Semi-supervised node classification method based on hypergraph structure learning

Abstract

The invention discloses a semi-supervised node classification method based on hypergraph structure learning, and the method comprises the steps: collecting graph structure data, and carrying out the data enhancement, and obtaining an 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 a teacher node hypergraph representation; constructing a consistency objective function, a teacher-student consistency objective function and a supervision objective function according to the teacher node representation, the student node representation and the teacher node hypergraph representation; constructing a joint objective function by adopting a consistency objective function, a teacher-student consistency objective function and a supervision objective function to carry out iterative optimization on the student network and the teacher network until training of the two networks is completed; and acquiring to-be-classified nodes of the semi-supervised classification data set, inputting the to-be-classified nodes into the trained teacher network, and inputting the output of the teacher network into the multi-layer perceptron for classification to obtain predicted category distribution of the nodes.

Description

Technical Field

[0001] The present invention relates to graph structure classification technology, and in particular to a semi-supervised node classification method based on hypergraph structure learning. Background Art

[0002] Graph is an efficient and natural representation method, because the intricate relationships and dependencies between different nodes can be effectively captured and analyzed through the graph structure, and can be used to model structured data and relational data in various fields and applications. In recent years, graph neural networks (GNNs) have performed well in many tasks such as analyzing and understanding graph structured data. These tasks include node classification, graph classification, graph clustering, link prediction, and so on. Among these tasks, semi-supervised node classification is one of the most important research directions, which aims to predict the category labels of unlabeled nodes in a given graph using only a small number of labeled nodes.

[0003] In recent years, the task of semi-supervised node classification has been widely studied, and several typical methods have emerged. For example, using the GNN classifier trained with labeled nodes to assign pseudo labels to unlabeled nodes, and selecting high-confidence pseudo labels from easy to difficult through curriculum learning to add to the labeled node set, and iteratively training the GNN classifier; for example, by comparing the encodings from two generated views (first-order neighbors and graph diffusion matrix, or using edge deletion and node feature masks) to perform self-supervised node representation learning, and by improving node-level consistency, the robustness of representation learning is enhanced; for example, combining graph contrast loss and graph reconstruction loss, the former is used to enhance the node representation of labeled and unlabeled data, and the latter is used to perform additional supervision by extracting the relationship between data features and graph topology.

[0004] Although semi-supervised node classification methods have achieved good results in practical applications, existing methods still have two major limitations. On the one hand, GNNs usually follow the idea of ​​neighbor aggregation in the message passing mechanism, resulting in each node only relying on neighbors within a few hops, which makes the captured local information very limited. At the same time, modeling high-order dependencies between nodes is crucial for exploring global information in the graph, but existing methods fail to effectively capture this information, resulting in suboptimal performance. For example, in biochemical networks modeling protein-protein interactions, GNNs limited to nearby neighbor nodes may ignore important interactions that occur through intermediate proteins. This problem leads to proteins with high-order dependencies that may not be fully represented, which often constitute complex biological pathways. On the other hand, these methods usually focus on fitting the set of labeled nodes through GNNs, but ignore the inherent unlabeled nodes in the graph, and the intrinsic information contained in them is not fully mined. This problem may 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 lead to an incomplete understanding of the network structure. Ignoring users with latent features, which often provide key information about community structure and interconnections, may lead to a shift in the representation of social relationships. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the semi-supervised node classification method based on hypergraph structure learning provided by the present invention solves the problem that the node classification method in the prior art only relies on neighbors within a few hops, resulting in very limited local information being captured.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

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

[0008] S1. Collect graph structure data in the semi-supervised classification data set, and perform data enhancement on the graph structure data to obtain an augmented graph structure;

[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. According to 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;

[0011] S4. According to the teacher node hypergraph representation and the student node representation, a consistency objective function is constructed to enhance the consistency between any unlabeled node and multiple labeled nodes in the hypergraph structure matrix and the graph structure data;

[0012] S5. Input the teacher node representation and the student node representation into a multi-layer perceptron to obtain the predicted classification distribution of nodes in the student network and the teacher network. According to the predicted classification distribution of unlabeled nodes, a teacher-student consistency objective function for guiding the student network learning is constructed.

[0013] S6. Construct a supervision objective function for supervising the training of the student network according to the distribution of the predicted types of the labeled nodes corresponding to the student network;

[0014] S7, using the consistency objective function, the teacher-student consistency objective function and the supervision objective function to construct a joint 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 in the semi-supervised classification data set and input them into the trained teacher network. Then, input the output of the teacher network into the multi-layer perceptron for classification to obtain the predicted category distribution of the nodes.

[0016] Furthermore, the expressions of the hypergraph structure matrix and the hyperedge embedding matrix are respectively:

[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; U is the trainable matrix; is the transpose of Λ;

[0019] The expression of teacher node hypergraph is:

[0020]

[0021] Among them, Z is the hypergraph representation of the teacher node.

[0022] Furthermore, step S4 further comprises:

[0023] S41, randomly selecting a preset number of labeled nodes as anchor points, and storing them in a memory library;

[0024] S42. Based on the student node representation, calculate the relationship 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 is the embedding representation of the i-th unlabeled node; s tis the embedding representation of the t-th anchor point in the memory bank, 1≤t≤T, T is the preset number; exp(·) is the exponential function; cos(·) is the cosine similarity; τ is the temperature coefficient; For i With s t Similarity of relationship; t′ is the embedding representation of the t′th anchor point in the memory bank, 1≤t′≤T;

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

[0028]

[0029] Among them, z i is the hypergraph representation of the i-th unlabeled node; z t is the hypergraph representation of the t-th anchor point in the memory bank; For z i With z t The similarity of the relationship; t′ is the hypergraph representation of the t′th anchor point in the memory bank;

[0030] S44. Based on relationship similarity and relational similarity Constructing the consistency objective function l r :

[0031]

[0032] in, is the label set of all unlabeled nodes in the graph structure data; D KL is the divergence; For i The embedding of the first anchor in the memory bank represents the relational similarity of s1; For i and the embedding representation s of the Tth anchor point in the memory bank T similarity of relationships; For z i The relational similarity with the hypergraph representation z1 of the first anchor in the memory bank; For z i The hypergraph representation z of the Tth anchor point in the memory bank T similarity of relationships; For i Relational similarity with the embedding representations of all anchors in the memory bank; For z i Relational similarity with the hypergraph representation of all anchors in the memory bank.

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

[0034] S51. Generate pseudo labels for unlabeled nodes based on the prediction vectors of unlabeled nodes in the prediction category distribution of the teacher network:

[0035]

[0036] Among them, q i is the predicted category distribution of the teacher network for the i-th unlabeled node; is the pseudo label of the i-th unlabeled node; argmax(·) returns the value of the independent variable when the given function reaches the maximum value;

[0037] S52, selecting the pseudo-labels whose category probability is greater than the pseudo-label threshold among all pseudo-labels, and then proceeding to step S53;

[0038] S53. Based on the pseudo label of the i-th unlabeled node, construct the teacher-student consistency objective function l for guiding student network learning t :

[0039]

[0040] in, is the label set of all unlabeled nodes in the graph structure data; max is the maximum value; for The transpose of i is the predicted category distribution of the student network for the unlabeled i-th node; 1(·) is the indicator function.

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

[0042]

[0043] in, is the label set of all annotated nodes in the graph structure data; k ∈{0,1} K is the true label vector of the kth labeled node, K is the total number of categories; for y k The transpose of k is the predicted category distribution of the kth node labeled by the student network.

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

[0045] l=l s +αl t +βl r

[0046] Among them, α and β are weight coefficients;

[0047] During the iterative optimization process, the student network is optimized by gradient descent, and the teacher network is optimized by the momentum update strategy; the momentum update strategy is:

[0048]

[0049] φ=∈φ+(1―∈)θ

[0050] Among them, θ and are the model parameters of the student network and the teacher network respectively; η is the learning rate; ∈ is the momentum coefficient.

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

[0052]

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

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

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

[0056] Furthermore, the method for data enhancement of graph structure data includes attribute masking or edge perturbation; the attribute masking is to randomly select a node subset of a first preset ratio and mask its attributes of a second preset ratio; the edge perturbation is to randomly remove edges of a third preset ratio from the graph structure data.

[0057] The beneficial effects of the present invention are as follows: this scheme obtains node representations through the teacher network, establishes a hypergraph representation of the teacher node, and considers using the hypergraph structure to learn and model high-order dependencies between nodes to explore the global semantic information in the structure graph, thereby improving the low accuracy of semi-supervised node classification; 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 accuracy of classification. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0059] Figure 2 These are the comparative test results of different algorithms corresponding to the six data sets of Cora, CiteSeer, PubMed, Amazon Computers, Amazon Photo and Coauthor CS in the embodiments of the present invention.

[0060] Figure 3 These are the comparative test results of different algorithms corresponding to different label ratio settings on the Cora dataset in an embodiment of the present invention.

[0061] Figure 4 These are the comparative test results of different algorithms corresponding to different label ratio settings on the CiteSeer dataset in an embodiment of the present invention.

[0062] Figure 5 The following is a comparison of the accuracy performance of this method under different hyperedge numbers on different datasets. (a) is the accuracy comparison of the Cora dataset and the CiteSeer dataset on different hyperedges; (b) is the accuracy comparison of PubMed and AmazonComputers on different hyperedges; (c) is the accuracy comparison of Amazon Photo and Coauthor CS on different hyperedges.

[0063] Figure 6The following is a comparison of the accuracy performance of this method under different pseudo-label threshold settings on different datasets. (a) is the accuracy comparison of the Cora dataset and the CiteSeer dataset at different pseudo-label thresholds; (b) is the accuracy comparison of PubMed and Amazon Computers at different pseudo-label thresholds; (c) is the accuracy comparison of Amazon Photo and Coauthor CS at different pseudo-label thresholds.

[0064] Figure 7 The following is a comparison of the accuracy performance of this method under different embedding dimensions on different datasets. (a) is the accuracy comparison of the Cora dataset and the CiteSeer dataset under different embedding dimensions; (b) is the accuracy comparison of PubMed and AmazonComputers under different embedding dimensions; (c) is the accuracy comparison of Amazon Photo and Coauthor CS under different embedding dimensions.

[0065] Figure 8 Visualization experiment of the original graph structure of the Cora dataset and the hypergraph structure learned by this method on the original structure. (a) is the original graph structure; (b) is the learned hypergraph structure. DETAILED DESCRIPTION

[0066] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations 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; Figure 1 As shown, the method S includes steps S1 to S8.

[0068] In step S1, the graph structure data in the semi-supervised classification data set is collected, and the graph structure data is enhanced to obtain an augmented graph structure. in Represents a set of N nodes in the graph structure, is the edge set of the graph.

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

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

[0071] In the paper citation network dataset, each node represents a paper and the edge represents the citation relationship between two papers. The purpose is to classify each node into different subject areas. In the Amazon-derived purchase network dataset, the node represents a product and the edge represents two products that are often purchased together. The purpose is to classify each node into different product categories. In the co-author network dataset, the node represents an author and the edge represents the cooperative relationship between authors. The purpose 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 Input the augmented graph structure into the student network to obtain the student node representation Where d is the embedding representation dimension,

[0073] The teacher network and the student network are composed of two graph neural networks (GNNs) with the same architecture, namely the student network Φ θ and teacher networkΦ φ . Based on the student network 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 , whose embedding in the mth layer is represented as The message passing process in GNN usually consists of two steps: first, aggregate the nodes v at the m-1th layer. i The neighbor’s embedding representation is then combined with the node’s own embedding representation to form a comprehensive representation of the mth layer. Formally, the message passing process of GNN is expressed as:

[0074]

[0075]

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

[0077] In step S3, a hypergraph structure matrix and a hyperedge embedding matrix are constructed according to the teacher node representation, 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 of the hypergraph structure matrix and the hyperedge embedding matrix are respectively:

[0079]

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

[0081] The expression of teacher node hypergraph is:

[0082]

[0083] Among them, Z is the hypergraph representation of the teacher node,

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

[0085] S41, randomly selecting a preset number of labeled nodes as anchor points, and storing them in a memory library;

[0086] S42. Based on the student node representation, calculate the relationship 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 is the embedding representation of the i-th unlabeled node; s t is the embedding representation of the t-th anchor point in the memory bank, 1≤t≤T, T is the preset number; exp(·) is the exponential function; cos(·) is the cosine similarity; τ is the temperature coefficient, which is set to 0.5; For i With s t Similarity of relationship; t′ is the embedding representation of the t′th anchor point in the memory bank, 1≤t′≤T;

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

[0090]

[0091] Among them, z i is the hypergraph representation of the i-th unlabeled node; z t is the hypergraph representation of the t-th anchor point in the memory bank; For z i With z t The similarity of the relationship; t′ is the hypergraph representation of the t′th anchor point in the memory bank;

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

[0093]

[0094] in, is the label set of all unlabeled nodes in the graph structure data; D KL is the divergence; For i The embedding of the first anchor in the memory bank represents the relational similarity of s1; For i and the embedding representation s of the Tth anchor point in the memory bank T similarity of relationships; For z i The relational similarity with the hypergraph representation z1 of the first anchor in the memory bank; For z i The hypergraph representation z of the Tth anchor point in the memory bank T similarity of relationships; For i Relational similarity with the embedding representations of all anchors in the memory bank; For zi Relational similarity with the hypergraph representation of all anchors in the memory bank.

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

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

[0097] Among them, P and They represent the student network Φ θ and teacher networkΦ φ The generated predicted category distribution, row vector p i and q i Represents two network pairs of nodes v i prediction.

[0098] According to the predicted classification distribution of unlabeled nodes, a teacher-student consistency objective function for guiding student network learning is constructed:

[0099] S51. Generate pseudo labels for unlabeled nodes based on the prediction vectors of unlabeled nodes in the prediction category distribution of the teacher network:

[0100]

[0101] Among them, q i is the predicted category distribution of the teacher network for the i-th unlabeled node; is the pseudo label of the i-th unlabeled node; argmax(·) returns the value of the independent variable when the given function reaches the maximum value;

[0102] S52, selecting the pseudo-labels whose category probability is greater than the pseudo-label threshold among all pseudo-labels, and then proceeding to step S53;

[0103] S53. Based on the pseudo label of the i-th unlabeled node, construct the teacher-student consistency objective function l for guiding student network learning t :

[0104]

[0105] in, is the label set of all unlabeled nodes in the graph structure data; max is the maximum value; for The transpose of i is the predicted category distribution of the student network for the unlabeled i-th node; 1(·) is the indicator function.

[0106] In step S6, according to the predicted type distribution of the labeled nodes corresponding to the student network, a supervision objective function for supervising the student network for training is constructed:

[0107]

[0108] in, is the label set of all annotated nodes in the graph structure data; k ∈{0,1} K is the true label vector of the kth labeled node, K is the total number of categories; for y k The transpose of k is the predicted category distribution of the kth node labeled by 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] During implementation, the preferred expression of the joint objective function l of this scheme is:

[0111] l=l s +αl t +βl r

[0112] Among them, α and β are weight 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 by gradient descent, and the teacher network is optimized by momentum update strategy; the momentum update strategy is:

[0114]

[0115] φ=∈φ+(1―∈)θ

[0116] Among them, θ and are the model parameters of the student network and the teacher network respectively; η is the learning rate; ∈ is the momentum coefficient.

[0117] In step S8, the nodes to be classified of the semi-supervised classification data set are obtained and input into the trained teacher network. Then, the output of the teacher network is input into a multi-layer perceptron for classification to obtain the predicted category distribution of the nodes.

[0118] In order to verify the effect of the semi-supervised node classification method of this scheme, the method proposed in this scheme is compared with 11 semi-supervised node classification algorithms in the prior art:

[0119] The 11 existing semi-supervised node classification algorithms include: (1) Chebyshev, (2) GCN, (3) GAT, (4) SGC, (5) DGI, (6) MVGRL, (7) GRACE, (8) CG 3 , (9) CLNode, (10) Gapformer, (11) RCL. These 11 semi-supervised node classification methods are compared with the node classification method of this scheme (abbreviated as Ours in the figure) in six different datasets; the six different datasets include: (1) Cora, (2) CiteSeer, (3) PubMed, (4) Amazon Computers, (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 the edge represents the citation relationship between two papers, with the purpose of classifying each node into different subject areas. In the Amazon-derived purchase network dataset, the node represents a commodity, and the edge represents two commodities that are often purchased together, with the purpose of classifying each node into different product categories. In the co-author network dataset, the node represents an author, and the edge represents the cooperative relationship between authors, with the purpose of classifying each node into different research fields.

[0121] 1) Experimental results analysis

[0122] Eleven existing semi-supervised node classification methods and the node classification method of this solution were tested on six different data sets. Each experiment was repeated five times, and the average and standard deviation were calculated for comparison. For ease of viewing, the best performance is bolded; the average and standard deviation are compared. For details, please refer to Figure 2 ,Depend on Figure 2 It can be seen that the node classification method of this scheme obviously achieves the best performance in all cases, which verifies the effectiveness of this method.

[0123] like Figure 3 and Figure 4 As shown in Figure 2, the performance of semi-supervised node classification is evaluated at different label ratios on the Cora and CiteSeer datasets. Figure 3 and Figure 4The data shown show that the proposed method outperforms the existing technology in all cases. This robust performance demonstrates the significant superiority of the proposed method when dealing with scarce supervised data. In the case of severely limited labeled samples, the proposed method shows significant performance advantages over the existing technology.

[0124] 2) Sensitivity analysis:

[0125] exist Figure 5-Figure 7 In this paper, the proposed method explores the impact of different hyperparameters, with a particular focus on three key aspects: the number of hyperedges, the pseudo-label threshold, and the embedding dimension. Figure 5 The comparison of different numbers of hyperedges on different data sets is shown in the figure. Figure 6 This is the comparison of different pseudo-label thresholds on different data sets. Figure 7 Comparison of different embedding dimensions on different datasets.

[0126] First, for the effect of the number of hyperedges, a range of values ​​from 16 to 512 were considered. Figure 5 As shown in (a) to (b) in Figure 3, initially increasing the number of hyperedges is associated with a significant improvement in performance. This observation suggests that a larger number of hyperedges enables the model to capture more complex relationships and dependencies between nodes, thereby improving its representation ability. However, it should be noted that when the value of the number of hyperedges is too high, the performance degrades. This phenomenon may be due to the fact that when a large number of hyperedges are used, overly complex specific hyperedge intersection node structures are generated. These complex structures may introduce noise and unnecessary complexity, ultimately weakening the generalization ability of the model.

[0127] Next, this method further studies the impact of the pseudo-label threshold, with a value range of {0.75, 0.8, 0.9, 0.95, 0.99}, to evaluate its impact on model performance. The results are shown in Figure 6 As shown in (a) to (c), it can be seen that as the threshold increases, the performance initially improves, but when the threshold is too large, the performance begins to decline. This behavior may be due to the fact that when the threshold increases, the model selects pseudo-labels with higher confidence, making the pseudo-labels more reliable for robust training of the model. However, when the threshold is too large, a considerable portion of the training data cannot meet the high confidence standard of the pseudo-label, resulting in a reduction in the available training data.

[0128] Finally, our approach explores the impact of varying the embedding dimensionality, considering different values ​​in the range {16, 32, 64, 128, 256, 512}. Figure 7As shown in (a) to (b), as the embedding dimension increases, the performance of all datasets is observed to improve accordingly. This result can be attributed to the fact that a larger embedding dimension enables the model to capture more complex features, thereby improving the quality of representation. However, after exceeding a certain threshold, increasing the embedding dimension no longer brings significant performance improvements, and the performance tends to stabilize. This phenomenon shows that there is an optimal range of embedding dimensions that can find a balance between capturing complex features and preventing overfitting.

[0129] 3) Visualization analysis:

[0130] The effectiveness of the hypergraph structure learned by our method is verified by visualizing it through a case study using the Cora dataset. In the Cora dataset, each node represents a scientific paper, which is classified into seven different categories, and the edges represent the citation relationship between papers. For a clearer presentation, our method selects a subgraph from the entire citation network, focusing on only 8 hyperedges. Figure 8 (a) shows that in the citation network, each paper is only connected to a few neighboring papers, which makes it challenging to model complex interactions. In addition, the sparsity of the network makes many nodes unconnected, hindering the flow of information between nodes.

[0131] exist Figure 8 (b) shows some of the hyperedges obtained by the proposed scheme through the hypergraph structure. As shown in the figure, many nodes that were originally unconnected in the original graph have now propagated information through the hypergraph. The hypergraph structure enables nodes in the network to interact at a higher order, effectively capturing more complex and detailed relationships in the complete network. The results show that the hypergraph structure constructed by the proposed method performs well in modeling complex node relationships, beyond the scope of pairwise interactions, thus providing significant flexibility in modeling complex data structures.

[0132] The technical principle of the present invention is described above in combination with the specific embodiments, which are only preferred implementations of the present invention. The protection scope of the present invention is not limited to the above embodiments, and all technical solutions under the idea of ​​the present invention belong to the protection scope of the present invention. Those skilled in the art can think of other specific implementations of the present invention without creative work, and these methods will 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: Includes steps: S1. Collect graph structure data in the semi-supervised classification data set, and perform data enhancement on the graph structure data to obtain an augmented graph structure; 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. According to 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; S4. According to the teacher node hypergraph representation and the student node representation, a consistency objective function is constructed to enhance the consistency between any unlabeled node and multiple labeled nodes in the hypergraph structure matrix and the graph structure data; S5. Input the teacher node representation and the student node representation into a multi-layer perceptron to obtain the predicted classification distribution of nodes in the student network and the teacher network. According to the predicted classification distribution of unlabeled nodes, a teacher-student consistency objective function for guiding the student network learning is constructed. S6. Construct a supervision objective function for supervising the training of the student network according to the distribution of the predicted types of the labeled nodes corresponding to the student network; S7, using the consistency objective function, the teacher-student consistency objective function and the supervision objective function to construct a joint 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 in the semi-supervised classification data set and input them into the trained teacher network. Then, input the output of the teacher network into the multi-layer perceptron for classification to obtain the predicted category distribution of the nodes.

2. The semi-supervised node classification method according to claim 1, characterized in that: The expressions of the hypergraph structure matrix and the hyperedge embedding matrix are respectively: 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; U is the trainable matrix; is the transpose of Λ; The expression of the teacher node hypergraph is: Among them, Z is the hypergraph representation of the teacher node.

3. The semi-supervised node classification method according to claim 1, characterized in that: Step S4 further comprises: S41, randomly selecting a preset number of labeled nodes as anchor points, and storing them in a memory library; S42. Based on the student node representation, calculate the relationship similarity between the embedding representation of any unlabeled node and the embedding representation of any anchor point in the memory library: Among them, s i is the embedding representation of the i-th unlabeled node; s t is the embedding representation of the t-th anchor point in the memory bank, 1≤t≤T, T is the preset number; exp(·) is the exponential function; cos(·) is the cosine similarity; τ is the temperature coefficient; For i With s t Similarity of relationship; t′ is the embedding representation of the t′th anchor point in the memory bank, 1≤t′≤T; S43. Based on the hypergraph representation of the teacher node, calculate the relationship similarity between the hypergraph representation of any unlabeled node and the hypergraph representation of any anchor point in the memory library: Among them, z i is the hypergraph representation of the i-th unlabeled node; z t is the hypergraph representation of the t-th anchor point in the memory bank; For z i With z t The similarity of the relationship; t′ is the hypergraph representation of the t′th anchor point in the memory bank; S44. Based on relationship similarity and relational similarity Constructing the consistency objective function l r : in, is the label set of all unlabeled nodes in the graph structure data; D KL is the divergence; For i The embedding of the first anchor in the memory bank represents the relational similarity of s1; For i and the embedding representation s of the Tth anchor point in the memory bank T similarity of relationships; For z i The relational similarity with the hypergraph representation z1 of the first anchor in the memory bank; For z i The hypergraph representation z of the Tth anchor point in the memory bank T similarity of relationships; For i Relational similarity with the embedding representations of all anchors in the memory bank; For z i Relational similarity with the hypergraph representation of all anchors in the memory bank.

4. The semi-supervised node classification method according to claim 1, characterized in that: The objective function for constructing teacher-student consistency in guiding students' online learning further includes: S51. Generate pseudo labels for unlabeled nodes based on the prediction vectors of unlabeled nodes in the prediction category distribution of the teacher network: Among them, q i is the predicted category distribution of the teacher network for the i-th unlabeled node; is the pseudo label of the i-th unlabeled node; argmax(·) returns the value of the independent variable when the given function reaches the maximum value; S52, selecting the pseudo-labels whose category probability is greater than the pseudo-label threshold among all pseudo-labels, and then proceeding to step S53; S53. Based on the pseudo label of the i-th unlabeled node, construct the teacher-student consistency objective function l for guiding student network learning t : in, is the label set of all unlabeled nodes in the graph structure data; max is the maximum value; for The transpose of i is the predicted category distribution of the student network for the unlabeled i-th node; 1(·) is the indicator function.

5. The semi-supervised node classification method according to claim 1, characterized in that: The expression of the supervision objective function is: in, is the label set of all annotated nodes in the graph structure data; k ∈{0,1} K is the true label vector of the kth labeled node, K is the total number of categories; for y k The transpose of k is the predicted category distribution of the kth node labeled by the student network.

6. The semi-supervised node classification method according to any one of claims 1 to 5, characterized in that: The expression of the joint objective function l is: l＝l s +αl t +βl r Among them, α and β are weight coefficients; The student network is optimized by gradient descent, and the teacher network is optimized by momentum update strategy; the momentum update strategy is: φ=∈φ+(1―∈)θ Among them, θ and are the model parameters of the student network and the teacher network respectively; η is the learning rate; ∈ is the momentum coefficient.

7. The semi-supervised node classification method according to any one of claims 1 to 5, 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 GNN is expressed as: in, For node v i Neighbors; and They represent the aggregation operator and combination operator of the mth layer respectively; after passing through m layers, the final node embedding representation is output; and The nodes v i Embedding representations at the mth and m-1th layers; For node v j Embedding representations at the mth and m-1th layers; For node v i The m-th layer embedding representation of the neighbors of .

8. The semi-supervised node classification method according to any one of claims 1 to 5, characterized in that: The semi-supervised classification dataset is any one of three paper citation network datasets Cora, CiteSeer, and PubMed, two purchase network datasets from Amazon Amazon Computers and Amazon Photo, and a co-author network dataset Coauthor CS; In the paper citation network dataset, each node represents a paper and the edge represents the citation relationship between two papers. The purpose is to classify each node into different subject areas. In the Amazon-derived purchase network dataset, the node represents a product and the edge represents two products that are often purchased together. The purpose is to classify each node into different product categories. In the co-author network dataset, the node represents an author and the edge represents the cooperative relationship between authors. The purpose is to classify each node into different research fields.

9. The semi-supervised node classification method according to claim 1, characterized in that: The method for data enhancement of graph structure data includes attribute masking or edge perturbation; the attribute masking is to randomly select a node subset of a first preset ratio and mask its attributes of a second preset ratio; the edge perturbation is to randomly remove edges of a third preset ratio from the graph structure data.

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