A semi-supervised node classification method based on hypergraph structure learning

Abstract

The application discloses a semi-supervised node classification method based on hypergraph structure learning, which comprises collecting graph structure data, and performing data enhancement to obtain augmented graph structure; inputting the graph structure into a teacher network to obtain teacher node representation; inputting the augmented graph structure into a student network to obtain student node representation; constructing teacher node hypergraph representation; constructing consistency objective function, teacher-student consistency objective function and supervision objective function according to the teacher node representation, the student node representation and the teacher node hypergraph representation; iteratively optimizing the student network and the teacher network by using the consistency objective function, the teacher-student consistency objective function and the supervision objective function to construct a joint objective function until the training of the two networks is completed; obtaining a node to be classified of a semi-supervised classification data set, and inputting the node to be classified into the trained teacher network; then inputting the output of the teacher network into a multilayer perceptron for classification to obtain a predicted class distribution of the node.

Description

Technical Field

[0001] This invention relates to graph structure classification technology, specifically to a semi-supervised node classification method based on hypergraph structure learning. Background Technology

[0002] Graphs are an efficient and natural representation method because the intricate relationships and dependencies between different nodes can be effectively captured and analyzed through graph structures. They can be used to model structured and relational data in various domains and applications. In recent years, Graph Neural Networks (GNNs) have demonstrated outstanding performance in numerous tasks, including node classification, graph classification, graph clustering, and link prediction. Among these tasks, semi-supervised node classification is one of the most important research directions, aiming to predict the class labels of unlabeled nodes in a given graph using only a small number of labeled nodes.

[0003] In recent years, semi-supervised node classification tasks have been extensively studied, resulting in several typical methods. For example, one approach uses a GNN classifier trained on labeled nodes to assign pseudo-labels to unlabeled nodes, and iteratively trains the GNN classifier by selecting high-confidence pseudo-labels from easy to difficult through a learning process. Another approach involves self-supervised node representation learning by comparing encodings from two generated views (first-order neighbors and graph diffusion matrices, or edge deletion and node feature masks), enhancing the robustness of representation learning by improving node-level consistency. Finally, a method combines graph contrast loss and graph reconstruction loss; the former enhances node representations in labeled and unlabeled data, while the latter provides additional supervision by extracting relationships between data features and graph topology.

[0004] While semi-supervised node classification methods have achieved good results in practical applications, existing methods still have two major limitations. Firstly, Generative Neural Networks (GNNs) typically follow the neighbor aggregation idea in message passing mechanisms, resulting in each node depending on only a few hops of its neighbors, thus capturing very limited local information. Simultaneously, modeling higher-order dependencies between nodes is crucial for exploring global information in the graph, but existing methods fail to effectively capture this information, leading to suboptimal performance. For example, in biochemical networks modeling protein-protein interactions, GNNs limited by nearby neighbor nodes may overlook important interactions occurring through intermediate proteins. This problem means that proteins with higher-order dependencies may not be fully represented, often constituting complex biological pathways. Secondly, these methods often focus on fitting labeled node sets through GNNs, neglecting the inherent unlabeled nodes in the graph, whose intrinsic information is not fully explored. This problem can lead to overfitting, especially when labeled nodes are scarce. For example, in social network analysis, focusing only on users with known preferences or attributes may result in an incomplete understanding of the network structure. Ignoring users with latent features, which often provide crucial information about community structure and interconnections, may lead to biases in the representation of social relationships. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, the semi-supervised node classification method based on hypergraph structure learning provided by this invention solves the problem that existing node classification methods rely only on neighbors within a few hops, resulting in very limited local information being captured.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A semi-supervised node classification method based on hypergraph structure learning is provided, which includes the following steps:

[0008] S1. Collect graph structure data from the semi-supervised classification dataset and perform data augmentation on the graph structure data to obtain augmented graph structures;

[0009] S2. Input the graph structure into the teacher network to obtain the teacher node representation; input the augmented graph structure into the student network to obtain the student node representation;

[0010] S3. Based on the teacher node representation, construct the hypergraph structure matrix and the hyperedge embedding matrix, and use the product of the hypergraph structure matrix and the hyperedge embedding matrix as the teacher node hypergraph representation;

[0011] S4. Based on the hypergraph representation of teacher nodes and student nodes, construct a consistency objective function to enhance the consistency between any unlabeled node and multiple labeled nodes in the graph structure data;

[0012] S5. Input the teacher node representation and student node representation into the multilayer perceptron to obtain the predicted classification distribution of nodes in the student network and teacher network. Based on the predicted classification distribution of unlabeled nodes, construct a teacher-student consistency objective function to guide student network learning.

[0013] S6. Based on the prediction type distribution of the labeled nodes corresponding to the student network, construct a supervision objective function for training the student network.

[0014] S7. Construct a joint objective function using the consistency objective function, the teacher-student consistency objective function, and the supervision objective function to iteratively optimize the student network and the teacher network until the training of the two networks is completed;

[0015] S8. Obtain the nodes to be classified from the semi-supervised classification dataset and input them into the trained teacher network. Then, input the output of the teacher network into the multilayer perceptron for classification to obtain the predicted class distribution of the nodes.

[0016] Furthermore, the expressions for the hypergraph structure matrix and the hyperedge embedding matrix are as follows:

[0017]

[0018] Where Λ is the hypergraph structure matrix; H is the teacher node representation; W is the learnable hyperedge weight matrix; R is the hyperedge embedding matrix; σ(·) is the activation function; and U is the trainable matrix. It is the transpose of Λ;

[0019] The expression for the hypergraph representing teacher nodes is:

[0020]

[0021] Where Z represents the hypergraph representation of teacher nodes.

[0022] Furthermore, step S4 further includes:

[0023] S41. Randomly select a preset number of labeled nodes as anchor points and store them in the memory library;

[0024] S42. Based on the student node representation, calculate the similarity between the embedding representation of any unlabeled node and the embedding representation of any anchor point in the memory library:

[0025]

[0026] Among them, s i s is the embedding representation of the i-th unlabeled node; tLet be the embedding representation of the t-th anchor point in the memory library, 1≤t≤T, where T is the preset number; exp(·) is the exponential function; cos(·) is the cosine similarity; τ is the temperature coefficient; For s i With s t Relational similarity; s t′ Let be the embedding representation of the t′-th anchor point in the memory library, 1≤t′≤T;

[0027] S43. Based on the hypergraph representation of teacher nodes, calculate the similarity between the hypergraph representation of any unlabeled node and the hypergraph representation of any anchor point in the memory database:

[0028]

[0029] Among them, z i Let z be the hypergraph representation of the i-th unlabeled node; t Let be the hypergraph representation of the t-th anchor point in the memory library; For z i With z t Relational similarity; z t′ Let be the hypergraph representation of the t′-th anchor point in the memory library;

[0030] S44. Based on relational similarity and relational similarity Construct a consistency objective function l r :

[0031]

[0032] in, D is the set of labels for all unlabeled nodes in the graph structure data; KL For divergence; For s i Similarity to the embedding representation s1 of the first anchor point in the memory library; For s i The embedding representation s of the T-th anchor point in the memory library T Relationship similarity; For z i Similarity to the hypergraph representation z1 of the first anchor point in the memory library; For z i The hypergraph representation z of the T-th anchor point in the memory library T Relationship similarity; For s i Similarity to the embedded representation of all anchors in the memory library; For z i Similarity to the hypergraph representation of all anchor points in the memory library.

[0033] Furthermore, the teacher-student consistency objective function for guiding students' online learning further includes:

[0034] S51. Based on the prediction vectors of unlabeled nodes in the predicted category distribution of the teacher network, generate pseudo-labels for the unlabeled nodes:

[0035]

[0036] Where, q i Let be the distribution of the predicted categories of the i-th unlabeled node in the teacher network; The pseudo-label is the i-th unlabeled node; argmax(·) returns the value of the argument when the given function reaches its maximum value;

[0037] S52. Select pseudo-labels whose category probability is greater than the pseudo-label threshold from all pseudo-labels, and then proceed to step S53.

[0038] S53. Based on the pseudo-label of the i-th unlabeled node, construct a teacher-student consistency objective function l to guide students' online learning. t :

[0039]

[0040] in, This is the set of labels for all unlabeled nodes in the graph structure data; max represents the maximum value. for transpose of; p i Let be the predicted class distribution of the student network for the unlabeled i-th node; 1(·) is the indicator function.

[0041] Furthermore, the expression for the supervision objective function is:

[0042]

[0043] in, y is the set of labels for all labeled nodes in the graph structure data; k ∈{0,1} K Let K be the true label vector of the kth labeled node, where K is the total number of categories; For y k transpose of; p k This represents the predicted class distribution of the k-th node in the student network.

[0044] Furthermore, the expression for the joint objective function l is:

[0045] l = l s +αl t +βl r

[0046] Where α and β are both weighting coefficients;

[0047] During the iterative optimization process, the student network is optimized using gradient descent, while the teacher network is optimized using a momentum update strategy. The momentum update strategy is as follows:

[0048]

[0049] φ=∈φ+(1―∈)θ

[0050] Where, θ and η represents the model parameters for the student network and the teacher network, respectively; η is the learning rate; and ∈ is the momentum coefficient.

[0051] Furthermore, both the teacher network and the student network are graph neural networks (GNNs) with the same structure. The message passing process of a GNN is represented as follows:

[0052]

[0053] in, For node v i Neighbors; and These represent the aggregation operator and the combination operator at the m-th layer, respectively; after passing through m layers, the final node embedding representation is output. and They are nodes v i Embedded representations of the m-th and m-1-th layers; For node v j Embedded representations of the m-th and m-1-th layers; For node v i The embedding representation of the m-th layer of the neighbor.

[0054] Furthermore, the semi-supervised classification dataset is any one of the following: three paper citation network datasets Cora, CiteSeer, and PubMed; two purchase network datasets from Amazon, Amazon Computers and Amazon Photo; and a coauthor network dataset, Coauthor CS.

[0055] In the paper citation network dataset, each node represents a paper, and the edges represent the citation relationship between two papers. The goal is to classify each node into different subject areas. In the Amazon-derived purchase network dataset, each node represents a product, and the edges represent two products that are frequently purchased together. The goal is to classify each node into different product categories. In the co-author network dataset, each node represents an author, and the edges represent the collaboration relationship between authors. The goal is to classify each node into different research fields.

[0056] Furthermore, the method for data augmentation of graph structure data includes attribute masking or edge perturbation; the attribute masking involves randomly selecting a subset of nodes with a first preset proportion and masking its attributes with a second preset proportion; the edge perturbation involves randomly removing edges with a third preset proportion from the graph structure data.

[0057] The beneficial effects of this invention are as follows: This scheme establishes a hypergraph representation of teacher nodes through the node representation obtained by the teacher network, and considers using the hypergraph structure to learn and model the high-order dependencies between nodes to explore the global semantic information in the structural graph, thereby improving the low classification accuracy of semi-supervised nodes; This scheme can generate high-confidence pseudo-labels through the collaborative distillation framework formed by the teacher network and the student network, making full use of unlabeled data, thereby further improving the classification accuracy. Attached Figure Description

[0058] Figure 1 This is a flowchart of a semi-supervised node classification method based on hypergraph structure learning.

[0059] Figure 2 This presents the comparative test results of different algorithms on six datasets—Cora, CiteSeer, PubMed, Amazon Computers, Amazon Photo, and Coauthor CS—in this embodiment of the invention.

[0060] Figure 3 This presents the comparative experimental results of different algorithms on the Cora dataset under different label ratio settings in this embodiment of the invention.

[0061] Figure 4 This presents the comparative experimental results of different algorithms on the CiteSeer dataset under different label ratio settings in this embodiment of the invention.

[0062] Figure 5 The graphs show the accuracy performance of the proposed method on different datasets with different numbers of hyperedges. (a) Accuracy comparison of the Cora and CiteSeer datasets with different numbers of hyperedges; (b) Accuracy comparison of PubMed and AmazonComputers with different numbers of hyperedges; (c) Accuracy comparison of Amazon Photo and Coauthor CS with different numbers of hyperedges.

[0063] Figure 6The graphs show the accuracy performance of the proposed method on different datasets with different pseudo-label thresholds. (a) Accuracy comparison of the Cora and CiteSeer datasets with different pseudo-label thresholds; (b) Accuracy comparison of PubMed and Amazon Computers with different pseudo-label thresholds; (c) Accuracy comparison of Amazon Photo and Coauthor CS with different pseudo-label thresholds.

[0064] Figure 7 The figures show the accuracy performance of the proposed method on different datasets with different embedding dimension settings. (a) Accuracy comparison of the Cora and CiteSeer datasets with different embedding dimensions; (b) Accuracy comparison of PubMed and AmazonComputers with different embedding dimensions; (c) Accuracy comparison of Amazon Photo and Coauthor CS with different embedding dimensions.

[0065] Figure 8 Visualization experiments of the original graph structure of the Cora dataset and the hypergraph structure learned by the proposed method on the original structure. (a) Original graph structure; (b) Learned hypergraph structure. Detailed Implementation

[0066] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0067] refer to Figure 1 , Figure 1 A flowchart of a semi-supervised node classification method based on hypergraph structure learning is shown; for example... Figure 1 As shown, the method S includes steps S1 to S8.

[0068] In step S1, graph structure data is collected from the semi-supervised classification dataset, and data augmentation is performed on the graph structure data to obtain augmented graph structures; in this scheme, the graph structure data... in Represents a set of N nodes in a graph structure. Let be the edge set of the graph.

[0069] In implementation, the preferred method for data augmentation of graph structure data in this scheme includes attribute masking or edge perturbation; the attribute masking is to randomly select a subset of nodes with a first preset ratio and mask its attributes with a second preset ratio; the edge perturbation is to randomly remove edges with a third preset ratio from the graph structure data.

[0070] The semi-supervised classification dataset for this scheme can be any one of the following: three paper citation network datasets Cora, CiteSeer, and PubMed; two purchase network datasets from Amazon, Amazon Computers and Amazon Photo; and a coauthor network dataset, Coauthor CS.

[0071] In the paper citation network dataset, each node represents a paper, and the edges represent the citation relationship between two papers. The goal is to classify each node into different subject areas. In the Amazon-derived purchase network dataset, each node represents a product, and the edges represent two products that are frequently purchased together. The goal is to classify each node into different product categories. In the co-author network dataset, each node represents an author, and the edges represent the collaboration relationship between authors. The goal is to classify each node into different research fields.

[0072] In step S2, the graph structure is input into the teacher network to obtain the teacher node representation. Inputting the augmented graph structure into the student network yields the student node representations. Where d is the embedding dimension.

[0073] The teacher network and the student network consist of two graph neural networks (GNNs) with the same architecture, namely the student network Φ. θ Teacher Network Φ φ Student network Φ θ For example, its architecture GNN uses a message passing mechanism to update node representations, that is, for a node v in the graph... i Its embedding at the m-th layer is represented as The message passing process in GNNs typically involves two steps: First, at the aggregation node v in the m-1 layer... i The embedding representations of neighbors are then combined with the node's own embedding representation to form a comprehensive representation at the m-th layer. Formally, the message passing process of a GNN is represented as:

[0074]

[0075]

[0076] in, For node vi Neighbors; and These represent the aggregation operator and the combination operator at the m-th layer, respectively; after passing through m layers, the final node embedding representation is output. and They are nodes v i Embedded representations of the m-th and m-1-th layers; For node v j Embedded representations of the m-th and m-1-th layers; For node v i The embedding representation of the m-th layer of the neighbor.

[0077] In step S3, based on the teacher node representation, a hypergraph structure matrix and a hyperedge embedding matrix are constructed, and the product of the hypergraph structure matrix and the hyperedge embedding matrix is ​​used as the teacher node hypergraph representation;

[0078] In one embodiment of the present invention, the expressions for the hypergraph structure matrix and the hyperedge embedding matrix are as follows:

[0079]

[0080] Where Λ is the hypergraph structure matrix, c represents the number of hyperedges; H represents the teacher node representation; W represents the learnable hyperedge weight matrix. R is the hyperedge embedding matrix. σ(·) is the activation function; U is the trainable matrix. It is the transpose of Λ;

[0081] The expression for the hypergraph representing teacher nodes is:

[0082]

[0083] Where Z represents the hypergraph representation of teacher nodes.

[0084] In step S4, based on the teacher node hypergraph representation and the student node representation, an enhanced hypergraph structure matrix and a consistency objective function are constructed to determine the consistency between any unlabeled node and multiple labeled nodes in the graph structure data:

[0085] S41. Randomly select a preset number of labeled nodes as anchor points and store them in the memory library;

[0086] S42. Based on the student node representation, calculate the similarity between the embedding representation of any unlabeled node and the embedding representation of any anchor point in the memory library:

[0087]

[0088] Among them, s i s is the embedding representation of the i-th unlabeled node; t Let be the embedding representation of the t-th anchor point in the memory library, 1≤t≤T, where T is the preset number; exp(·) is the exponential function; cos(·) is the cosine similarity; τ is the temperature coefficient, set to 0.5; For s i With s t Relational similarity; s t′ Let be the embedding representation of the t′-th anchor point in the memory library, 1≤t′≤T;

[0089] S43. Based on the hypergraph representation of teacher nodes, calculate the similarity between the hypergraph representation of any unlabeled node and the hypergraph representation of any anchor point in the memory database:

[0090]

[0091] Among them, z i Let z be the hypergraph representation of the i-th unlabeled node; t Let be the hypergraph representation of the t-th anchor point in the memory library; For z i With z t Relational similarity; z t′ Let be the hypergraph representation of the t′-th anchor point in the memory library;

[0092] S44. Based on relational similarity and relational similarity Constructing the consistency objective function l r :

[0093]

[0094] in, D is the set of labels for all unlabeled nodes in the graph structure data; KL For divergence; For s i Similarity to the embedding representation s1 of the first anchor point in the memory library; For s i The embedding representation s of the T-th anchor point in the memory library T Relationship similarity; For z i Similarity to the hypergraph representation z1 of the first anchor point in the memory library; For z i The hypergraph representation z of the T-th anchor point in the memory library T Relationship similarity; For s i Similarity to the embedded representation of all anchors in the memory library; For zi Similarity to the hypergraph representation of all anchor points in the memory library.

[0095] In step S5, the teacher node representation and student node representation are input into the multilayer perceptron to obtain the predicted classification distribution of nodes in the student network and teacher network:

[0096] P = MLP(S), Q = MLP(H)

[0097] Among them, P and Representing student network Φ θ Teacher Network Φ φ The generated predicted class distribution, row vector p i and q i This indicates that there are two network pairs of nodes v. i The prediction.

[0098] Based on the predicted classification distribution of unlabeled nodes, a teacher-student consistency objective function is constructed to guide students' online learning:

[0099] S51. Based on the prediction vectors of unlabeled nodes in the predicted category distribution of the teacher network, generate pseudo-labels for the unlabeled nodes:

[0100]

[0101] Where, q i Let be the distribution of the predicted categories of the i-th unlabeled node in the teacher network; The pseudo-label is the i-th unlabeled node; argmax(·) returns the value of the argument when the given function reaches its maximum value;

[0102] S52. Select pseudo-labels whose category probability is greater than the pseudo-label threshold from all pseudo-labels, and then proceed to step S53.

[0103] S53. Based on the pseudo-label of the i-th unlabeled node, construct a teacher-student consistency objective function l to guide students' online learning. t :

[0104]

[0105] in, This is the set of labels for all unlabeled nodes in the graph structure data; max represents the maximum value. for transpose of; p i Let be the predicted class distribution of the student network for the unlabeled i-th node; 1(·) is the indicator function.

[0106] In step S6, based on the prediction type distribution of the labeled nodes corresponding to the student network, a supervision objective function for training the supervised student network is constructed:

[0107]

[0108] in, y is the set of labels for all labeled nodes in the graph structure data; k ∈{0,1} K Let K be the true label vector of the kth labeled node, where K is the total number of categories; For y k transpose of; p k This represents the predicted class distribution of the k-th node in the student network.

[0109] In step S7, a joint objective function is constructed using the consistency objective function, the teacher-student consistency objective function, and the supervision objective function to iteratively optimize the student network and the teacher network until the training of the two networks is completed;

[0110] In implementation, the preferred expression for the joint objective function l in this scheme is:

[0111] l = l s +αl t +βl r

[0112] Here, α and β are both weighting coefficients used to control their respective contributions, and are set to α = β = 0.1.

[0113] In the iterative optimization process of this scheme, the student network is optimized using gradient descent, and the teacher network is optimized using a momentum update strategy; the momentum update strategy is as follows:

[0114]

[0115] φ=∈φ+(1―∈)θ

[0116] Where, θ and η represents the model parameters for the student network and the teacher network, respectively; η is the learning rate; and ∈ is the momentum coefficient.

[0117] In step S8, the nodes to be classified in the semi-supervised classification dataset are obtained and input into the trained teacher network. Then, the output of the teacher network is input into the multilayer perceptron for classification to obtain the predicted class distribution of the nodes.

[0118] To verify the effectiveness of the proposed semi-supervised node classification method, a comparative experiment is conducted below with 11 existing semi-supervised node classification algorithms:

[0119] The 11 semi-supervised node classification algorithms in the prior art include: (1) Chebyshev, (2) GCN, (3) GAT, (4) SGC, (5) DGI, (6) MVGRL, (7) GRACE, and (8) CG. 3 (9) CLNode, (10) Gapformer, (11) RCL. These 11 semi-supervised node classification methods were compared with the node classification method of this scheme (abbreviated as Ours in the figure) on six different datasets. The six different datasets include: (1) Cora, (2) CiteSeer, (3) PubMed, (4) AmazonComputers, (5) Amazon Photo, and (6) Coauthor CS.

[0120] Cora, CiteSeer, and PubMed are three paper citation network datasets; Amazon Computers and Amazon Photo are two purchase network datasets from Amazon; and Coauthor CS is a co-author network dataset. In the paper citation network dataset, each node represents a paper, and edges represent citation relationships between two papers, aiming to categorize each node into different subject areas. In the Amazon-derived purchase network dataset, nodes represent a product, and edges represent two products that are frequently purchased together, aiming to categorize each node into different product categories. In the co-author network dataset, nodes represent an author, and edges represent collaboration relationships between authors, aiming to categorize each node into different research areas.

[0121] 1) Analysis of experimental results

[0122] Eleven existing semi-supervised node classification methods and the node classification method proposed in this scheme were tested on six different datasets. Each experiment was repeated five times, and the mean and standard deviation were calculated for comparison. For easier viewing, the best performance is bolded; for a comparison of the mean and standard deviation, please refer to [reference needed]. Figure 2 ,Depend on Figure 2 It is evident that the node classification method in this scheme achieves optimal performance in all cases, which verifies the effectiveness of this method.

[0123] like Figure 3 and Figure 4 As shown, the impact of semi-supervised node classification performance is evaluated on the Cora and CiteSeer datasets with different label ratios. Figure 3 and Figure 4The data presented demonstrates that our proposed method outperforms existing techniques in all cases. This robust performance showcases the significant superiority of our method when dealing with supervised but scarce data. Even with a severely limited number of labeled samples, our proposed method exhibits a significant performance advantage over existing techniques.

[0124] 2) Sensitivity analysis:

[0125] exist Figures 5-7 In this paper, the method explores the impact of different hyperparameters, focusing particularly on three key aspects: the number of hyperedges, the pseudo-label threshold, and the embedding dimension. Figure 5 The image shows a comparison of different numbers of hyperedges on different datasets. Figure 6 This section compares the results of different pseudo-label thresholds across different datasets. Figure 7 This section compares the results of different embedding dimensions on different datasets.

[0126] First, the impact of the number of hyperedges was considered, taking into account a range of values ​​from 16 to 512. For example... Figure 5 As shown in (a) to (b), initially increasing the number of hyperedges was associated with a significant performance improvement. This observation suggests that a larger number of hyperedges allows the model to capture more complex relationships and dependencies between nodes, thereby improving its representational power. However, it is important to note that performance degrades when the number of hyperedges is too high. This phenomenon may be due to the generation of overly complex specific hyperedge-crossing node structures when using a large number of hyperedges. These complex structures may introduce noise and unnecessary complexity, ultimately weakening the model's generalization ability.

[0127] Next, this method further investigated the impact of the pseudo-label threshold, with values ​​ranging from {0.75, 0.8, 0.9, 0.95, 0.99}, to evaluate its effect on model performance. The results are as follows... Figure 6 As shown in (a) to (c), it can be seen that performance initially improves with increasing threshold, but begins to decline when the threshold becomes too large. This behavior may be because the model selects pseudo-labels with higher confidence as the threshold increases, making the pseudo-labels more reliable for robust training of the model. However, when the threshold is too large, a significant portion of the training data fails to meet the high confidence criterion of the pseudo-labels, resulting in a reduction in usable training data.

[0128] Finally, this approach explores the impact of variations in embedding dimensions, considering different values ​​within the range {16, 32, 64, 128, 256, 512}. The results are as follows: Figure 7As shown in (a) to (b), the performance of all datasets improved accordingly with increasing embedding dimension. This result can be attributed to the fact that a larger embedding dimension allows the model to capture more complex features, thereby improving the representation quality. However, after a certain threshold, increasing the embedding dimension no longer brings significant performance improvements, and the performance tends to plateau. This phenomenon suggests that there is an optimal range for the embedding dimension, which can find a balance between capturing complex features and preventing overfitting.

[0129] 3) Visual analysis:

[0130] The effectiveness of the hypergraph structure is validated by visualizing the hypergraph structure learned by the proposed method using the Cora dataset as a case study. In the Cora dataset, each node represents a scientific paper categorized into seven different classes, and edges represent citation relationships between papers. To illustrate this more clearly, the proposed method selects a subgraph from the entire citation network, focusing on a subgraph containing only eight hyperedges. Figure 8 (a) shows that in the citation network, each paper is connected to only a few neighboring papers, which poses a challenge to modeling complex interactions. Furthermore, the sparsity of the network means that many nodes are not interconnected, hindering the flow of information between nodes.

[0131] exist Figure 8 (b) illustrates some of the hyperedges obtained through the hypergraph structure in this scheme. As shown in the figure, many nodes that were initially unconnected in the original graph are now propagating information through the hypergraph. The hypergraph structure enables nodes in the network to engage in higher-order interactions, effectively capturing more complex and nuanced relationships within the complete network. The results demonstrate that the hypergraph structure constructed by our method excels in modeling complex node relationships, going beyond pairwise interactions and thus providing significant flexibility for modeling complex data structures.

[0132] The technical principles of the present invention have been described above with reference to specific embodiments, which are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments; all technical solutions falling within the scope of the present invention's concept are within its protection scope. Those skilled in the art can conceive of other specific embodiments of the present invention without creative effort, and these embodiments will all fall within the protection scope of the present invention.

Claims

1. A semi-supervised node classification method based on hypergraph structure learning, characterized in that, Including the following steps: S1. Collect graph structure data from the semi-supervised classification dataset and perform data augmentation on the graph structure data to obtain augmented graph structures; S2. Input the graph structure into the teacher network to obtain the teacher node representation; input the augmented graph structure into the student network to obtain the student node representation; S3. Based on the teacher node representation, construct the hypergraph structure matrix and the hyperedge embedding matrix, and use the product of the hypergraph structure matrix and the hyperedge embedding matrix as the teacher node hypergraph representation; S4. Based on the hypergraph representation of teacher nodes and student nodes, construct a consistency objective function to enhance the consistency between any unlabeled node and multiple labeled nodes in the graph structure data; S5. Input the teacher node representation and student node representation into the multilayer perceptron to obtain the predicted classification distribution of nodes in the student network and teacher network. Based on the predicted classification distribution of unlabeled nodes, construct a teacher-student consistency objective function to guide student network learning. S6. Based on the prediction type distribution of the labeled nodes corresponding to the student network, construct a supervision objective function for training the student network. S7. Construct a joint objective function using the consistency objective function, the teacher-student consistency objective function, and the supervision objective function to iteratively optimize the student network and the teacher network until the training of the two networks is completed; S8. Obtain the nodes to be classified from the semi-supervised classification dataset and input them into the trained teacher network. Then, input the output of the teacher network into the multilayer perceptron for classification to obtain the predicted class distribution of the nodes. The semi-supervised classification dataset is any one of the following: three paper citation network datasets Cora, CiteSeer, and PubMed; two purchase network datasets from Amazon, Amazon Computers and Amazon Photo; and a coauthor network dataset, Coauthor CS. In the paper citation network dataset, each node represents a paper, and the edges represent the citation relationship between two papers. The goal is to classify each node into different subject areas. In the Amazon-derived purchase network dataset, each node represents a product, and the edges represent two products that are frequently purchased together. The goal is to classify each node into different product categories. In the co-author network dataset, each node represents an author, and the edges represent the collaboration relationship between authors. The goal is to classify each node into different research areas. Step S4 further includes: S41. Randomly select a preset number of labeled nodes as anchor points and store them in the memory library; S42. Based on the student node representation, calculate the similarity between the embedding representation of any unlabeled node and the embedding representation of any anchor point in the memory library: in, Let i be the embedding representation of the i-th unlabeled node; Let be the embedding representation of the t-th anchor point in the memory library. , For preset quantity; It is an exponential function; Cosine similarity; τ is the temperature coefficient; for and Relationship similarity; For the first in the memory library Embedded representation of anchor points ; S43. Based on the hypergraph representation of teacher nodes, calculate the similarity between the hypergraph representation of any unlabeled node and the hypergraph representation of any anchor point in the memory database: in, Let i be the hypergraph representation of the i-th unlabeled node; Let be the hypergraph representation of the t-th anchor point in the memory library; for and Relationship similarity; For the first in the memory library Hypergraph representation with anchor points; S44. Based on relational similarity and relational similarity Construct a consistency objective function : ， in, This is the set of labels for all unlabeled nodes in the graph structure data; For divergence; for Embedded representation of the first anchor point in the memory library Relationship similarity; for Embedded representation of the T-th anchor point in the memory library Relationship similarity; for Hypergraph representation with the first anchor point in the memory library Relationship similarity; for Hypergraph representation with the T-th anchor point in the memory library Relationship similarity; for Similarity to the embedded representation of all anchors in the memory library; for Similarity to the hypergraph representation of all anchor points in the memory library.

2. The semi-supervised node classification method according to claim 1, characterized in that, The expressions for the hypergraph structure matrix and the hyperedge embedding matrix are as follows: ， in, is the hypergraph structure matrix; H is the teacher node representation; W is the learnable hyperedge weight matrix; R is the hyperedge embedding matrix; U is the activation function; U is the trainable matrix; for transpose; The expression for the hypergraph representing teacher nodes is: Where Z represents the hypergraph representation of teacher nodes.

3. The semi-supervised node classification method according to claim 1, characterized in that, The teacher-student consistency objective function for guiding students' online learning further includes: S51. Based on the prediction vectors of unlabeled nodes in the predicted category distribution of the teacher network, generate pseudo-labels for the unlabeled nodes: in, Let be the distribution of the predicted categories of the i-th unlabeled node in the teacher network; This is the pseudo-label for the i-th unlabeled node; To return the value of the argument when a given function reaches its maximum value; S52. Select pseudo-labels whose category probability is greater than the pseudo-label threshold from all pseudo-labels, and then proceed to step S53. S53. Based on the pseudo-label of the i-th unlabeled node, construct a teacher-student consistency objective function to guide students' online learning. : in, This is the set of labels for all unlabeled nodes in the graph structure data; max represents the maximum value. for transpose; Let be the predicted class distribution of the student network for the unlabeled i-th node; This is an indicator function.

4. The semi-supervised node classification method according to claim 1, characterized in that, The expression for the supervision objective function is: in, This is the set of labels for all labeled nodes in the graph structure data; Let K be the true label vector of the kth labeled node, where K is the total number of categories; for transpose; This represents the predicted class distribution of the k-th node in the student network.

5. The semi-supervised node classification method according to any one of claims 1-4, characterized in that, Joint objective function The expression is: Where α and β are both weighting coefficients; The objective function for teacher-student consistency in guiding students' online learning; The student network is optimized using gradient descent, while the teacher network is optimized using a momentum update strategy. The momentum update strategy is as follows: Where, θ and η represents the model parameters for the student network and the teacher network, respectively; η is the learning rate. This is the momentum coefficient.

6. The semi-supervised node classification method according to any one of claims 1-4, characterized in that, During the iterative optimization process, both the teacher network and the student network are graph neural networks (GNNs) with the same structure. The message passing process of the GNN is represented as follows: in, For nodes Neighbors; and These represent the aggregation operator and the combination operator at the m-th level, respectively. and They are nodes No. Embedded representation of layers m and m-1; For nodes Embedded representation of the (m-1)th layer; For nodes The neighbor's first Layer embedding representation.

7. The semi-supervised node classification method according to claim 1, characterized in that, Methods for data augmentation of graph structure data include attribute masking or edge perturbation; the attribute masking involves randomly selecting a subset of nodes at a first preset ratio and masking its attributes at a second preset ratio; the edge perturbation involves randomly removing edges at a third preset ratio from the graph structure data.

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