A learning resource recommendation method and system based on heterogeneous graph denoising attention network

Abstract

This invention provides a learning resource recommendation method and system based on a heterogeneous graph denoising attention network. It introduces a propagation constraint probability based on meta-paths to measure the reliability relationship between students, resources, and knowledge points, effectively reducing the weight of noisy neighbors. Differentiable masking operations are used to dynamically filter out low-confidence noisy neighbors, thereby purifying the attention mechanism and improving the matching accuracy between students and learning resources. This method can more efficiently capture the multi-semantic relationships between students, resources, and knowledge points, while mitigating noise interference, significantly improving the effectiveness of learning resource recommendation, providing students with precise personalized learning support, and thus effectively improving learning efficiency and outcomes.

Description

Technical Field

[0001] This invention relates to the field of intelligent recommendation technology, specifically a learning resource recommendation method and system based on heterogeneous graph denoising attention networks. Background Technology

[0002] With the rapid development of information technology, the number of learning resources on intelligent education platforms has exploded, including various forms of learning content such as video courses, handouts, test questions, and e-books. Faced with this massive amount of learning resources, students often need to spend a lot of time filtering materials that suit their needs, and the quality and matching degree of these resources directly affect learning efficiency and effectiveness. Therefore, how to provide personalized learning resource recommendations by analyzing students' learning behavior and knowledge status has become an important research direction in the field of intelligent education. In recent years, recommendation algorithms have been widely used in many fields, such as video recommendation and e-commerce recommendation, achieving remarkable results. Introducing them into the education field can also effectively improve user experience and help students quickly find high-quality learning resources.

[0003] In recent years, the development of Graph Neural Networks (GNNs) has brought about a new breakthrough in recommender systems, especially Heterogeneous Graph Attention Networks (HANs). As a deep learning model designed for heterogeneous graphs, HANs can effectively model multiple types of nodes and their complex relationships, and are widely used in e-commerce, social networks, and other scenarios. In learning resource recommendation, the relationships between students and learning resources (such as videos, test questions, and lecture notes) as well as knowledge points constitute a typical heterogeneous graph. For example, students establish connections with resources through learning behaviors, resources are associated with courses through knowledge points, and students can also indirectly establish connections through similar learning interests or knowledge mastery. How to fully utilize these multi-type relationships is the key to building an efficient learning resource recommendation system.

[0004] Heterogeneous graphs are usually represented as ,in It represents a set of nodes (such as students, learning resources, knowledge points, courses, etc.). Represents a set of edges (such as the relationship between students and resources, or the relationship between resources and knowledge points). Represents a set of node types. This represents a set of edge types. Heterogeneous graph attention networks, by introducing meta-paths, can capture the semantic relationships between nodes. For example, the meta-path "student-resource-student" represents a connection established by students through sharing resources. Different meta-paths carry different semantic information. By assigning weights to each meta-path and utilizing a semantic-level attention mechanism, heterogeneous graph attention networks learn the importance of these meta-paths in recommendation tasks, thereby better modeling the diverse relationships in resource recommendation scenarios.

[0005] However, in evasion attack scenarios, attackers may deliberately insert noisy information (such as fake student behavior records) to interfere with the results generated by the recommendation system. This noisy information can negatively impact the recommendation results, mislead the model's output, and thus reduce the accuracy of the recommendations. Therefore, designing effective denoising mechanisms to cope with the noise inserted by evasion attacks is crucial to improving the robustness and performance of recommendation algorithms. Summary of the Invention

[0006] The technical problem to be solved by this invention is to determine the method for denoising heterogeneous graphs to improve the accuracy of learning resource recommendations.

[0007] The present invention solves the above-mentioned technical problems through the following technical means:

[0008] A learning resource recommendation method based on heterogeneous graph denoising attention networks includes the following steps:

[0009] S1. Collect data on students and learning resources from the education platform, construct student-resource interaction graphs and other relationship graphs, generate heterogeneous graphs and divide them into training set, validation set and test set, and initialize node features as model input;

[0010] S2. Capture semantic relationships between nodes in a heterogeneous graph through multiple meta-paths; aggregate neighbor information using node-level attention, and then fuse different meta-path embeddings through semantic-level attention to generate multi-semantic node representations;

[0011] S3. Introduce propagation constraint probability in meta-path aggregation, and calculate neighbor confidence by combining node feature similarity, thereby identifying noisy neighbors and guiding the model to aggregate information of positive neighbors;

[0012] S4. Design a differentiable masking operation to filter neighbor nodes based on confidence, mask unreliable nodes, and generate clean attention values ​​through softmax for node-level aggregation; finally, fuse node-level embeddings through semantic-level attention to generate the final representation of the node.

[0013] S5. Using semantically aggregated node embeddings, the interaction probability between students and learning resources is predicted through dot products; BPR loss is used to optimize the difference between positive and negative sample scores, and the model is trained with SGD and Adam optimizers. Finally, the performance is evaluated by tuning the validation set and testing the test set.

[0014] Furthermore, S1 specifically includes the following:

[0015] S101: Collect student, resource, and knowledge point information from the education platform to construct a student set. Resource collection Student age set and a collection of knowledge points ;

[0016] S102: Construct an interaction relationship graph based on the interaction behavior between students and learning resources; define an adjacency matrix. When students With learning resources When there is interaction, set Otherwise, set it to 0; other relationship interaction graphs follow the same principle.

[0017] S103: Constructing Heterogeneous Graphs: Utilizing different relationship interaction graphs to construct heterogeneous graphs. ,in Represents a set of nodes. Denotes the set of edges. Represents a set of node types. Represents a set of edge types;

[0018] S104: Divide the dataset randomly into training, validation, and test sets; the dataset division primarily focuses on the direct interaction data between students and learning resources. The validation set is used for intermediate model evaluation and parameter tuning, while the test set retains each student's interaction behavior proportionally and is used to generate candidate resources. ;

[0019] S105: Initialize node representation vectors, and initialize representation vectors for various types of nodes in the heterogeneous graph. ,in The dimension of the representation vector is specified; the initialized representation vectors are stored in their respective representation vector dictionaries and used as the initial input for subsequent models.

[0020] Furthermore, S2 specifically includes the following:

[0021] S201: Construct meta-paths. Based on the adjacency matrix generated in step S1, construct a heterogeneous graph and design four meta-paths suitable for resource recommendation: For students - resources - students, For students-age-student, For resources - students - resources and These meta-paths, representing resource-knowledge point-resource, are used to extract various semantic relationships in heterogeneous graphs, providing a foundation for subsequent node information aggregation.

[0022] S202: Node-level attention mechanism. This mechanism captures key information from local nodes and aggregates information from adjacent nodes in a subgraph constructed from a specific meta-path. The node-level aggregation process is defined as follows:

[0023]

[0024] in Represents the target node For neighboring nodes The attention coefficient is obtained from steps four and five; Indicates the target node obtained through the metapath. Node-level embedding representation; It is a node The initial vector; via metapath Determined nodes The set of neighboring nodes; It is an activation function.

[0025] S203: Semantic-level attention mechanism. Since the node-level embeddings learned by each meta-path carry unique semantic information, a semantic-level attention mechanism is needed to synthesize these embeddings to generate the final embedding representation of the target node. The semantic-level aggregation process is defined as follows:

[0026]

[0027] in, Represents a node Semantic-level embedding representation; For nodes In the Node-level embedding under a single meta-path; These are semantic-level attention weights, reflecting the importance of different meta-paths. Semantic-level attention mechanisms can effectively integrate diverse semantic information, generating high-quality embedded representations of nodes and further enhancing the model's ability to express heterogeneous graphs.

[0028] Furthermore, S3 specifically includes the following:

[0029] S301: Unified mapping of node features, for type target node Through a feature transformation matrix specific to the node type Projecting the feature vectors of nodes onto the common space, their feature representation is as follows: in, For the target node Projection characteristics in public spaces For nodes In metapath The initial feature vectors are as follows;

[0030] S302: Similarity calculation between nodes, given a meta-path In certain situations, nodes with similar features are more important to the target node than nodes with significantly different features; therefore, the similarity between neighboring nodes is defined by the dot product of node features, thereby evaluating neighboring nodes. For the target node The importance of this similarity; this similarity is represented as: ;

[0031] S303: Calculation of the propagation constraint probability matrix. To enhance the model's ability to model node relationships, a propagation constraint probability based on meta-paths is introduced; given a meta-path... First, calculate the propagation constraint probability matrix of a single adjacency matrix: in, edge type The adjacency matrix, This is the inverse of the corresponding degree matrix; each element in the matrix... Indicates from node By edge type To the node The propagation constraint probability can be calculated by progressively multiplying the individual propagation constraint probability matrices along the metapath. The overall propagation constraint probability matrix: ;

[0032] S304: Combining propagation constraint probability and similarity to calculate confidence scores, the propagation constraint probability based on metapaths can be seen as a constraint condition in the node propagation process, used to guide the model to learn effective information more accurately; in order to identify target nodes. Unreliable neighbors, combined with node feature importance and propagation constraint probability Define neighbor nodes Confidence vector: in, Neighboring nodes The confidence score.

[0033] Furthermore, S4 specifically includes the following:

[0034] S401: Design a differentiable mask operation for the target node. The masking operation is modeled by constructing a mask vector, i.e., the confidence level:

[0035]

[0036] in, Used to control neighbor nodes' behavior towards the target node. The impact;

[0037] S402: Mask unreliable neighbor nodes. Following step S401, unreliable neighbor nodes have been identified, and their mask values ​​have been set to... When the mask value of neighboring nodes and feature-based importance When the softmax function is applied to the sum, unreliable neighbor nodes will be effectively pruned;

[0038] S403: Generate cleaned attention weights and mask vectors. It is used as an attention mask to filter out unreliable neighbor nodes, and the purified attention value is calculated using the softmax function. :

[0039] ;

[0040] S404: Node-level aggregation based on cleansing attention values, for target nodes Purified attention value Introduced into the node-level aggregation process of heterogeneous graph neural networks, it is used to mask unreliable neighbors and remove noise from heterogeneous graphs; node-level embedding vectors Calculated using the following formula:

[0041]

[0042] in, via metapath Target node obtained Node-level embedding representation, Neighboring nodes The projection vector, Based on metapath A defined set of neighboring nodes It is an activation function;

[0043] S405: A semantic-level attention mechanism is employed to further evaluate the contribution of different meta-paths to the target node embedding; for a set of meta-paths and target node Obtain a set of node-level embedding vectors for the node. Subsequently, the metapath is calculated using the following formula. Importance:

[0044]

[0045] in and These represent the weight matrix and bias term of the multilayer perceptron (MLP), respectively. It is an attention vector used to capture semantic-level importance;

[0046] S406: Semantic attention weight normalization and final node embedding, through the importance weight of the meta-path. Normalization is performed using the softmax function to obtain semantic-level attention weights. Finally, through semantic-level aggregation, the node-level embeddings under different meta-paths are integrated into the target node. The final embedding representation :

[0047]

[0048] Furthermore, S5 specifically includes the following:

[0049] S501: Student interaction score prediction, through semantic-level aggregation, can obtain student scores separately. and learning resources The final embedding vector and The likelihood of interaction between students and resources is predicted by the dot product of their embedding vectors: in, Students With learning resources Predicted score of the probability of interaction between them; score The larger the resource, the more likely students are to interact with it;

[0050] S502: For learning resource recommendation tasks, a pairwise loss function based on Bayesian personalized ranking is adopted;

[0051] S503: Definition of the Bayesian Personalized Ranking Loss Function. For each training sample, the objective is to maximize the difference between the predicted scores of positive and negative samples, thereby optimizing the model. The Bayesian Personalized Ranking Loss Function is defined as follows:

[0052]

[0053] It is a training set of triples. This indicates that students are interacting with resources. This indicates that the student has not interacted with the resource; function and These refer to the logarithmic function and the sigmoid function, respectively. This is the hyperparameter that determines the weight of the regularization term; by optimizing the BPR loss function mentioned above, the model attempts to maximize the difference in predicted scores between positive and negative samples, i.e. This satisfies the ranking requirements of the learning resource recommendation task;

[0054] S504: Model Training and Evaluation. During model training, stochastic gradient descent and the Adam optimizer are used to optimize the model parameters.

[0055] This invention also provides a learning resource recommendation system based on a heterogeneous graph denoising attention network, comprising:

[0056] Dataset construction module: Collects data such as students and learning resources from the education platform, constructs student-resource interaction graphs and other relationship graphs, generates heterogeneous graphs and divides them into training set, validation set and test set, and initializes node features as model input;

[0057] Multi-semantic node representation module: Captures semantic relationships between nodes in a heterogeneous graph through multiple meta-paths; aggregates neighbor information using node-level attention, and then fuses different meta-path embeddings through semantic-level attention to generate multi-semantic node representations;

[0058] Confidence calculation module: Introduces propagation constraint probability into meta-path aggregation, and calculates neighbor confidence by combining node feature similarity, thereby identifying noisy neighbors and guiding the model to aggregate information of positive neighbors;

[0059] The denoising module employs a differentiable masking operation to filter neighboring nodes based on confidence levels, mask unreliable nodes, and generates clean attention values ​​using softmax for node-level aggregation. Finally, it fuses node-level embeddings through semantic-level attention to generate the final representation of the nodes.

[0060] Model optimization module: It uses semantically aggregated node embeddings to predict the probability of student interaction with learning resources through dot product; it uses BPR loss to optimize the difference between positive and negative sample scores, and trains the model with SGD and Adam optimizers. Finally, it evaluates the performance through parameter tuning on the validation set and evaluation on the test set.

[0061] Furthermore, the multi-semantic node representation module specifically includes the following:

[0062] S201: Construct meta-paths. Based on the adjacency matrix generated in step S1, construct a heterogeneous graph and design four meta-paths suitable for resource recommendation: For students - resources - students, For students - age - students For resources - students - resources and These meta-paths, representing resource-knowledge point-resource, are used to extract various semantic relationships in heterogeneous graphs, providing a foundation for subsequent node information aggregation.

[0063] S202: Node-level attention mechanism. This mechanism captures key information from local nodes and aggregates information from adjacent nodes in a subgraph constructed from a specific meta-path. The node-level aggregation process is defined as follows:

[0064]

[0065] in Represents the target node For neighboring nodes The attention coefficient is obtained from steps four and five; Indicates the target node obtained through the metapath. Node-level embedding representation; It is a node The initial vector; via metapath Determined nodes The set of neighboring nodes; It is an activation function.

[0066] S203: Semantic attention mechanism. Since the node-level embeddings learned by each meta-path carry unique semantic information, a semantic attention mechanism is needed to synthesize these embeddings to generate the final embedding representation of the target node. The semantic aggregation process is defined as follows:

[0067]

[0068] in, Represents a node Semantic-level embedding representation; For nodes In the Node-level embedding under a single meta-path; These are semantic-level attention weights, reflecting the importance of different meta-paths. Semantic-level attention mechanisms can effectively integrate diverse semantic information, generating high-quality embedded representations of nodes and further enhancing the model's ability to express heterogeneous graphs.

[0069] Furthermore, the confidence calculation module specifically includes the following:

[0070] S301: Unified mapping of node features, for type target node Through a feature transformation matrix specific to the node type Projecting the feature vectors of nodes onto the common space, their feature representation is as follows: in, For the target node Projection characteristics in public spaces For nodes In metapath The initial feature vectors are as follows;

[0071] S302: Similarity calculation between nodes, given a meta-path In certain situations, nodes with similar features are more important to the target node than nodes with significantly different features; therefore, the similarity between neighboring nodes is defined by the dot product of node features, thereby evaluating neighboring nodes. For the target node The importance of this similarity; this similarity is represented as: ;

[0072] S303: Calculation of the propagation constraint probability matrix. To enhance the model's ability to model node relationships, a propagation constraint probability based on meta-paths is introduced; given a meta-path... First, calculate the propagation constraint probability matrix of a single adjacency matrix: in, edge type The adjacency matrix, This is the inverse of the corresponding degree matrix; each element in the matrix... Indicates from node By edge type To the node The propagation constraint probability can be calculated by progressively multiplying the individual propagation constraint probability matrices along the metapath. The overall propagation constraint probability matrix: ;

[0073] S304: Combining propagation constraint probability and similarity to calculate confidence scores, the propagation constraint probability based on metapaths can be seen as a constraint condition in the node propagation process, used to guide the model to learn effective information more accurately; in order to identify target nodes. Unreliable neighbors, combined with node feature importance and propagation constraint probability Define neighbor nodes Confidence vector: in, Neighboring nodes The confidence score.

[0074] Furthermore, the noise reduction module specifically includes the following:

[0075] S401: Design a differentiable mask operation for the target node. The masking operation is modeled by constructing a mask vector, i.e., the confidence level:

[0076]

[0077] in, Used to control neighbor nodes' behavior towards the target node. The impact;

[0078] S402: Mask unreliable neighbor nodes. Following step S401, unreliable neighbor nodes have been identified, and their mask values ​​have been set to... When the mask value of neighboring nodes and feature-based importance When the softmax function is applied to the sum, unreliable neighbor nodes will be effectively pruned;

[0079] S403: Generate cleaned attention weights and mask vectors. It is used as an attention mask to filter out unreliable neighbor nodes, and the purified attention value is calculated using the softmax function. :

[0080] ;

[0081] S404: Node-level aggregation based on cleansing attention values, for target nodes Purified attention value Introduced into the node-level aggregation process of heterogeneous graph neural networks, it is used to mask unreliable neighbors and remove noise from heterogeneous graphs; node-level embedding vectors Calculated using the following formula:

[0082]

[0083] in, via metapath Target node obtained Node-level embedding representation, Neighboring nodes The projection vector, Based on metapath A defined set of neighboring nodes It is an activation function;

[0084] S405: A semantic-level attention mechanism is employed to further evaluate the contribution of different meta-paths to the target node embedding; for a set of meta-paths and target node Obtain a set of node-level embedding vectors for the node. Subsequently, the metapath is calculated using the following formula. Importance:

[0085]

[0086] in and These represent the weight matrix and bias term of the multilayer perceptron (MLP), respectively. It is an attention vector used to capture semantic-level importance;

[0087] S406: Semantic attention weight normalization and final node embedding, through the importance weight of the meta-path. Normalization is performed using the softmax function to obtain semantic-level attention weights. Finally, through semantic-level aggregation, the node-level embeddings under different meta-paths are integrated into the target node. The final embedding representation :

[0088]

[0089] The advantages of this invention are:

[0090] This invention proposes an improved method based on heterogeneous graph attention networks. Specifically, it introduces a propagation constraint probability based on meta-paths to measure the reliability relationship between students, resources, and knowledge points, thereby effectively mitigating the impact of noisy neighbors inserted by evasion attacks. Simultaneously, it employs differentiable masking operations to dynamically detect and block low-confidence noisy neighbors, thus purifying the attention mechanism. In complex scenarios involving evasion attacks, this method can more efficiently capture the multi-semantic relationships between students, resources, and knowledge points, and significantly alleviate the impact of noise interference on recommendation results, thereby improving the matching accuracy between students and learning resources. Attached Figure Description

[0091] Figure 1 This is a flowchart of the method in an embodiment of the present invention. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0093] This embodiment aims to improve the accuracy of resource recommendation by denoising heterogeneous graphs. Specifically, it introduces meta-path-based propagation constraint probabilities into the heterogeneous graph attention network to guide the learning of the recommendation model and weaken the influence of noisy neighbors' weights. Simultaneously, it combines differentiable masking operations to accurately block noisy neighbors, further removing noise from the heterogeneous graph and significantly improving the accuracy of resource recommendation. Figure 1 As shown, the specific steps are as follows:

[0094] Step 1: Data Collection and Preprocessing: First, collect data from the heterogeneous graph, including students, learning resources (such as videos, handouts, test questions, etc.), knowledge points, and student interactions with resources (such as clicks, downloads, ratings, etc.). Clean the raw data, removing missing values, outliers, and redundant data, and format the data into a uniform structure. Simultaneously, define corresponding fields, such as node type (student, resource, knowledge point, etc.) and edge type (clicks, coverage, etc.). Next, construct the heterogeneous graph based on the cleaned data, defining the node set (such as students, learning resources, knowledge points, etc.) and edge set (such as student-resource interactions, resource-knowledge point coverage relationships, etc.). Finally, generate initial feature vectors for the nodes based on the information in the heterogeneous graph, preparing for subsequent model input.

[0095] Step Two: Define and design a heterogeneous graph attention network. Based on the requirements of the learning resource recommendation task, design and construct suitable meta-paths (such as "student-resource-student", "resource-knowledge point-resource", etc.) to extract various semantic relationships contained in the heterogeneous graph. In the model design, a node-level attention mechanism is used to capture key information of local nodes, and a semantic-level attention mechanism is used to evaluate the importance of different meta-paths, thereby integrating the semantic information of multiple paths. In addition, a dynamic parameter adjustment mechanism is introduced to more accurately represent the characteristics of students and learning resources, further optimizing model performance.

[0096] Step 3: Introduce propagation constraint probabilities based on meta-paths. To enhance the model's ability to model node relationships in heterogeneous graphs, propagation constraint probabilities based on meta-paths are introduced during training. Specifically, by using the propagation probabilities of meta-paths to weight the information of neighboring nodes, the model's focus on important neighbors and effective paths is enhanced, while effectively suppressing the propagation influence of noisy neighbors, thereby improving the quality of model embedding vector learning.

[0097] Step 4: Introduce differentiable masking operations to further remove noise. To further improve the denoising effect, differentiable masking operations are introduced to effectively filter noisy neighbors and aggregate the most reliable neighbor information. This method constructs a mask vector and combines it with the correction mechanism of the Softmax function to select trustworthy neighbors based on their trust scores, while completely blocking untrustworthy neighbors. This process ensures the accuracy of noise filtering while maintaining the differentiability of the operation, allowing the model to be optimized during training through gradient backpropagation, thereby further enhancing the model's denoising ability and stability.

[0098] Step 5: Loss Function and Model Optimization. Design a suitable loss function based on the requirements of the recommendation task. For example, the BPR loss function can be used for ranking recommendation tasks. Optimize the model parameters using gradient descent algorithms (such as Adam) to minimize the loss function. Evaluate the model performance on the validation set and further optimize the model performance by adjusting hyperparameters (such as learning rate, hidden dimension, etc.). Finally, evaluate the final model performance on the test set, using common evaluation metrics (such as NDCG, Recall, etc.) to measure the recommendation effect and verify the model's actual recommendation capability.

[0099] The following is a detailed description of each of the five steps:

[0100] Step one includes:

[0101] Step 101: Collect information such as students, resources, and knowledge points from the education platform to construct a student set. Resource collection Student age set and a collection of knowledge points .

[0102] Step 102: Analyze student interactions with learning resources (e.g., clicks, downloads, ratings) and construct an interaction graph. For example, when building the student-resource interaction graph, define an adjacency matrix. When students With learning resources When there is interaction, set Otherwise, set it to 0. Other relationship interaction graphs (such as the relationship graph between learning resources and knowledge points) can be deduced in the same way.

[0103] Step 103: Construct a heterogeneous graph. Utilize different relationship interaction graphs to construct a heterogeneous graph. ,in Represents a set of nodes. Denotes the set of edges. Represents a set of node types. This represents a set of edge types. For example, student nodes. Interaction between students and learning resources Student type nodes Student-learning resource interaction relationship .

[0104] Step 104: Split the dataset. Randomly divide the dataset into a training set, a validation set, and a test set in a ratio of 7:1:2. The dataset split primarily focuses on the direct interaction data between students and learning resources. The validation set is used for intermediate model evaluation and parameter tuning, while the test set retains each student's interaction behavior proportionally and is used to generate candidate resources. .

[0105] Step 105: Initialize node representation vectors, and initialize representation vectors for various types of nodes in the heterogeneous graph. ,in This represents the dimension of the vector. For example, the initialization vector for a student node is... The initialization vector of the resource node is The initialized representation vectors are stored in their respective representation vector dictionaries and used as the initial input for subsequent models.

[0106] Step two includes:

[0107] Step 201: Construct meta-paths. Based on the adjacency matrix generated in Step 1, construct a heterogeneous graph and design four meta-paths suitable for resource recommendation: (Student-Resource-Student) (Student-Age-Student) (Resources-Students-Resources) and (Resources - Knowledge Points - Resources). These meta-paths are used to extract various semantic relationships in heterogeneous graphs, providing a foundation for subsequent node information aggregation.

[0108] Step 202: Node-level attention mechanism. This mechanism captures key information from local nodes and aggregates information from neighboring nodes in the subgraph constructed from a specific meta-path. The node-level aggregation process is defined as follows:

[0109]

[0110] in Represents the target node For neighboring nodes The attention coefficient is obtained from steps four and five; Indicates the target node obtained through the metapath. Node-level embedding representation; It is a node The initial vector; via metapath Determined nodes The set of neighboring nodes; It is an activation function.

[0111] Step 203: Semantic Attention Mechanism. Since the node-level embeddings learned by each meta-path carry unique semantic information, a semantic attention mechanism is needed to synthesize these embeddings to generate the final embedding representation of the target node. The semantic aggregation process is defined as follows:

[0112]

[0113] in, Represents a node Semantic-level embedding representation; For nodes In the Node-level embedding under a single meta-path; These are semantic-level attention weights, reflecting the importance of different meta-paths. Semantic-level attention mechanisms can effectively integrate diverse semantic information, generating high-quality embedded representations of nodes and further enhancing the model's ability to express heterogeneous graphs.

[0114] Step three includes:

[0115] Step 301: Unified Mapping of Node Features. Since different types of nodes possess different informational features, these features are typically distributed within their respective feature spaces. To uniformly process this differentiated information, it is necessary to map the features of different node types to a common feature space. Specifically, for nodes of type... target node Through a feature transformation matrix specific to the node type Projecting the feature vectors of nodes onto the common space, their feature representation is as follows: in, For the target node Projection characteristics in public spaces For nodes In metapath The initial eigenvectors are given below.

[0116] Step 302: Calculate the similarity between nodes, given the metapath. In such cases, nodes with similar features are more important to the target node than nodes with significantly different features. Therefore, this embodiment defines the similarity of neighboring nodes by using the dot product of node features, thereby evaluating neighboring nodes. For the target node The importance of this similarity is expressed as: .

[0117] Step 303: Calculation of the propagation constraint probability matrix. To enhance the model's ability to model node relationships, a propagation constraint probability based on meta-paths is introduced. Given a meta-path... First, calculate the propagation constraint probability matrix of a single adjacency matrix: in, edge type The adjacency matrix, This is the inverse of the corresponding degree matrix. Each element in the matrix... Indicates from node By edge type To the node The propagation constraint probability can be calculated by progressively multiplying the individual propagation constraint probability matrices along the metapath. The overall propagation constraint probability matrix: .

[0118] Step 304: Calculate the confidence score by combining the propagation constraint probability and similarity. The propagation constraint probability based on the meta-path can be seen as a constraint condition in the node propagation process, used to guide the model to learn effective information more accurately. This is to identify the target node. Unreliable neighbors, this embodiment combines the importance of node characteristics and propagation constraint probability Define neighbor nodes Confidence vector: in, Neighboring nodes The confidence score is used to determine the reliability of neighboring nodes. Nodes with higher confidence scores are considered reliable and typically exhibit higher feature similarity and propagation probability. By introducing meta-path-based propagation constraint probabilities into the heterogeneous graph attention network, the model effectively mitigates interference from noisy nodes in the graph and better aggregates high-quality neighbor information, thereby improving the performance of learning resource recommendation.

[0119] Accurately distinguishing between normal edges and noisy edges introduced by evasion attacks is a core challenge in addressing evasion attacks. Therefore, this embodiment introduces a propagation constraint probability based on meta-paths as a solution strategy. Specifically, this embodiment denotes this propagation constraint probability as... Indicates from node Along the metapath propagation to nodes The probability of propagating constraints is determined by prior knowledge. This embodiment can more accurately guide the recommendation model to perform random walks on meta-path-based subgraphs. This mechanism enables the model to learn and generate high-quality node embeddings. Notably, this prior knowledge is extracted from uncontaminated (i.e., clean) graph structures. Therefore, it plays a crucial role when applied to attacked subgraphs, helping this embodiment effectively distinguish between normal edges and noisy edges inserted to evade attacks.

[0120] For the overall propagation constraint probability This embodiment can be obtained in the following way:

[0121]

[0122] For range Each of the inside This embodiment defines The inverse of the degree matrix and adjacency matrix The product of these can be expressed as:

[0123] This formula shows that, with a given metapath Associated propagation constraint probability This implies two key aspects: (1) connectivity, which reflects the metapath Next node and The number of paths between them and (2) degree information, which includes the degree of all nodes along the meta-path, contains the edge information of the original graph, providing valuable prior knowledge for subsequent noise removal.

[0124] Then, this embodiment uses the elements in the propagation probability matrix. As the target node In metapath Down and adjacent nodes Prior estimates (i.e., node) To the node (The probability of the existence of an edge). It is foreseeable that if the node... Indirectly connect to the node by attacking a malicious node. Then as neighbors Prior estimate Relatively small, because, It is calculated based on the clean map, therefore it retains the graph structure information of the clean map. Utilizing this characteristic, This can be used as a basis for determining the possibility of an edge existing between two nodes in the noise graph in this embodiment, and can also be regarded as an indicator of the importance of the edge. Specifically, when When the value is low, this embodiment tends to consider that the edge may be a noise edge introduced by an attack.

[0125] Propagation probability matrix This provides a reliable input to the model, enabling this embodiment to evaluate the credibility of edges in a noisy graph. In step 304, to more accurately identify noisy edges, this embodiment propagates the probability matrix. This is combined with node feature similarity. By combining these metrics, this embodiment calculates a confidence vector that can be used to identify noisy edges. This is because both the propagation probability matrix and node feature similarity can reflect the importance of an edge, together providing a strong basis for identifying noisy edges.

[0126] Step four includes:

[0127] Step 401: Design a differentiable masking operation. To effectively reduce the attention weight of malicious neighbor nodes, this embodiment designs a differentiable masking operation to filter out low-confidence neighbor nodes, thereby pruning noisy neighbors. For the target node... The masking operation is modeled by constructing a mask vector (i.e., confidence level):

[0128]

[0129] in, Used to control neighbor nodes' behavior towards the target node. The impact. Specifically, based on confidence scores. , Operation Selection Select 1 trusted neighbor and set its mask value to 0; treat the remaining neighbors as unreliable nodes and set their mask value to 0. .here, This indicates the number of neighboring nodes that need to be retained.

[0130] Step 402: Mask unreliable neighbor nodes. Following step 401, unreliable neighbor nodes have been identified, and their mask values ​​have been set to... When the mask value of a neighboring node... and feature-based importance When applying the softmax function to the sum of elements, unreliable neighbor nodes will be effectively pruned. This is because the softmax function will reduce the mask value... The neighbor attention value is converted to 0, and these unreliable neighbors will no longer affect the aggregation process of the target node.

[0131] Step 403: Generate cleaned attention weights and mask vectors. It is used as an attention mask to filter out unreliable neighbor nodes, and the purified attention value is calculated using the softmax function. :

[0132]

[0133] This mechanism enhances the denoising capability of node-level attention mechanisms by effectively encoding the propagation constraint probability matrix based on meta-paths and aggregating only the information of the most reliable neighbors.

[0134] Step 404: Node-level aggregation based on clean attention values, for the target node Purified attention value Introduced into the node-level aggregation process of heterogeneous graph neural networks, it is used to mask unreliable neighbors and remove noise from heterogeneous graphs. Node-level embedding vectors Calculated using the following formula:

[0135]

[0136] in, via metapath Target node obtained Node-level embedding representation, Neighboring nodes The projection vector, Based on metapath A defined set of neighboring nodes It is an activation function.

[0137] Step 405: Semantic Attention Mechanism. After node-level aggregation, to further evaluate the contribution of different meta-paths to the target node embedding, the heterogeneous graph neural network employs a semantic attention mechanism. For a set of meta-paths... and target node This embodiment can obtain a set of node-level embedding vectors for a node. Then, the metapath is calculated using the following formula. Importance:

[0138]

[0139] in and These represent the weight matrix and bias term of the multilayer perceptron (MLP), respectively. It is an attention vector used to capture semantic level importance.

[0140] Step 406: Semantic attention weight normalization and final node embedding, through the importance weight of the meta-path. Normalization is performed using the softmax function to obtain semantic-level attention weights. Finally, through semantic-level aggregation, the node-level embeddings from different meta-paths are combined into the target node. The final embedding representation :

[0141]

[0142] Step five includes:

[0143] Step 501: Student interaction score prediction. Through semantic-level aggregation, this embodiment can obtain student scores separately. and learning resources The final embedding vector and The likelihood of interaction between students and resources is predicted by the dot product of their embedding vectors: in, Students With learning resources A score predicting the likelihood of interaction between them. The larger the resource, the more likely it is that students will interact with the resources.

[0144] Step 502: Employ the Bayesian Personalized Ranking (BPR) loss function. For the learning resource recommendation task, the pairwise loss function of Bayesian Personalized Ranking (BPR) is used. Specifically, each training sample is composed of a student... Positive sample resources that interact with students And negative sample resources that did not interact with students composition.

[0145] Step 503: Definition of the BPR loss function. For each training sample, the goal is to maximize the difference between the predicted scores of positive and negative samples, thereby optimizing the model. The BPR loss function is defined as follows:

[0146]

[0147] It is a training set of triples. This indicates that students are interacting with resources. This indicates that the student has not interacted with the resource; function and These refer to the logarithmic function and the sigmoid function, respectively. This is the hyperparameter that determines the weight of the regularization term. By optimizing the BPR loss function described above, the model attempts to maximize the difference in predicted scores between positive and negative samples, i.e. This satisfies the ranking requirements of the learning resource recommendation task.

[0148] Step 504: Model Training and Evaluation. During model training, stochastic gradient descent (SGD) and the Adam optimizer are used to optimize the model parameters. After training, the internal parameters and related feature representations of the heterogeneous graph neural network are further adjusted using a validation set to improve the model's generalization ability. Finally, the model performance is evaluated on the test set, using common recommendation metrics (such as NDCG, Recall, etc.) to measure the recommendation effect and verify the effectiveness of the method.

[0149] This embodiment aims to improve the recommendation accuracy of learned resources during evasion attacks by denoising heterogeneous graphs. Specifically, it introduces meta-path-based propagation constraint probabilities into the heterogeneous graph attention network to guide the learning of the recommendation model and weaken the influence of noisy neighbors' weights. Simultaneously, it combines differentiable masking operations to accurately block noisy neighbors, further removing noise from the heterogeneous graph, thereby significantly improving the robustness and accuracy of learned resource recommendations.

[0150] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A learning resource recommendation method based on heterogeneous graph denoising attention network, characterized in that, Includes the following steps: S1. Collect student and learning resource data from the education platform, construct student-resource interaction graphs and other relationship graphs, generate heterogeneous graphs and divide them into training set, validation set and test set, and initialize node features as model input; S2. Capture semantic relationships between nodes in a heterogeneous graph through multiple meta-paths; aggregate neighbor information using node-level attention, and then fuse different meta-path embeddings through semantic-level attention to generate multi-semantic node representations; S3. Introduce propagation constraint probability in meta-path aggregation, and calculate neighbor confidence by combining node feature similarity, thereby identifying noisy neighbors and guiding the model to aggregate information of positive neighbors; S4. Design a differentiable masking operation to filter neighbor nodes based on confidence, mask unreliable nodes, and generate clean attention values ​​through softmax for node-level aggregation; finally, fuse node-level embeddings through semantic-level attention to generate the final representation of the node. S5. Using semantically aggregated node embeddings, the interaction probability between students and learning resources is predicted through dot product; BPR loss is used to optimize the difference between positive and negative sample scores, and the model is trained with SGD and Adam optimizers. Finally, the performance is evaluated by parameter tuning on the validation set and testing the test set. S4 specifically includes the following: S401: Design a differentiable mask operation for the target node. The masking operation is modeled by constructing a mask vector, i.e., the confidence level: in, Used to control neighbor nodes' behavior towards the target node. The impact; S402: Mask unreliable neighbor nodes. Following step S401, unreliable neighbor nodes have been identified, and their mask values ​​have been set to... When the mask value of neighboring nodes and feature-based importance When the softmax function is applied to the sum, unreliable neighbor nodes will be effectively pruned; S403: Generate cleaned attention weights and mask vectors. It is used as an attention mask to filter out unreliable neighbor nodes, and the purified attention value is calculated using the softmax function. : ； S404: Node-level aggregation based on cleansing attention values, for target nodes Purified attention value Introduced into the node-level aggregation process of heterogeneous graph neural networks, it is used to mask unreliable neighbors and remove noise from heterogeneous graphs; node-level embedding vectors Calculated using the following formula: in, via metapath Target node obtained Node-level embedding representation, Neighboring nodes The projection vector, Based on metapath A defined set of neighboring nodes It is an activation function; S405: A semantic-level attention mechanism is employed to further evaluate the contribution of different meta-paths to the target node embedding; for a set of meta-paths and target node Obtain a set of node-level embedding vectors for the node. Subsequently, the metapath is calculated using the following formula. Importance: in and These represent the weight matrix and bias term of the multilayer perceptron (MLP), respectively. It is an attention vector used to capture semantic-level importance; S406: Semantic attention weight normalization and final node embedding, through the importance weight of the meta-path. Normalization is performed using the softmax function to obtain semantic-level attention weights. Finally, through semantic-level aggregation, the node-level embeddings under different meta-paths are integrated into the target node. The final embedding representation : 。 2. The learning resource recommendation method based on heterogeneous graph denoising attention network according to claim 1, characterized in that, S1 specifically includes the following: S101: Collect student, resource, and knowledge point information from the education platform to construct a student set. Resource collection Student age set and a collection of knowledge points ; S102: Construct an interaction relationship graph based on the interaction behavior between students and learning resources; define an adjacency matrix. When students With learning resources When there is interaction, set Otherwise, set it to 0; other relationship interaction graphs follow the same principle. S103: Constructing Heterogeneous Graphs: Utilizing different relationship interaction graphs to construct heterogeneous graphs. ,in Represents a set of nodes. Denotes the set of edges. Represents a set of node types. Represents a set of edge types; S104: Divide the dataset randomly into training, validation, and test sets; the dataset division primarily focuses on the direct interaction data between students and learning resources. The validation set is used for intermediate model evaluation and parameter tuning, while the test set retains each student's interaction behavior proportionally and is used to generate candidate resources. ; S105: Initialize node representation vectors, and initialize representation vectors for various types of nodes in the heterogeneous graph. ,in The dimension of the representation vector is specified; the initialized representation vectors are stored in their respective representation vector dictionaries and used as the initial input for subsequent models.

3. The learning resource recommendation method based on heterogeneous graph denoising attention network according to claim 2, characterized in that, S2 specifically includes the following: S201: Construct meta-paths. Based on the adjacency matrix generated in step S1, construct a heterogeneous graph and design four meta-paths suitable for resource recommendation: For students - resources - students, For students - age - students For resources - students - resources and These meta-paths, representing resource-knowledge point-resource, are used to extract various semantic relationships in heterogeneous graphs, providing a foundation for subsequent node information aggregation. S202: Node-level attention mechanism. This mechanism captures key information from local nodes and aggregates information from adjacent nodes in a subgraph constructed from a specific meta-path. The node-level aggregation process is defined as follows: in Represents the target node For neighboring nodes The attention coefficient is obtained from steps four and five; Indicates the target node obtained through the metapath. Node-level embedding representation; It is a node The initial vector; via metapath Determined nodes The set of neighboring nodes; It is an activation function; S203: Semantic attention mechanism. Since the node-level embeddings learned by each meta-path carry unique semantic information, these embeddings need to be integrated through a semantic attention mechanism to generate the final embedding representation of the target node. The semantic-level aggregation process is defined as follows: in, Represents a node Semantic-level embedding representation; For nodes In the Node-level embedding under a single meta-path; These are semantic-level attention weights, reflecting the importance of different meta-paths; Semantic attention mechanisms can effectively integrate diverse semantic information to generate high-quality embedded representations of nodes, further enhancing the model's ability to express heterogeneous graphs.

4. The learning resource recommendation method based on heterogeneous graph denoising attention network according to claim 3, characterized in that, The S3 specifically Includes the following: S301: Unified mapping of node features, for type target node v Through a feature transformation matrix specific to the node type Projecting the feature vectors of nodes onto the common space, their feature representation is as follows: in, For the target node v Projection characteristics in public spaces For nodes v In metapath The initial feature vectors are as follows; S302: Similarity calculation between nodes, given a meta-path In certain situations, nodes with similar features are more important to the target node than nodes with significantly different features; therefore, the similarity between neighboring nodes is defined by the dot product of node features, thereby evaluating neighboring nodes. For the target node The importance of this similarity; this similarity is represented as: ; S303: Calculation of the propagation constraint probability matrix. To enhance the model's ability to model node relationships, a propagation constraint probability based on meta-paths is introduced; given a meta-path... First, calculate the propagation constraint probability matrix of a single adjacency matrix: in, edge type The adjacency matrix, This is the inverse of the corresponding degree matrix; each element in the matrix... Indicates from node By edge type To the node The propagation constraint probability can be calculated by progressively multiplying the individual propagation constraint probability matrices along the metapath. The overall propagation constraint probability matrix: ; S304: Combining propagation constraint probability and similarity to calculate confidence scores, the propagation constraint probability based on metapaths can be seen as a constraint condition in the node propagation process, used to guide the model to learn effective information more accurately; in order to identify target nodes. Unreliable neighbors, combined with node feature importance and propagation constraint probability Define neighbor nodes Confidence vector: in, Neighboring nodes The confidence score.

5. The learning resource recommendation method based on heterogeneous graph denoising attention network according to claim 4, characterized in that, S5 specifically includes the following: S501: Student interaction score prediction, through semantic-level aggregation, can obtain student scores separately. and learning resources The final embedding vector and The likelihood of interaction between students and resources is predicted by the dot product of their embedding vectors: in, Students With learning resources Predicted score of the probability of interaction between them; score The larger the resource, the more likely students are to interact with it; S502: For learning resource recommendation tasks, a pairwise loss function based on Bayesian personalized ranking is adopted; S503: Definition of the Bayesian Personalized Ranking Loss Function. For each training sample, the objective is to maximize the difference between the predicted scores of positive and negative samples, thereby optimizing the model. The Bayesian Personalized Ranking Loss Function is defined as follows: It is a training set of triples. This indicates that students are interacting with resources. This indicates that the student has not interacted with the resource; function and These refer to the logarithmic function and the sigmoid function, respectively. It is a hyperparameter that determines the weight of the regularization term; by optimizing the BPR loss function, the model attempts to maximize the difference in predicted scores between positive and negative samples, i.e. This satisfies the ranking requirements of the learning resource recommendation task; S504: Model Training and Evaluation. During model training, stochastic gradient descent and the Adam optimizer are used to optimize the model parameters.

6. A learning resource recommendation system based on heterogeneous graph denoising attention network, characterized in that, include: Dataset construction module: Collects student and learning resource data from the education platform, constructs student-resource interaction graphs and other relationship graphs, generates heterogeneous graphs and divides them into training set, validation set and test set, and initializes node features as model input; Multi-semantic node representation module: Captures semantic relationships between nodes in a heterogeneous graph through multiple meta-paths; aggregates neighbor information using node-level attention, and then fuses different meta-path embeddings through semantic-level attention to generate multi-semantic node representations; Confidence calculation module: Introduces propagation constraint probability into meta-path aggregation, and calculates neighbor confidence by combining node feature similarity, thereby identifying noisy neighbors and guiding the model to aggregate information of positive neighbors; Denoising module: Design a differentiable masking operation to filter neighbor nodes based on confidence level, mask unreliable nodes, and generate clean attention values ​​through softmax for node-level aggregation; Finally, semantic-level attention is used to fuse node-level embeddings to generate the final representation of the node; Model optimization module: Utilizes semantically aggregated node embeddings to predict the interaction probability between students and learning resources through dot products; employs BPR loss to optimize the difference between positive and negative sample scores, and trains the model using SGD and Adam optimizers. Finally, performance is evaluated through parameter tuning on the validation set and testing on the test set. The noise reduction module specifically includes the following: S401: Design a differentiable mask operation for the target node. The masking operation is modeled by constructing a mask vector, i.e., the confidence level: in, Used to control neighbor nodes' behavior towards the target node. The impact; S402: Mask unreliable neighbor nodes. Following step S401, unreliable neighbor nodes have been identified, and their mask values ​​have been set to... When the mask value of neighboring nodes and feature-based importance When the softmax function is applied to the sum, unreliable neighbor nodes will be effectively pruned; S403: Generate cleaned attention weights and mask vectors. It is used as an attention mask to filter out unreliable neighbor nodes, and the purified attention value is calculated using the softmax function. : ； S404: Node-level aggregation based on cleansing attention values, for target nodes Purified attention value Introduced into the node-level aggregation process of heterogeneous graph neural networks, it is used to mask unreliable neighbors and remove noise from heterogeneous graphs; node-level embedding vectors Calculated using the following formula: in, via metapath Target node obtained Node-level embedding representation, Neighboring nodes The projection vector, Based on metapath A defined set of neighboring nodes It is an activation function; S405: A semantic-level attention mechanism is employed to further evaluate the contribution of different meta-paths to the target node embedding; for a set of meta-paths and target node Obtain a set of node-level embedding vectors for the node. Subsequently, the metapath is calculated using the following formula. Importance: in and These represent the weight matrix and bias term of the multilayer perceptron (MLP), respectively. It is an attention vector used to capture semantic-level importance; S406: Semantic attention weight normalization and final node embedding, through the importance weight of the meta-path. Normalization is performed using the softmax function to obtain semantic-level attention weights. Finally, through semantic-level aggregation, the node-level embeddings under different meta-paths are integrated into the target node. The final embedding representation : 。 7. The learning resource recommendation system based on heterogeneous graph denoising attention network according to claim 6, characterized in that, The multi-semantic node representation module specifically includes the following: S201: Construct meta-paths. Based on the adjacency matrix generated in step S1, construct a heterogeneous graph and design four meta-paths suitable for resource recommendation: For students - resources - students, For students - age - students For resources - students - resources and These meta-paths, representing resource-knowledge point-resource, are used to extract various semantic relationships in heterogeneous graphs, providing a foundation for subsequent node information aggregation. S202: Node-level attention mechanism. This mechanism captures key information from local nodes and aggregates information from adjacent nodes in a subgraph constructed from a specific meta-path. The node-level aggregation process is defined as follows: in Represents the target node For neighboring nodes The attention coefficient is obtained from steps four and five; Indicates the target node obtained through the metapath. Node-level embedding representation; It is a node The initial vector; via metapath Determined nodes The set of neighboring nodes; It is an activation function; S203: Semantic attention mechanism. Since the node-level embeddings learned by each meta-path carry unique semantic information, these embeddings need to be integrated through a semantic attention mechanism to generate the final embedding representation of the target node. The semantic-level aggregation process is defined as follows: in, Represents a node Semantic-level embedding representation; For nodes In the Node-level embedding under a single meta-path; These are semantic-level attention weights, reflecting the importance of different meta-paths; Semantic attention mechanisms can effectively integrate diverse semantic information to generate high-quality embedded representations of nodes, further enhancing the model's ability to express heterogeneous graphs.

8. The learning resource recommendation system based on heterogeneous graph denoising attention network according to claim 6, characterized in that, The confidence calculation module specifically includes the following: S301: Unified mapping of node features, for type target node Through a feature transformation matrix specific to the node type Projecting the feature vectors of nodes onto the common space, their feature representation is as follows: in, For the target node Projection characteristics in public spaces For nodes In metapath The initial feature vectors are as follows; S302: Similarity calculation between nodes, given a meta-path In certain situations, nodes with similar features are more important to the target node than nodes with significantly different features; therefore, the similarity between neighboring nodes is defined by the dot product of node features, thereby evaluating neighboring nodes. For the target node The importance of this similarity; this similarity is represented as: ; S303: Calculation of the propagation constraint probability matrix. To enhance the model's ability to model node relationships, a propagation constraint probability based on meta-paths is introduced; given a meta-path... First, calculate the propagation constraint probability matrix of a single adjacency matrix: in, edge type The adjacency matrix, This is the inverse of the corresponding degree matrix; each element in the matrix... Indicates from node By edge type To the node The propagation constraint probability can be calculated by progressively multiplying the individual propagation constraint probability matrices along the metapath. The overall propagation constraint probability matrix: ; S304: Combining propagation constraint probability and similarity to calculate confidence scores, the propagation constraint probability based on metapaths can be seen as a constraint condition in the node propagation process, used to guide the model to learn effective information more accurately; in order to identify target nodes. Unreliable neighbors, combined with node feature importance and propagation constraint probability Define neighbor nodes Confidence vector: in, Neighboring nodes The confidence score.

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