path to minimize information redundancy and ensure sufficiently broad knowledge coverage. The process is as follows:

[0090] First, for any two concepts Calculate the squared Euclidean distance between concepts : (9) in, and The concepts obtained through formula (8) are respectively and The representation of; This method allows us to record the distance matrix between all concepts, which can then be used in the subsequent greedy selection process.

[0091] The core objective of constructing a candidate concept set based on a minimax greedy strategy is to ensure the inclusion of the target concept while balancing the diversity and representativeness of the candidate set. By iteratively selecting the concept furthest from the current set, the final candidate paths are more dispersed in the representation space.

[0092] Hypothetical candidate concept set The number of concepts that should be included in the middle is , This represents the number of concepts in the current candidate concept set; the initialization form of the candidate concept set is: ;in For the purpose of setting a goal.

[0093] Then the first The candidate concepts were determined using the following criteria: (10) in Indicates the first Candidate concepts This represents the existing set of candidate concepts, among which there already exist One concept; Represents the set of all concepts This indicates that the result obtained through formula (9) and The square Euclidean distance between them.

[0094] The physical meaning of the criterion determined by formula (10) is as follows: For each concept that has not yet been selected Calculate the distance between the concept and each concept in the selected set, and record the minimum value; then, by traversing all candidate concepts, select the concept with the largest minimum distance and include it in the candidate concept set.

[0095] The above process is repeated until the candidate concept set reaches a predetermined size. The time complexity for calculating the distance matrix using this method is O(log n). The worst-case time complexity of the greedy selection process is O(n log n). .

[0096] Although the computational cost of both steps is on the quadratic level, the actual computational overhead is within an acceptable range due to the limited number of knowledge concepts involved in real-world educational datasets, and will not create a bottleneck for the training and inference efficiency of the model.

[0097] Step 3.2. Learning path generation.

[0098] In obtaining heterogeneous graphs After comprehensively representing all concept nodes and candidate paths, a ranking and probability estimate of them are generated; to ensure the effectiveness of learning path recommendations, the learning status of students needs to be monitored at all times.

[0099] Therefore, an LSTM module is used to track changes in students' learning status, as follows: First, the student's initial state is calculated by analyzing the knowledge concepts and their corresponding mastery levels in the student's historical interaction sequence: (11) in This represents the students' initial state. For conceptual representation, This represents the corresponding answer record. For a trainable weight matrix, For connection operations, This indicates the number of concepts that students have learned. .

[0100] Next, update the student status step by step as follows: (12) in For learning path The first in step, In order to conduct the first Student status after recommendation For the first The concept of step recommendation is represented as follows: This represents the length of the learning path; during the recommendation process, the probability distribution of candidate concepts will be modeled, as follows: First, taking into account the student's status, the characteristics of each concept, and the ultimate learning objective, scores are calculated for the candidate concepts: (13) in Representing candidate concepts The score, For the first A comprehensive representation of the candidate concepts. For the representation of the target concept, , and All are learnable projection matrices. For bias terms; Next, the candidate concept scores are converted into a probability distribution using softmax normalization, as shown in the following formula: (14) in The first in the recommended learning path The concept of step is The probability of; Candidate concepts Score, Indicates the first The set of concepts that have already been recommended before the step; This is the set of candidate concepts that were not recommended. Based on this, the final recommendation path provided to students is gradually generated. The probability corresponding to each step is ;in Indicates the first The probability corresponding to the concept of step recommendation.

[0101] Step 3.2. Knowledge Tracking.

[0102] The evolution of students' cognitive states during the learning process lacks authentic labels, making it difficult to directly assess learning outcomes.

[0103] To address this issue, this invention references existing research practices and employs DKT as a simulator to pre-train students using dynamic learning data, thereby achieving the goal of accurately tracking changes in students' abilities.

[0104] This simulator is data-driven, taking the student's status as input and outputting the probability of correctly answering the current concept.

[0105] The ultimate goal of the model is to generate conceptual paths that maximize learning gain.

[0106] Based on existing work, the training phase of the model is modeled from a reinforcement learning perspective, in which the learning path generation module samples progressively from the candidate set, and the simulator module provides reward signals.

[0107] The training employs a reinforcement-based policy gradient objective, which achieves differentiability by log-probability weighting of the sampled trajectories.

[0108] Define the total loss of the learning path recommendation method Defined as: (15) in The policy gradient loss of the model, This represents the knowledge tracking training loss; when the KT module is enabled, The value is 1, otherwise The policy gradient loss of the model is 0. The formula is as follows: (16) in This represents the learning gain metric, which is equivalent to maximizing the expected reward. When a path yields a higher reward, the log probability of its corresponding learning sequence is increased, so that the strategy tends to reproduce the high-reward path. To enhance training signal density and learning stability, an additional knowledge tracking training loss is introduced. Constraints are imposed on the mastery prediction within the learning path generation module; this loss term adopts the form of binary cross-entropy: (17) in Indicates students' opinion The actual grasp of the concept, when students master this concept The value is 1, otherwise =0; This represents the concept in the path. The probability of being answered correctly; The DKT simulator is used. This simulator is data-driven, taking student status as input and outputting the probability of correctly answering the current concept, and for concepts in the path... The probability of being answered correctly is calculated as follows: (18) in, For a multilayer perceptron, This is the sigmod activation function.

[0109] In the path generation stage, this invention uses a maximum-minimum greedy strategy to filter the set of candidate concepts and optimizes the sampling path from the perspective of sequence modeling, thereby improving search efficiency while maintaining the semantic integrity of the knowledge structure.

[0110] In addition, to verify the effectiveness of the method proposed in this invention, three educational datasets were used to verify the effectiveness of the method in the learning path recommendation task. The size of the datasets is shown in Table 1.

[0111] Table 1. Statistics on Dataset Size

[0112] The Assist09 dataset, collected by the online education platform ASSISTments during the 2009-2010 academic year, is a knowledge tracking dataset that clearly reflects students' actual learning process and can be used to study students' mastery of various concepts and questions. The Assist12 dataset contains data collected by ASSISTments during the 2012-2013 academic year. This dataset is larger than Assist09 and contains more information, such as students' emotional states and response times. The SLP dataset is a large-scale, multi-dimensional K-12 education dataset collected by a university.

[0113] This dataset records the learning trajectories of students from 32 secondary schools between 2016 and 2019, and is suitable for learning process analysis and educational data mining research. We selected student learning data in mathematics for our experiment.

[0114] To demonstrate the effectiveness of the method of the present invention, a comparison was made with the following baseline methods: Random method: Randomly selects concepts from candidate paths, sorts them, and generates learning paths.

[0115] Rule-based method: Learns all concepts in the candidate concept set through a simulator, and then returns the learning effect on the target concept. Based on this effect, the candidate concepts are ranked to generate a learning path.

[0116] The MPC method combines the predictive control model and knowledge tracking in reinforcement learning to predict the effects of multiple search paths before generating each learning path, and then makes recommendations.

[0117] The GRU4Rec method is a classic sequence recommendation method that predicts the probability distribution of the next interaction based on past input sequences. We adapt it to the learning path recommendation task to generate learning paths.

[0118] SRC method: A learning path recommendation method based on set sequence sorting. By combining a knowledge tracking model to dynamically obtain user feedback, it can adjust the recommendation strategy in real time.

[0119] LIGHT method: A learning path recommendation method based on knowledge topology awareness. It learns concept representations by constructing a composite concept graph, and then generates learning paths by combining cluster sampling and sequence optimization.

[0120] The experimental environment for this invention is based on the Ubuntu operating system, and all experiments are run on an NVIDIA GeForce RTX 4090 GPU. The experimental environment is managed via Anaconda. This invention employs the Xavier parameter initialization method for weight allocation and uses the Adam optimizer for model optimization.

[0121] The model's learning rate is in {1e -3 , 3e -4 , 1e -5 The search is performed within the specified range, indicating that the vector dimension is set to 128 and the batch size is 64. The value is set to 1, and the learning path length takes a value from {5, 10, 20, 30}.

[0122] The performance of the proposed method in learning path recommendation on three datasets and the results compared with the baseline model are shown in Table 2.

[0123] Table 2 Comparison of experimental results

[0124] In Table 2, "*" indicates the comparison with the best baseline in the significance test. Bold data represents the optimal results, while suboptimal results are highlighted with an underline. Based on the experimental results in Table 2, the following phenomena can be observed: 1. The method of this invention outperforms the baseline method on all datasets.

[0125] Compared to suboptimal methods, the performance improvement of the proposed method is particularly significant on the Assist09 dataset, with a maximum gain of 120%. This may be attributed to the stronger structural characteristics of Assist09, where student response sequences are more coherent and the relationships between knowledge points are relatively clear. This characteristic is beneficial for the model to learn conceptual representations and stably select learning content that can improve performance.

[0126] The proposed method also performed well on the Assist12 and SLP datasets, with average gain improvements of 14.89% and 4.97%, respectively. Although Assist12 is larger than Assist09, student behavior is more dispersed and the mapping relationship between questions and knowledge concepts is more complex, thus reducing the gap with the suboptimal method.

[0127] The method of this invention shows the smallest gap with the suboptimal model on the SLP dataset. This may be due to two factors. Firstly, the SLP dataset has a limited scope of knowledge points and question coverage, and student behavior patterns are more homogeneous, with many samples explainable by relatively simple rules, allowing the suboptimal method to achieve good results. Secondly, the supervision signals in SLP are coarser-grained, compressing information on changes in student learning states and long-term knowledge transfer, making it difficult to fully utilize the modeling capabilities.

[0128] 2. Within a certain range, model performance is linearly related to the learning path length, such as... Figure 3 As shown, this phenomenon is most pronounced on the Assist12 dataset: as the value of n increases, the model performance also improves. This indicates that a longer recommendation step size provides the model with more decision space, and knowledge gains accumulate gradually. Simultaneously, HCGT can better integrate neighborhood information and cross-type relationships, thus being more conducive to the model capturing long-range dependencies and showing greater advantage as the step size increases. However, on the Assist09 and SLP datasets, the performance of the method in this invention declines when n=30. This is usually because the dataset size is small, and knowledge structures and student answer patterns are easily mined in the early stages of recommendation. When the step size increases to 30, low-return concepts are more likely to appear in the newly generated content, leading to a decrease in model performance compared to the peak. This phenomenon is also reflected in suboptimal methods. This trend also varies depending on the strategies adopted by each method; for example, the performance of MPC on the SLP dataset fluctuates.

[0129] Modeling the relationships between concepts and optimizing paths are effective ways to improve performance. SRC and LIGHT outperform other baseline methods on all three datasets, confirming the necessity of mining knowledge structures and ranking students based on the dynamic characteristics of concepts in learning path recommendation tasks. Simple random selection and arrangement are insufficient for effective recommendations and can even lead to negative gains. LIGHT's superior performance compared to SRC further illustrates the positive effects of modeling relationships between concepts. However, its gap with the method of this invention also indicates room for improvement in the sufficiency of its modeling. This may stem from LIGHT's reliance solely on concept node graph construction, neglecting the complex heterogeneous interactions between students, questions, and concepts.

[0130] This invention first uses a pre-prep graph convolutional neural network to mine the semantic meaning of concepts as both pre-prep providers and pre-prep dependencies in the pre-prep graph. Then, an HCGT module is designed to learn representations on a heterogeneous student-question-concept graph from a full-view perspective. This HCGT module can model node features at both semantic and topological levels, possessing strong capabilities in mining and distinguishing the widespread and significant medium- to long-range heterogeneous dependencies in the graph. The resulting comprehensive representation of concept nodes is particularly suitable for sequential decision-making tasks such as learning path recommendation. Because the concept pre-prep representation is used to initialize the concept node representation in the heterogeneous graph, the resulting comprehensive representation of concept nodes naturally includes pre-prep relationships between concepts. Furthermore, a candidate path generation method is designed to select a set of concepts with both representativeness and knowledge coverage, and based on inferences about the student's real-time state, performs deep decoding from a sequence optimization perspective to generate the final learning path.

[0131] Example 2 This embodiment 2 describes a learning path recommendation system based on deep heterogeneous learning and topology awareness. This system is based on the same concept as the learning path recommendation method based on deep heterogeneous learning and topology awareness in embodiment 1 above.

[0132] The learning path recommendation system based on deep heterogeneous learning and topology awareness in this embodiment includes the following modules: The concept prerequisite relation mining module is used to construct a directed prerequisite relation graph and generate a concept prerequisite representation that contains prerequisite dependencies. The concept node comprehensive representation learning module is used to construct a heterogeneous graph that integrates three types of entities: students, questions, and concepts. ; in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories; The obtained concept pre-modification representation is used as a graph. The initial representation of the conceptual nodes; For the graph For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question. Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set; The Graph Transformer module HCGT, designed for heterogeneous graph representation learning, has the following processing flow: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node. And a learning path recommendation module, which is used to design a candidate path generation method based on the comprehensive representation of all concept nodes obtained, so as to select a set of candidate concepts that are both representative and have broad knowledge coverage; Based on the student's answer history and the comprehensive representation of concept nodes, the system infers the student's real-time status, thereby further filtering concepts from the candidate concept set and generating the final learning path.

[0133] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0134] Example 3 This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the learning path recommendation method based on deep heterogeneous learning and topology awareness described in embodiment 1 above.

[0135] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0136] Example 4 This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the learning path recommendation method based on deep heterogeneous learning and topology awareness in embodiment 1 above.

[0137] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0138] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A learning path recommendation method based on deep heterogeneous learning and topology awareness, characterized in that, Includes the following steps: Step 1. Construct a directed prior relation graph to generate conceptual prior representations that imply prior dependencies; Step 2. Construct a heterogeneous graph that integrates three types of entities: students, questions, and concepts. ; in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories; The obtained concept pre-modification representation is used as a graph. The initial representation of the conceptual nodes; For the graph For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question. Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set; the Graph Transformer module HCGT for heterogeneous graph representation learning is designed, and its processing flow is as follows: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node. Step 3. Based on the comprehensive representation of all concept nodes obtained in Step 2, design a candidate path generation method to select a set of candidate concepts that are both representative and have broad knowledge coverage; Based on the student's answer history and the comprehensive representation of concept nodes, the system infers the student's real-time status, thereby further filtering concepts from the candidate concept set and generating the final learning path.

2. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 1, characterized in that, In step 1, the process of constructing the directed prior relationship graph is as follows: Construct a prerequisite relationship graph by using knowledge concepts as nodes and the prerequisite relationships between concepts as edges. , means as follows: ;in For a set of concept nodes, For the first set of edges; The transition probability of adjacent concepts is used as the basis for constructing the pre-trimmed edges. The process is as follows: First, construct a counting matrix based on the students' answer records. ;definition For this matrix The Middle line, number The elements of the column represent the concepts that students answered correctly. Then immediately answer the question correctly. The number of times; For the number of concepts; Next, the counting matrix Perform a normalization operation to obtain the probabilistic transition matrix. ; definition Transition matrix The Middle line, number Column elements, Used to quantify student responses Then immediately answer correctly The probability of; For counting matrix The Middle The sum of the elements in a row, representing The total number of times a question was answered correctly; Then, the final transition matrix is ​​obtained through Min-Max normalization. ; definition For the final transition matrix The Middle line, number The elements of the column have the following formulas: ； in and Represents the transition matrix The maximum and minimum values ​​in; Set threshold To construct a binary transition matrix ; definition Binary transition matrix The Middle line, number The elements of the column; if Greater than but =1, otherwise =0; This represents the sum of all elements in the final transition matrix; The design of asymmetric rules further filters the prior relationships: For any pair of concepts If and only if and Only then can As Prerequisite concepts; Based on this, the final diagram is obtained. adjacency matrix ; definition Adjacency matrix Elements; when and hour, Otherwise Adding self-loop connections yields a matrix. Afterwards, statistics The degree matrix is ​​obtained by calculating the degree of all nodes in the matrix. ; in Represents the identity matrix; , representing the degree matrix The diagonal elements in the diagram; next, the prior relationship diagram. Perform symmetric normalization to obtain the symmetric normalized adjacency matrix. As shown in equation (1): （1）。 3. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 2, characterized in that, In step 1, the process of learning the conceptual prior representation that implies prior dependencies is as follows: Two representations are assigned to each concept node: a source representation and a target representation. A pre-graph convolutional neural network is designed to learn the source representation and the target representation respectively. The process is as follows: First, use trainable representations and The concept representation is encoded to obtain the initial source and target representations for each concept node; whereby... For source representation and target representation dimensions; Then, based on the symmetric normalized adjacency matrix To conduct layered information dissemination and integration: （2） （3） in, and They are respectively The knowledge concept source representation matrix and target representation matrix of the layer. For activation functions; and This is a trainable weight matrix; and They are respectively The feature matrix of the source representation and the feature matrix of the target representation of the knowledge concept in the layer; go through After layer propagation, the source representation matrix is ​​obtained. and target representation matrix ;right and Perform a join operation to obtain the concept prior representation of the concept nodes, which includes prior dependencies. : （4）。 4. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 3, characterized in that, In step 2, the process of extracting and classifying neighboring nodes is as follows: Define heterogeneous graph The concept nodes that need to be represented in the learning process are the target nodes; The target node Jump neighbor division The target node is formed by three non-overlapping rings, where each neighboring node is equidistant from the target node. Based on this, different features are extracted for each concept node. Ring neighborhood; Given concept nodes ,definition for of The set of neighboring nodes in the ring, where express and In heterogeneous graphs The shortest structural distance on is ; express The set of zero-ring neighborhood nodes is the node itself. hour, ; Based on this, The neighborhood nodes are further divided into the following three subsets: ； ； ； in , , They represent The set of student, question, and concept nodes in the neighborhood. , , They are respectively , , The nodes in , , express , , The types of the three nodes; For each set The features of all nodes are aggregated through average pooling to obtain a dimension of The representation of That is, extracting a length of 3. of Ring neighborhood represents sequence ; ;in, , and They represent The representation of student, question, and concept node features in the neighborhood after average pooling.

5. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 4, characterized in that, In step 2, the HCGT module includes a hierarchical Transformer and a type-level Transformer. Both the hierarchical Transformer and the type-level Transformer consist of a multi-head self-attention module and a feedforward neural network module; the feedforward neural network module includes a linear layer and a non-linear activation function. Heterogeneous graph The initial representations of student nodes and question nodes, as well as the concept prerequisites, are used as inputs to the HCGT module; For a concept node, its pre-defined concept representation and the representations of its neighboring nodes are first fed into a type-level Transformer. Following the neighbor node extraction and classification mechanism in step 2, type-level attention aggregation is performed through a multi-head self-attention module. Then, the entire hierarchical set representation obtained by type-level attention aggregation is fed into the hierarchical Transformer, and hierarchical attention aggregation is performed through the multi-head self-attention module to obtain the comprehensive representation of the concept node.

6. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 5, characterized in that, In step 2, HCGT performs attention aggregation in the type dimension as follows: Define type-level attention as follows: （5） in For attention weights, For dot product operation, The node obtained in step 1 The concept of prerequisite representation. After 3 layers of Transformer encoding The overall representation of the middle node; final Hierarchical set representation of ring neighborhood The calculation is as follows: （6） in , , for Information about students, questions, and concept nodes in a ring is crucial for representation learning. Contributions; , , After 3 layers of Transformer encoding A hierarchical set representation of students, questions, and concept nodes within a layer; According to the above formulas (5) and (6), for the set of neighboring nodes in each ring, the type-level Transformer encodes them and learns attention weights, and then performs weighted aggregation to obtain the hierarchical set representation of the neighboring nodes in that layer; Finally, the maximum length is obtained as The hierarchical set representation of is denoted as . ;in They are respectively layer 0- Layer hierarchical set representation; definition for Simplified representation; The process by which HCGT performs aggregation at the hierarchical level is as follows: The hierarchical Transformer is designed to enable HCGT to adaptively emphasize the most relevant ring neighborhood for the target node during representation learning. The specific form of the hierarchical attention is as follows: （7） in For attention weights, for , for That is, the result obtained after type-level Transformer encoding. The overall representation of the middle node, Let be the projection matrix. For connection operation; For concept nodes The hierarchical Transformer input is ; Obtaining attention weights Then, the conceptual node comprehensive representation is calculated. : （8）。 7. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 1, characterized in that, In step 3, the candidate path generation process is as follows: A candidate path generation method is designed, and the process is as follows: First, for any two concepts Calculate the squared Euclidean distance between concepts : （9） in, and The concepts obtained through formula (8) are respectively and The representation of; Construct a candidate concept set based on a maximum-minimum greedy strategy; Hypothetical candidate concept set The number of concepts that should be included in the middle is , This represents the number of concepts in the current candidate concept set; the initialization form of the candidate concept set is... ;in For the purpose of defining the target concept; Then the first The candidate concepts were determined using the following criteria: （10） in Indicates the first Candidate concepts This represents the existing set of candidate concepts, among which there already exist One concept; Represents the set of all concepts. This indicates that the result obtained through formula (9) and The square Euclidean distance between them; The physical meaning of the criterion determined by formula (10) is as follows: For each concept that has not yet been selected Calculate the distance between it and each concept in the selected set, and record the minimum value; then, by traversing all candidate concepts, select the concept with the largest minimum distance and include it in the candidate concept set; The above process is repeated until the size of the candidate concept set reaches a predetermined number.

8. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 7, characterized in that, In step 3, the learning path generation process is as follows: In obtaining heterogeneous graphs After comprehensively representing all concept nodes and candidate paths, a ranking and probability estimate of them are generated. Therefore, an LSTM module is used to track changes in the student's learning state, and the processing procedure is as follows: First, the student's initial state is calculated by analyzing the knowledge concepts and their corresponding mastery levels in the student's historical interaction sequence: （11） in This represents the students' initial state. For conceptual representation, This represents the corresponding answer record. For a trainable weight matrix, For connection operations, This indicates the number of concepts that students have learned. ; Next, update the student status step by step as follows: （12） in For learning path The first in step, In order to conduct the first Student status after recommendation For the first The concept of step recommendation is represented as follows: Indicates the length of the learning path; During the recommendation process, probability distribution modeling of candidate concepts will be performed, as follows: First, taking into account the student's status, the characteristics of each concept, and the ultimate learning objective, scores are calculated for the candidate concepts: （13） in Representing candidate concepts The score, For the first A comprehensive representation of the candidate concepts. For the representation of the target concept, , and All are learnable projection matrices. For bias terms; Next, the candidate concept scores are converted into a probability distribution using softmax normalization, as shown in the following formula: （14） in The first in the recommended learning path The concept of step is The probability of; Candidate concepts Score, In the first The set of concepts that have already been recommended before the step; This is the set of candidate concepts that were not recommended. Based on this, the final recommendation path provided to students is gradually generated. The probability corresponding to each step is ;in Indicates the first The probability corresponding to the concept of step recommendation.

9. The learning path recommendation method based on deep heterogeneous learning and topology awareness according to claim 8, characterized in that, Define the total loss of the learning path recommendation method Defined as: （15） in The policy gradient loss of the model, This indicates the knowledge tracking training loss; When the KT module is enabled The value is 1, otherwise The policy gradient loss of the model is 0. The formula is as follows: （16） in This represents the learning gain metric, which is equivalent to maximizing the expected reward. When a path yields a higher reward, the log probability of its corresponding learning sequence is increased, so that the strategy tends to reproduce the high-reward path. To enhance training signal density and learning stability, an additional knowledge tracking training loss is introduced. Constraints are imposed on the mastery prediction within the learning path generation module; this loss term adopts the form of binary cross-entropy: （17） in Indicates students' opinion The actual grasp of the concept, when students master this concept The value is 1, otherwise =0; This represents the concept in the path. The probability of being answered correctly; The DKT simulator is used. This simulator is data-driven, taking student status as input and outputting the probability of correctly answering the current concept, and for concepts in the path... The probability of being answered correctly is calculated as follows: （18） in, For a multilayer perceptron, This is the sigmod activation function.

10. A learning path recommendation system based on deep heterogeneous learning and topology awareness, characterized in that, Includes the following modules: The concept prerequisite relation mining module is used to construct a directed prerequisite relation graph and generate a concept prerequisite representation that contains prerequisite dependencies. The concept node comprehensive representation learning module is used to construct a heterogeneous graph that integrates three types of entities: students, questions, and concepts. ； in , and The diagrams are shown below. The set of all nodes, the set of edges, and the set of edge types in the array; For the image The set of all node types, including student nodes. Nodes of the question Concept nodes Three categories; The obtained concept pre-modification representation is used as a graph. The initial representation of the conceptual nodes; For the graph For each concept node, its neighbors are divided into different sets, and the division process is as follows: First, neighboring nodes that are the same number of levels away from the concept node are grouped into the same set, resulting in multiple hierarchical sets. For each hierarchical set, it is further divided into three type sets: student, concept, and question. Based on this, each neighbor node of a concept node belongs to a certain type set under a certain level set; The Graph Transformer module HCGT, designed for heterogeneous graph representation learning, has the following processing flow: For a concept node, firstly, attention aggregation along the type dimension is performed based on all type sets in each level set to obtain a level set representation. Then, attention aggregation along the level dimension is performed on all level set representations of this concept node to obtain a comprehensive representation of the concept node. And a learning path recommendation module, which is used to design a candidate path generation method based on the comprehensive representation of all concept nodes obtained, so as to select a set of candidate concepts that are both representative and have broad knowledge coverage; Based on the student's answer history and the comprehensive representation of concept nodes, the system infers the student's real-time status, thereby further filtering concepts from the candidate concept set and generating the final learning path.

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