Citation classification method and system based on double robust adaptive graph neural network

Abstract

The application discloses a kind of based on double robust self-adaptive graph neural network citation classification method and system, the method of the present application includes according to paper and its cited relationship Clean graph is constructed, and Clean graph is encoded as adjacency matrix;Extract the attribute of paper as feature and construct node feature matrix;Adjacency matrix and node feature matrix are scrambled, and the perturbed graph formed by the adjacency matrix and node feature matrix after scrambling is obtained;The perturbed graph is input into double robust self-adaptive graph neural network, and the adjacency matrix after scrambling in the perturbed graph is learned by structure learning module and topological purification to obtain optimized adjacency matrix, the optimized adjacency matrix and the node feature matrix after scrambling are propagated through graph neural network layer by layer to obtain the final node feature matrix, and citation classification of node is realized.The present application aims to improve the effectiveness and robustness in the process of citation classification based on graph structure data under the double modal disturbance that structure and feature disturbance occur simultaneously.

Description

Technical Field

[0001] This invention relates to the fields of graph structure data processing and citation classification technology, specifically to a citation classification method and system based on a dual robust adaptive graph neural network. Background Technology

[0002] Graph neural networks (GNNs) have become an important tool for processing graph-structured data and have achieved significant success in applications such as recommender systems, social network analysis, financial risk control, and bioinformatics. However, most GNN models rely on the reliability of graph structure and node features, while real-world graph data often contains noise and even malicious attacks. This sensitivity leads to a significant performance degradation of traditional GNNs when graph data is perturbed, making robustness enhancement an important research direction in the field of graph learning. In real-world scenarios, attacks often affect not only the graph structure but also node features simultaneously, resulting in more complex dual-modal perturbations. For example, in financial networks, attackers may simultaneously manipulate transaction relationships between customers and attribute information such as credit scores, thereby affecting the decisions of fraud detection systems. Furthermore, in social networks, users may provide inaccurate or exaggerated information about their interests or attributes, introducing noise into node features. These phenomena indicate that real-world graph data is often simultaneously affected by both structural and feature perturbations. Existing robust graph learning methods mainly focus on single-type perturbations. Some methods mitigate topological noise through graph structure learning or graph cleansing strategies, while others enhance robustness to feature noise by improving feature propagation mechanisms. However, these methods often fail to maintain stable performance when structural and feature perturbations occur simultaneously. On the one hand, many structural learning methods rely on Frobenius norm regularization, which proves inadequate when dealing with high-intensity topological perturbations. On the other hand, while residual connections commonly used in traditional graph neural networks alleviate the oversmoothing problem, the fixed fusion ratio may preserve corrupted node features under adversarial perturbations and further amplify the negative impact of noise. Therefore, designing robust graph learning methods capable of handling complex dual-modal perturbations remains a highly challenging problem. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a citation classification method and system based on a dual robust adaptive graph neural network, which addresses the above-mentioned problems in the prior art. This invention aims to improve the effectiveness and robustness of citation classification based on graph structure data under dual modal perturbations that occur simultaneously with structural and feature perturbations.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A citation classification method based on a dual robust adaptive graph neural network includes the following steps: S1, constructing a clean graph based on papers and their citation relationships, wherein nodes in the clean graph represent papers and edges represent citation relationships of papers; encoding the clean graph into an adjacency matrix; extracting paper attributes as features and constructing a node feature matrix; S2, scrambling the adjacency matrix and the node feature matrix to obtain a perturbed graph composed of the scrambled adjacency matrix and the node feature matrix; S3, inputting the perturbed graph into the dual robust adaptive graph neural network, performing structure learning and topology purification on the scrambled adjacency matrix in the perturbed graph through a structure learning module to obtain an optimized adjacency matrix, propagating the optimized adjacency matrix and the scrambled node feature matrix layer by layer through the graph neural network to obtain the final node feature matrix, and classifying the citations of nodes based on the node features in the final node feature matrix.

[0005] Optionally, when scrambling the adjacency matrix and the node feature matrix in step S2, scrambling the adjacency matrix includes modifying the values ​​of the elements in the adjacency matrix; scrambling the node feature matrix includes modifying the values ​​of the elements in the node feature matrix.

[0006] Optionally, in step S3, when performing structure learning and topology purification on the scrambled adjacency matrix in the perturbation graph through the structure learning module to obtain an optimized adjacency matrix, the following steps are included: minimizing the objective function of structure learning. The scrambled adjacency matrix is ​​updated using gradient descent to obtain the updated adjacency matrix. : ; in, This is the adjacency matrix before the update. For learning rate, For the objective function The gradient; the objective function of the structure learning The function expression is: ; ; in, This is the scrambled adjacency matrix. The adjacency matrix obtained by encoding the clean graph. For feasible sets, for The α norm, and These are the weighting coefficients. for Matrix Norms are used to implement sparsity constraints. for The nuclear norm of a matrix is ​​used to implement low-rank constraints. For characteristic smoothness loss, The number of nodes in the graph. For nodes eigenvectors, For nodes eigenvectors, For the adjacency matrix, the first... Okay, number The element values ​​of the column, for The square of the norm; in the objective function of structure learning After convergence, the final updated adjacency matrix will be obtained. Projected onto interval This process is repeated to obtain the final optimized adjacency matrix. Optionally, in step S3, when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through a graph neural network to obtain the final node feature matrix, the function expression for the first layer forward propagation of the graph neural network is: ; in, This is the node feature matrix output by the first layer of the graph neural network. This is the first layer of a graph neural network. This is the scrambled node feature matrix. These are the parameters of the first layer of the graph neural network. To optimize the adjacency matrix, the function expression for the forward propagation of the layers other than the first layer of the graph neural network is as follows: ; in, For graph neural networks The node feature matrix output by the layer. For the first graph neural network layer, For graph neural networks The node feature matrix of the layer, For graph neural networks Layer parameters.

[0007] Optionally, the function expression for each layer of the graph neural network is: ; ; ; in, For the i-th node, the first node passes through the graph neural network. The node feature matrix output by the layer. Let be the adaptive coefficient of the i-th node. Input the i-th node into the graph neural network. The node feature matrix of the layer, The intermediate representation of the i-th node is obtained by neighborhood aggregation with self-loops. For the number of nodes, To obtain the maximum value, Step size, For balance coefficient, This is an intermediate representation obtained through neighborhood aggregation with self-loops. For graph neural networks The node feature matrix of the layer, This is the normalized adjacency matrix.

[0008] Optionally, in step S3, when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through a graph neural network to obtain the final node feature matrix, the following steps are included: minimizing the preset objective function of representation learning. We will update the network parameters of the graph neural network using gradient descent to obtain the updated network parameters: ; in, For the updated network parameters, For update operations, For the network parameters before the update, For learning rate, Preset objective function The gradient.

[0009] Optionally, the preset objective function The function expression is: ; in, This is the final node feature matrix. For balance coefficient, This is the original node feature matrix; L is the difference between the final node feature matrix and the original node feature matrix. 2,1 Norm, for traces, for The transpose operation, The normalized adjacency matrix, It is an identity matrix.

[0010] The present invention also provides a citation classification system based on a dual robust adaptive graph neural network, comprising a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the citation classification method based on the dual robust adaptive graph neural network.

[0011] The present invention also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the citation classification method based on a dual robust adaptive graph neural network by a processor.

[0012] The present invention also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the citation classification method based on a dual robust adaptive graph neural network via a processor.

[0013] Compared with existing technologies, the present invention mainly achieves the following beneficial effects: The present invention includes constructing a clean graph based on papers and their citation relationships, encoding the clean graph into an adjacency matrix; extracting the attributes of the papers as features and constructing a node feature matrix; scrambling the adjacency matrix and the node feature matrix to obtain a perturbed graph composed of the scrambled adjacency matrix and the node feature matrix; inputting the perturbed graph into a dual robust adaptive graph neural network, performing structure learning and topology purification on the scrambled adjacency matrix in the perturbed graph through a structure learning module to obtain an optimized adjacency matrix, and propagating the optimized adjacency matrix and the scrambled node feature matrix layer by layer through the graph neural network to obtain the final node feature matrix, and realizing the citation classification of nodes. The present invention can improve the effectiveness and robustness of citation classification based on graph structure data under dual-modal perturbation where structure and feature perturbation occur simultaneously. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0015] Figure 2 This is a schematic diagram illustrating the working principle in an embodiment of the present invention. Detailed Implementation

[0016] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0017] make Represent a graph where the set of nodes is edge set is Graph structures are constructed using adjacency matrices. Encode the adjacency matrix element in row i and column j Represents a node and The connection relationships between them, the perturbed adjacency matrix is ​​denoted as Node features are represented by a matrix. It means that among them It is a node The feature vector. In the adversarial setting, consider the perturbed features: Let Represents a node The perturbation eigenvectors are defined, and the following is defined: This is the perturbed node feature matrix. For node classification tasks, there is only one subset. Have tags The goal of a dual robust adaptive graphical neural network (RA-GNN) is to learn a function. ,Will Mapped to To predict unlabeled nodes. The optimization problem under perturbation is formulated as follows: ; in, Indicates a node The prediction This is a loss function used to measure prediction error. For example... Figure 1 As shown, the citation classification method based on the dual robust adaptive graph neural network (RA-GNN) in this embodiment includes the following steps: S1, constructing a clean graph based on papers and their citation relationships, wherein the nodes in the clean graph are papers and the edges are the citation relationships of the papers; encoding the clean graph into an adjacency matrix; extracting the attributes of the papers as features and constructing a node feature matrix; S2, scrambling the adjacency matrix and the node feature matrix to obtain a perturbed graph composed of the scrambled adjacency matrix and the node feature matrix; S3, inputting the perturbed graph into the dual robust adaptive graph neural network, performing structure learning and topological purification on the scrambled adjacency matrix in the perturbed graph through the structure learning module to obtain an optimized adjacency matrix, propagating the optimized adjacency matrix and the scrambled node feature matrix layer by layer through the graph neural network to obtain the final node feature matrix, and realizing the citation classification of nodes based on the node features in the final node feature matrix.

[0018] In step S2 of this embodiment, when scrambling the adjacency matrix and the node feature matrix, scrambling the adjacency matrix includes modifying the values ​​of the elements in the adjacency matrix; scrambling the node feature matrix includes modifying the values ​​of the elements in the node feature matrix.

[0019] like Figure 2 As shown, in step S3 of this embodiment, when the structure learning module performs structure learning and topology purification on the scrambled adjacency matrix in the perturbation graph to obtain an optimized adjacency matrix, it includes: minimizing the objective function of structure learning. The scrambled adjacency matrix is ​​updated using gradient descent to obtain the updated adjacency matrix. : ; in, This is the adjacency matrix before the update. For learning rate, For the objective function The gradient.

[0020] Existing research indicates that clean graph data inherently possesses properties such as low rank, sparsity, and feature smoothness. Based on this prior knowledge, RA-GNN formulates structure reconstruction as a multi-constraint joint optimization problem. The goal is to minimize the following objective function. To restore robust graph structures The objective function of the structure learning The function expression is: ; ; in, This is the scrambled adjacency matrix. The adjacency matrix obtained by encoding the clean graph. For feasible sets, for The α norm, and These are the weighting coefficients. for Matrix Norms are used to implement sparsity constraints. for The nuclear norm of a matrix is ​​used to implement low-rank constraints. For characteristic smoothness loss, The number of nodes in the graph. For nodes eigenvectors, For nodes eigenvectors, For the adjacency matrix, the first... Okay, number The element values ​​of the column, for The square of the norm; in the objective function of structure learning After convergence, the final updated adjacency matrix will be obtained. Projected onto interval This process is repeated to obtain the final optimized adjacency matrix. The feasible set... The symmetry of undirected graphs is required, while It is a feature smoothness constraint. While existing methods mainly rely on constraint terms of fixed strength, the method in this embodiment introduces an adjustable one. - Norms serve as a measure of structural dissimilarity, enabling more flexible graph structure cleansing: ; in, and for - Two matrices with a norm. This metric exhibits adaptive properties: when When it is large, it approximates the square. Distance imposes a strict penalty on minute deviations to maintain structural stability; conversely, when When the value is small, it approaches a linear form in regions of significant deviation, thereby enhancing tolerance to severe disturbances. This mechanism allows the model to dynamically adjust the constraint strength based on noise intensity. For the topological characteristics of real-world graph data, two different regularization constraints are applied in this embodiment: (1) Sparsity constraint: Norm is defined as , used to penalize non-zero elements. This effectively filters out redundant edges introduced by attacks while preserving the key topological skeleton. (2): Low-rank constraint: In this embodiment, the nuclear norm is used. (in Represents the first of the matrix (a number of singular values) are used as convex relaxations. This encourages the structure matrix to maintain low-rank properties, and these constraints work together to ensure that the reconstructed graph is both concise and has a clear macroscopic organizational pattern.

[0021] Furthermore, based on the graph isomorphism assumption (i.e., connected nodes tend to share similar features), this embodiment introduces a graph Laplacian regularization term to couple the structure with node features:

[0022] Where tr is the trace function. It is the Laplacian matrix of the graph. To ensure effective edge weights, we will... Projected onto interval Above, that is, truncating each element: .

[0023] In step S3 of this embodiment, when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through a graph neural network to obtain the final node feature matrix, the function expression for the first layer forward propagation of the graph neural network is: ; in, This is the node feature matrix output by the first layer of the graph neural network. This is the first layer of a graph neural network. This is the scrambled node feature matrix. These are the parameters of the first layer of the graph neural network. To optimize the adjacency matrix, the function expression for the forward propagation of the layers other than the first layer of the graph neural network is as follows: ; in, For graph neural networks The node feature matrix output by the layer. For the first graph neural network layer, For graph neural networks The node feature matrix of the layer, For graph neural networks Layer parameters.

[0024] In this embodiment, the function expression for each layer of the graph neural network is: ; ; ; in, For the i-th node, the first node passes through the graph neural network. The node feature matrix output by the layer. Let be the adaptive coefficient of the i-th node. Input the i-th node into the graph neural network. The node feature matrix of the layer, The intermediate representation of the i-th node is obtained by neighborhood aggregation with self-loops. For the number of nodes, To obtain the maximum value, Step size, For balance coefficient, This is an intermediate representation obtained through neighborhood aggregation with self-loops. For graph neural networks The node feature matrix of the layer, This is the normalized adjacency matrix.

[0025] During the representation learning phase, the optimized adjacency matrix from the structure learning module... Keep it fixed. Forward propagation proceeds layer by layer: For the first layer, the input consists of the purified features. Composition, described as For subsequent layers The features are aggregated from the representation of the previous layer, that is... ,in This represents the set of learnable parameters for each layer. The model minimizes the task loss function using gradient descent. End-to-end training is performed. In step S3 of this embodiment, when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through the graph neural network to obtain the final node feature matrix, it includes: minimizing the preset objective function of representation learning. We will update the network parameters of the graph neural network using gradient descent to obtain the updated network parameters: ; in, For the updated network parameters, For update operations, For the network parameters before the update, For learning rate, Preset objective function The gradient is calculated. This process alternates between forward inference and backward gradient propagation until convergence.

[0026] In this embodiment, the preset objective function The function expression is: ; in, This is the final node feature matrix. For balance coefficient, This is the original node feature matrix; L is the difference between the final node feature matrix and the original node feature matrix. 2,1 Norm, for traces, for The transpose operation, The normalized adjacency matrix, The identity matrix is ​​used. In real-world graph data, some nodes possess reliable features and should retain more of their original information, while noisy nodes need to be corrected using neighborhood information. To address this limitation, this embodiment designs the aforementioned adaptive residual aggregation mechanism, which dynamically adjusts the fusion weights between residual features and neighborhood information at the node level. Inspired by robust optimization principles, this embodiment uses L... 2,1 Norm regularization terms are used to construct the learning objective to promote row-level sparsity of feature bias: ; The above formula allows for large deviations in abnormal nodes while strictly preserving reliable features.

[0027] To comprehensively evaluate the performance and robustness of the Dual Robust Adaptive Graph Neural Network (RA-GNN) in this embodiment, experiments were conducted on five widely used public datasets: Cora, Citeseer, ACM, Polblogs, and Chameleon. The first four datasets cover typical citation networks and pure structured scenarios, and their preprocessing and attack construction followed standard experimental protocols in the field. Furthermore, the Chameleon dataset was introduced in this embodiment to further validate the model's generalization ability in complex web page classification tasks. This dataset originates from hyperlinks between Wikipedia pages, contains 2,277 nodes and 36,101 edges, and has rich node attributes (2,325 dimensions). Data partitioning: For Cora, Citeseer, ACM, and Polblogs, this embodiment adopted the partitioning protocol used in the Pro-GNN model (10% for training, 10% for validation, and 80% for testing). For Chameleon, this embodiment followed... - Experimental protocol for GNN[1] (60% for training, 20% for validation, 20% for testing). All reported results are the mean and standard deviation of five independent runs (using different random seeds).

[0028] In the experiment, the dual robust adaptive graph neural network (RA-GNN) in this embodiment was compared with a series of representative graph neural networks as baseline methods: GCN: As a standard baseline without any defense mechanisms.

[0029] Air-GNN: Mitigates feature perturbations through residual propagation mechanism.

[0030] Pro-GNN: Achieves structural cleansing by jointly optimizing graph structure and model parameters.

[0031] β-GNN: Jointly learns node representations by combining GNN and MLP components.

[0032] To ensure a fair comparison, all baseline methods were implemented strictly according to the settings of their original papers.

[0033] To simulate complex adversarial environments, the experiments employed the dual-modal perturbation mechanism proposed by ACGMAE. This mechanism consists of two phases: first, the Meta-Attack method is applied to corrupt the graph topology with a budget of 25% of the total edges; then, 50% of the nodes are randomly selected, and noise vectors sampled from a standard Gaussian distribution are added as feature perturbations. It is important to note that the Polblogs dataset lacks meaningful node features, making it impossible to conduct dual-modal perturbation experiments on this dataset. All experiments were conducted in a computing environment equipped with an Intel Core i7-12700 processor, 48 GB of memory, and an NVIDIA GeForce RTX4090D GPU. Finally, the node classification performance of different models under various attack scenarios is shown in Table 1.

[0034] Table 1: Comparison of Experimental Results

[0035] As shown in Table 1, Meta25 represents the structural perturbation generated by Metaattack (budgeted at 25% of the total number of edges), while Dual represents a dual-modal perturbation attack. Overall, the dual robust adaptive graph neural network in this embodiment achieves best or competitive results on most datasets and settings, demonstrating its strong robustness while maintaining high prediction accuracy. In the Clean (no attack) setting, the dual robust adaptive graph neural network in this embodiment achieves results comparable to or better than most baselines, such as 84.82% on the Cora dataset and 95.70% on the Polblogs dataset, indicating that its robustness mechanism does not sacrifice performance on clean graphs. Although RA-GNN slightly outperforms the dual robust adaptive graph neural network in this embodiment in a few cases (such as the Citeseer dataset), the difference is negligible, and the dual robust adaptive graph neural network in this embodiment still achieves very competitive results. When the graph is subjected to... Meta25When subjected to topological perturbations, the dual robust adaptive graph neural network in this embodiment demonstrates a significant advantage over traditional methods such as GCN and Air-GNN. For example, it achieves approximately 23.9% higher accuracy than GCN on the Cora dataset and over 6% higher accuracy than Air-GNN on the Polblogs dataset, proving its effectiveness in handling topological perturbations. Under the more challenging Dual (dual-modal perturbation attack), the dual robust adaptive graph neural network in this embodiment maintains strong robustness. It achieves accuracies of 62.22%, 63.56%, and 55.04% on the Cora, Citeseer, and ACM datasets, respectively, outperforming most baselines. For example, it achieves an improvement of over 12% over Air-GNN on the Cora dataset. These results indicate that the structure learning module and adaptive residual propagation of the dual robust adaptive graph neural network in this embodiment effectively mitigate structural and feature noise. Overall, the results confirm the effectiveness and robustness of the dual robust adaptive graph neural network in this embodiment across different datasets and attack scenarios. Furthermore, experiments revealed that the performance improvement of the dual robust adaptive graph neural network in this embodiment becomes increasingly significant with increasing attack intensity, demonstrating its strong robustness under high-intensity structural perturbations. The feature smoothness distribution of the dual robust adaptive graph neural network in this embodiment shows that the cleaned representation exhibits a distribution that better conforms to the isomatch hypothesis, indicating that the dual robust adaptive graph neural network effectively suppresses feature noise during the aggregation process. The adaptive score distribution of the dual robust adaptive graph neural network in this embodiment shows that perturbed nodes generally have higher adaptive scores, leading to a reduction in residual contribution and thus limiting the propagation of noise features; while clean nodes are assigned relatively lower scores, preserving their original information. A visual example of graph cleansing of the dual robust adaptive graph neural network in this embodiment, where false edges are removed and reliable connections are preserved, further demonstrates the effectiveness of the dual robust adaptive graph neural network in restoring cleaner graph structures.

[0036] Those skilled in the art will understand that the technical solutions provided by this invention can take the form of a method, a system, or a computer program product. Therefore, this invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. For example, this invention can provide a citation classification system based on a dual robust adaptive graph neural network, including an interconnected microprocessor and a memory, the microprocessor being programmed or configured to execute the citation classification method based on the dual robust adaptive graph neural network. This invention can provide a computer-readable storage medium storing a computer program or instructions programmed or configured to execute the citation classification method based on the dual robust adaptive graph neural network via a processor. This invention can provide a computer program product including a computer program or instructions programmed or configured to execute the citation classification method based on the dual robust adaptive graph neural network via a processor. Furthermore, this invention can take the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0037] The above description is merely a preferred embodiment 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 the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A citation classification method based on a dual robust adaptive graph neural network, characterized in that, The process includes the following steps: S1, constructing a clean graph based on papers and their citation relationships, where nodes in the clean graph represent papers and edges represent citation relationships; encoding the clean graph into an adjacency matrix; extracting paper attributes as features and constructing a node feature matrix; S2, scrambling the adjacency matrix and the node feature matrix to obtain a perturbed graph composed of the scrambled adjacency matrix and the node feature matrix; S3, inputting the perturbed graph into a dual robust adaptive graph neural network, performing structure learning and topology purification on the scrambled adjacency matrix in the perturbed graph through a structure learning module to obtain an optimized adjacency matrix, propagating the optimized adjacency matrix and the scrambled node feature matrix layer by layer through the graph neural network to obtain the final node feature matrix, and classifying the citations of nodes based on the node features in the final node feature matrix; when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through the graph neural network to obtain the final node feature matrix, the function expression of the first layer forward propagation of the graph neural network is: ； in, This is the node feature matrix output by the first layer of the graph neural network. This is the first layer of a graph neural network. This is the scrambled node feature matrix. These are the parameters of the first layer of the graph neural network. To optimize the adjacency matrix, the function expression for the forward propagation of the layers other than the first layer of the graph neural network is as follows: ； in, For graph neural networks The node feature matrix output by the layer. For the first graph neural network layer, For graph neural networks The node feature matrix of the layer, For graph neural networks Layer parameters; The function expression for each layer of the graph neural network is: ； ； ； in, For the i-th node, the first node passes through the graph neural network. The node feature matrix output by the layer. Let be the adaptive coefficient of the i-th node. Input the i-th node into the graph neural network. The node feature matrix of the layer, The intermediate representation of the i-th node is obtained by neighborhood aggregation with self-loops. For the number of nodes, To obtain the maximum value, Step size, For balance coefficient, This is an intermediate representation obtained through neighborhood aggregation with self-loops. For graph neural networks The node feature matrix of the layer, This is the normalized adjacency matrix.

2. The citation classification method based on a dual robust adaptive graph neural network according to claim 1, characterized in that, In step S2, when scrambling the adjacency matrix and the node feature matrix, scrambling the adjacency matrix includes modifying the values ​​of the elements in the adjacency matrix; scrambling the node feature matrix includes modifying the values ​​of the elements in the node feature matrix.

3. The citation classification method based on a dual robust adaptive graph neural network according to claim 1, characterized in that, In step S3, when the structure learning module performs structure learning and topology purification on the scrambled adjacency matrix in the perturbation graph to obtain the optimized adjacency matrix, it includes: minimizing the objective function of structure learning. The scrambled adjacency matrix is ​​updated using gradient descent to obtain the updated adjacency matrix. : ； in, This is the adjacency matrix before the update. For learning rate, For the objective function The gradient; the objective function of the structure learning The function expression is: ； ； in, This is the scrambled adjacency matrix. The adjacency matrix obtained by encoding the clean graph. For feasible sets, for The α norm, and These are the weighting coefficients. for Matrix Norms are used to implement sparsity constraints. for The nuclear norm of a matrix is ​​used to implement low-rank constraints. For characteristic smoothness loss, The number of nodes in the graph. For nodes eigenvectors, For nodes eigenvectors, For the adjacency matrix, the first... Okay, number The element values ​​of the column, for The square of the norm; the objective function in structure learning After convergence, the final updated adjacency matrix will be obtained. Projected onto interval This process is repeated to obtain the final optimized adjacency matrix.

4. The citation classification method based on a dual robust adaptive graph neural network according to claim 1, characterized in that, In step S3, when the optimized adjacency matrix and the scrambled node feature matrix are propagated layer by layer through a graph neural network to obtain the final node feature matrix, this includes: minimizing the preset objective function of representation learning. We will update the network parameters of the graph neural network using gradient descent to obtain the updated network parameters: ； in, For the updated network parameters, For update operations, For the network parameters before the update, For learning rate, Preset objective function The gradient.

5. The citation classification method based on a dual robust adaptive graph neural network according to claim 4, characterized in that, The preset objective function The function expression is: ； in, This is the final node feature matrix. For balance coefficient, This is the original node feature matrix; L is the difference between the final node feature matrix and the original node feature matrix. 2,1 Norm, for traces, for The transpose operation, The normalized adjacency matrix, It is an identity matrix.

6. A citation classification system based on a dual robust adaptive graph neural network, comprising an interconnected microprocessor and a memory, characterized in that, The microprocessor is programmed or configured to execute the citation classification method based on a dual robust adaptive graph neural network as described in any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the citation classification method based on a dual robust adaptive graph neural network as described in any one of claims 1 to 5.

8. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the citation classification method based on a dual robust adaptive graph neural network as described in any one of claims 1 to 5.

Images