Method and system for classifying citation network nodes based on hidden equidistant manifold

Abstract

The invention discloses a citation network node classification method and system based on a hidden equidistant manifold. The invention provides a node classification algorithm for a citation network structure. The method comprises the following steps of: firstly, maximizing mutual information between paired sub-graph views related to a literature citation relationship through comparative learning by adopting a path mask strategy so as to fully capture structural characteristics of a citation network; meanwhile, calculating the matching degree between the degree prediction of the paper node and the degree of the original node in the mask quotation graph so as to ensure the structural consistency; and obtaining a potential space coordinate keeping the equidistant constraint through equidistant learning. The method can effectively improve the classification accuracy and robustness in the citation network node classification task, not only solves the node classification problem of high-dimensional complex data in the citation network, but also can retain the manifold structure information of the hidden space of the citation network.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of network node classification, and relates to a citation network node classification method and system based on implicit isometric manifold. BACKGROUND

[0002] In recent years, with the rapid development of scientific research and the continuous growth of academic achievements, the number of academic papers and patents worldwide has shown an explosive growth trend. As an important tool for depicting the citation relationship between academic literature, citation networks have gradually become a key foundation in the analysis of subject evolution, knowledge discovery, scientific research evaluation and recommendation systems. People's demand for efficient academic search, accurate topic identification and multi-field knowledge graph construction is also increasing. However, with the continuous expansion of the scale of citation networks and the improvement of node attribute dimensions, how to accurately and efficiently classify nodes in citation networks has become an important problem to be solved in the field of academic big data processing.

[0003] Although in recent years, graph neural networks and their improved methods have made some progress in citation network node classification tasks, there are still obvious deficiencies. First, existing methods usually rely on pre-defined adjacency matrices or local neighbor aggregation when modeling citation relationships, which is difficult to fully capture the complex path structure and high-order dependency relationship in citation networks, resulting in insufficient use of global structure information. Second, paper nodes are often accompanied by high-dimensional semantic features such as title, abstract and keyword embeddings, but existing algorithms are prone to feature redundancy and noise when processing high-dimensional data, reducing classification accuracy. Third, the latent representation of citation networks is often distributed on a low-dimensional manifold, and most existing methods ignore the need to maintain the isometry of the latent space, causing the geometric structure of the hidden space to be distorted, thereby affecting the generalization ability and robustness of the model. Finally, in practical applications, citation networks often have noisy citations or missing partial citation relationships, and existing methods perform significantly worse in such incomplete or uncertain data environments, making it difficult to ensure stability and reliability in real citation network scenarios. SUMMARY

[0004] The purpose of the present application is to provide a citation network node classification method and system based on implicit isometric manifold, which can more effectively utilize node attributes and path information while maintaining the latent manifold structure of the citation network, improving the accuracy and robustness of node classification.

[0005] Technical scheme: In order to achieve the above-mentioned purpose of the application, the technical scheme adopted by the present application is as follows:

[0006] A citation network node classification method based on implicit isometric manifold, comprising the following steps:

[0007] (1) In the citation network, the reference link is masked by using the path mask strategy, and the mutual information between the paired subgraph views related to the masked reference edge is maximized by contrast learning to learn the structure information of the citation network;

[0008] (2) Calculate the matching degree between node degree prediction and original node degree in the masked citation network, and construct an isometric regularization loss, and obtain a node latent space coordinate representation that preserves local isometric constraints by implicit isometric manifold learning;

[0009] (3) Weighted fusion of structure reconstruction loss, degree regression loss and isometric regularization loss, define the total loss function on the citation network dataset, and use it to train the citation network node classification model based on implicit isometric manifold; In the training process, input the citation network training set into the pre-trained model to obtain the node hidden layer feature representation, then input the classification module to obtain the category feature vector, and finally output the predicted label through the classifier.

[0010] Further, the citation network node classification model comprises an encoder f E , a structure decoder h, an attribute decoder f A and a degree decoder f D , the encoder f E inputs the visible subgraph of the citation network, and outputs the node latent representation; the structure decoder h inputs the node latent representation, and outputs the node category; the attribute decoder f A inputs the node latent representation, and outputs the node semantic attribute, and the degree decoder f D inputs the node latent representation, and outputs the reference degree of the node in the citation network.

[0011] Further, in step (1), a path mask strategy is introduced in the citation network, and part of the citation relationship edges are masked, and a set of edge sets ε mask based on the masked path is obtained by random tree sampling:

[0012]

[0013] wherein, is a set of random walk root nodes sampled from the citation network node set, and d is the maximum tree depth of the tree; is the sampling ratio of the nodes in the graph, represents the masked citation subgraph from , and represents the remaining visible graph; z v is the node v representation obtained from the encoder f E .

[0014] Further, in the step (1), the structure reconstruction loss of the graph is learned by maximizing the mutual information between the pair-wise subgraph views associated with the citation edges The form of the structure decoder h is:

[0015]

[0016] where z u , z v is the node representation output by the encoder f E , y u , y v is the corresponding class label, ° denotes element-wise product, MLP is a multi-layer perceptron, and MLP y (z) denotes a class-aware projection network that maps the node representation to a subspace associated with the class, and λ is a contrastive strength coefficient that controls the participation degree of negative samples.

[0017]

[0018] where p(u,v) denotes the probability of the existence of a citation relationship between two citation nodes, and ε denotes the citation edge of the citation network undirected graph.

[0019] Further, in the step (2), the matching degree of the paper node degree prediction and the original node degree in the masked citation graph is calculated to reflect the importance of the paper in the citation relationship, and a paper node attribute reconstruction error is introduced to measure the recovery ability of the embedding representation to the node text features, and a comprehensive degree regression loss is obtained

[0020]

[0021] where, denotes the number of nodes in the citation network, z v is the node representation output by the encoder f E , deg mask (v) denotes the paper node degree in the masked citation graph, x v is a d-dimensional feature vector of node v, and ‖·‖ F denotes the F-norm, and θ ∈ (0, 1] denotes a hyperparameter that controls the weight of the node attribute reconstruction loss.

[0022] Further, in the step (2), an isometric regularization loss is constructed to keep the Euclidean distance in the latent space corresponding to the citation network distance in the observation space, which is specifically represented as follows:

[0023]

[0024] where z mixrepresents a linear interpolation point in latent space represented by two nodes, G(z mix ) represents a Riemannian metric of a Riemannian manifold with local coordinates z mi , J represents a Jacobian matrix, H(f D (z mix )) represents a Riemannian metric of a Riemannian manifold with local coordinates f D (z mix ), H(f D (z mix )) = I, and the Euclidean distance is defined as the distance metric;

[0025]

[0026] where P D (x i ,x j ) is the empirical distribution of node pairs in the citation network dataset, is the approximate posterior distribution, is the average scaling rate of all dimensions, and m is the dimension of G(z mix ), represents the mathematical expectation, ‖·‖ F represents the F-norm, I represents the unit matrix, and tr represents the trace operation of a matrix.

[0027] Further, in the step (3), the model is trained by taking cross entropy as a loss function , and the specific formula is as follows:

[0028] Y pred = f cls (z v )

[0029]

[0030] where z v is the node representation output by the encoder f E , f cls represents a classification function, crossEntropy(·) is a cross entropy function, Y pred is a predicted label, and Y label is a true label.

[0031] A computer system includes a memory, a processor, and a computer program / instruction stored on the memory and executable on the processor, which, when executed by the processor, implements the steps of the citation network node classification method of the hidden isometric manifold.

[0032] A computer readable storage medium stores computer programs / instructions, which, when executed by a processor, implement the steps of the citation network node classification method of the implicit isometric manifold.

[0033] A computer program product includes computer programs / instructions, which, when executed by a processor, implement the steps of the citation network node classification method of the implicit isometric manifold.

[0034] Beneficial effects: the citation network node classification method based on the implicit isometric manifold provided by the application breaks the local connection between document nodes by adopting a path random mask strategy in the citation network. The reconstruction ability of the graph structure is obtained by maximizing the mutual information between the pair graph views related to the citation relationship using a contrast learning mechanism. The representation of the nodes is further optimized by combining the node degree prediction and attribute reconstruction loss. On this basis, the geometric structure of the latent space is maintained through isometric manifold learning, so that the node implicit representation can accurately reflect the intrinsic manifold distribution of the citation network. Finally, better classification effect is obtained in the citation network node classification task. Compared with the prior art, the application has the following advantages:

[0035] (1) a novel citation network node classification method is proposed, which combines isometric manifold learning and mask graph auto-encoding strategy, and can effectively improve the classification performance of the paper node in the citation network, and enhance the robustness of the model while maintaining the latent manifold structure.

[0036] (2) a path random mask strategy for citation relationship is proposed, which effectively breaks the short-range citation connection between paper nodes, so that the model can better utilize the structural dependence pattern in the citation network, thereby capturing higher-order citation relationships and realizing a more meaningful masked citation modeling task.

[0037] (3) a citation network node classification method combining implicit isometric manifold learning is proposed, which can maintain the relative distance relationship between original nodes in the latent space, thereby effectively preserving the topological structure information of the citation network and improving the expression ability of the node representation.

[0038] (4) a large number of experiments are carried out on three real data sets, and the experimental results show that, compared with the existing common node classification methods, the method of the application achieves better classification effect and stronger generalization ability. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The figure is a schematic diagram of the citation network node classification algorithm of the implicit isometric manifold of the application. DETAILED DESCRIPTION

[0040] The application will be further described below in connection with the drawings and specific embodiments.

[0041] The citation network node classification method based on implicit isometric manifold disclosed in the embodiments of the application first masks the citation links in the citation network by using a path mask strategy, maximizes the mutual information between the pair graph views related to the masked citation edges through contrast learning, and thus effectively learns the structural information of the citation network; then, the matching degree between the node degree prediction and the original node degree in the masked citation network is calculated, an isometric regularization loss is constructed, and the node latent space coordinate representation that maintains the local isometric constraint is obtained through implicit isometric manifold learning; finally, the structural reconstruction loss, the degree regression loss and the isometric regularization loss are weighted and fused, a total loss function on the citation network dataset is defined, and the citation network node classification model based on implicit isometric manifold is trained. In the training process, the citation network training set is input into the pre-trained model to obtain the node hidden layer feature representation, the classification module is input to obtain the category feature vector, and finally the prediction label is output through the classifier.

[0042] Specifically, for a given citation network dataset, let be a directed graph, where is a set of literature nodes, is a corresponding citation edge. Each node v∈V is associated with a d-dimensional feature vector . A model including an encoder f E , a structure decoder h, an attribute decoder f A and a degree decoder f D is constructed for training the citation network node classification model based on implicit isometric manifold and outputting the node latent representation and the reconstruction quantity.

[0043] The structural reconstruction loss can effectively capture the adjacency relationship in the citation network. In order to enhance the representation ability of the model on the local and global structures, a path mask strategy is introduced in the citation network to mask part of the citation relationship edges, and a set of edge sets ε mask based on the masked path is obtained through random tree sampling:

[0044]

[0045] wherein, is a set of random walk root nodes sampled from the citation network node set, and d is the maximum tree depth of the tree. is the sampling ratio of the nodes in the graph, represents the masked citation subgraph from , and represents the remaining visible graph. z v is the encoder f EThe obtained node v represents. In this embodiment, the encoder f E The common graph convolution network structure is adopted.

[0046] The structural reconstruction loss of the graph is learned by maximizing the mutual information between the pair subgraph view related to the citation edge through contrastive learning The form of the structure decoder h is:

[0047]

[0048] Where z u , is the node representation output by the encoder f E , y u , y v are the corresponding category labels. represents the element-wise product, and MLP is a multi-layer perceptron. MLP y (z) represents a category-aware projection network that maps the node representation to a subspace related to the category, and λ is a contrast intensity coefficient that controls the participation degree of negative samples. h is a structure decoder composed of an MLP+Sigmoid layer, and the output result is between (0, 1).

[0049]

[0050] Where p(u, v) represents the probability of the existence of a citation relationship between two citation nodes.

[0051] The degree regression loss and the attribute reconstruction loss are introduced to capture the structural and node semantic information. The degree decoder and the attribute decoder are respectively:

[0052] f D (z v ) = MLP D (z v )

[0053] f A (z v ) = MLP A (z v )

[0054] Where the degree decoder f D and the attribute decoder f A are respectively composed of two independent MLPs, and the outputs are the citation degree of the paper node in the citation network and the semantic attribute thereof.

[0055] The matching degree of the paper node degree prediction and the original node degree in the mask citation graph is calculated to reflect the importance of the paper in the citation relationship; and the paper node attribute reconstruction error is introduced to measure the recovery ability of the embedding representation to the node text features, so as to obtain the comprehensive degree regression loss

[0056]

[0057] where, denotes the number of nodes in the citation network, deg mask (v) denotes the paper node degree in the masked citation graph, θ ∈ (0, 1] denotes a hyperparameter that controls the loss weight of node attribute reconstruction, ||·||F F denotes the F-norm.

[0058] In the case of mapping between Riemannian manifolds, f: is a smooth map, is a Riemannian manifold with local coordinates whose Riemannian metric is a Riemannian manifold with local coordinates whose Riemannian metric The differential of f is denoted by the Jacobian matrix J f (z) as: x = f(z). In the case of mapping between Riemannian manifolds, f: is isometric, then it satisfies:

[0059] G(z) = J f (z) T H(f(z))J f (z)

[0060] where H(f(z)) = I.

[0061] The isometric regularization loss is constructed to keep the Euclidean distance in the latent space corresponding to the citation network distance in the observation space, which is specifically represented as follows:

[0062]

[0063] where H(f D (z mix )) = I, and the Euclidean distance is defined as the distance metric. It is required that the Riemannian metric tensor G ∝ I. Therefore, the Euclidean distance in the latent space can be approximately corresponding to the semantic and structural similarity between nodes in the citation network. The specific formula is as follows:

[0064]

[0065] where P D (x i , x j ) is the empirical distribution of node pairs in the citation network data set, from uniformly sampled, is the approximate posterior distribution, is the average scaling rate of all dimensions, m is the G(z mix ) dimension, z mix =(1-γ)z i +γz j represents the linear interpolation point represented by two nodes in the latent space, and γ is the interpolation weight parameter. represents the mathematical expectation, ‖·‖ F represents the F-norm, I represents the unit matrix, and tr represents the trace operation of the matrix.

[0066] Thus, the total loss function of the citation network node classification model is defined as:

[0067]

[0068] where α and β are hyperparameters for adjusting the loss of each part.

[0069] Further, the citation network training set is input into the pre-trained node classification model to obtain the hidden layer features, input into the classification module to obtain the category feature vector, and finally input into the softmax classifier to obtain the predicted label Y pred , the loss between Y pred and the real label Y label is calculated. In addition to the total loss function for maintaining the hidden isometric manifold structure, cross entropy is introduced as the loss function for training the model in the downstream node classification task to optimize the classification performance, and the specific formula is as follows:

[0070] Y pred =f cls (z v )

[0071]

[0072] where f cls represents the classification function, and crossEntropy(·) is the cross entropy function.

[0073] To prove the effect of the embodiment of the application, experiments are performed on public data sets CiteSeer, Pubmed, and Computer, and are compared with commonly used graph autoencoder variants: GAE, GraphMAE, GCA, SUGRL, CCA-SSG, and MaskGAE. The experiment process is performed according to the optimal experimental parameter settings of the model.

[0074] The classification performance of each network model on each dataset is evaluated using classification accuracy (ACC), precision (Micro-F1), and recall (Macro-F1):

[0075] 1) ACC: The ratio of the number of correctly classified samples to the total number of samples

[0076]

[0077] where, represents the classification result of the model prediction x i , y i represents the true label of x i , and n is the number of samples.

[0078] 2) AUC

[0079] AUC = p(p 正样本 > p 负样本 )

[0080] 3) F1-score

[0081]

[0082]

[0083] where precision represents the proportion of correct results among those predicted as positive, and recall represents the proportion of correctly identified positive samples among those that are actually positive. F1-score is the harmonic mean of precision and recall. Macro-F1 calculates the arithmetic mean of F1-score for each class, which treats all classes equally without considering the importance of different classes. Micro-F1 calculates F1-score by calculating the global TP, FN, and FP.

[0084] As shown in Tables 1-3, the table shows the performance comparison of different methods on CiteSeer, Pubmed, and Computer datasets. Traditional graph neural network methods can extract structural information from citation networks to a certain extent and achieve relatively stable classification results. Methods such as GAE based on autoencoders and GCA combined with contrastive learning have further improved by enhancing feature representation capabilities. Methods such as GraphMAE and MaskGAE have shown certain advantages in feature robustness and have achieved performance breakthroughs in some indicators. Overall, the proposed model has achieved the best performance in all evaluation indicators, especially significantly outperforming existing methods in complex citation networks such as CiteSeer and Pubmed.

[0085] Table 1 Comparison of classification performance ACC

[0086]

[0087] Table 2 Comparison of AUC of classification performance

[0088]

[0089] Table 3 Comparison of Macro-F1 of classification performance

[0090]

[0091] The computer system disclosed by the embodiment of the present application comprises a memory, a processor and a computer program / instruction stored on the memory and executable on the processor, and the computer program / instruction is executed by the processor to implement the steps of the citation network node classification method of the hidden isometric manifold.

[0092] The computer readable storage medium disclosed by the embodiment of the present application stores a computer program / instruction, and the computer program / instruction is executed by the processor to implement the steps of the citation network node classification method of the hidden isometric manifold.

[0093] The computer program product disclosed by the embodiment of the present application comprises a computer program / instruction, and the computer program / instruction is executed by the processor to implement the steps of the citation network node classification method of the hidden isometric manifold.

[0094] The program code for implementing the method of the present application can be written in any combination of one or more programming languages. The program code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the program code, when executed by the processor or controller, causes the steps of the method of the present application to be implemented. The program code can be executed entirely on a machine, partially on a machine, partially on a machine as a separate software package and partially on a remote machine, or entirely on a remote machine or server. The present application does not detail the known technology of those skilled in the art.

Claims

1. A citation network node classification method based on implicit isometric manifolds, characterized in that, Includes the following steps: (1) In the citation network, the path masking strategy is used to mask the citation links. By contrastive learning, the mutual information between the paired subgraph views related to the masked citation edges is maximized, and the structural information of the citation network is learned. (2) Calculate the matching degree between the node degree prediction and the original node degree in the masked citation network, and construct the equidistant regularization loss. Through implicit equidistant manifold learning, obtain the latent spatial coordinate representation of the node that maintains the local equidistant constraint. (3) The structural reconstruction loss, degree regression loss and isometric regularization loss are weighted and fused together to define the total loss function on the citation network dataset, which is used to train the citation network node classification model based on the hidden isometric manifold. During the training process, the citation network training set is input into the pre-trained model to obtain the hidden layer feature representation of the node, and then input into the classification module to obtain the category feature vector. Finally, the predicted label is output through the classifier.

2. The citation network node classification method based on implicit isometric manifold according to claim 1, characterized in that, The citation network node classification model includes an encoder f. E Structure decoder h, attribute decoder f A Sum Degree Decoder f D The encoder f E The input citation network's visible subgraph outputs a node latent representation; the structure decoder h takes the node latent representation as input and outputs a node category; the attribute decoder f... A Input node latent representation, output node semantic attributes, the degree decoder f D Input node latent representation, output node citation degree in the citation network.

3. The citation network node classification method based on implicit isometric manifold according to claim 2, characterized in that, In step (1), a path masking strategy is introduced into the citation network to mask some citation relationship edges, and the edge set ε based on the masked path is obtained by random tree sampling. mask : Among them, is a set of random walk root nodes sampled from the citation network node set, and d is the maximum tree depth of the tree; 0 < p < 1 is the sampling ratio of nodes in the graph, denotes the masked citation subgraph, denotes the remaining visible graph; z v is the representation of node v obtained from the encoder f E ​ 4. The citation network node classification method based on implicit isometric manifold according to claim 2, characterized in that, In step (1), the graph structure reconstruction loss is learned by contrastive learning to maximize the mutual information between paired subgraph views related to the referenced edges. The structure decoder h has the following form: Where z u z v It is encoder f E The output node representation, y u y v These are the corresponding category tags. MLP represents element-wise multiplication; MLP stands for Multilayer Perceptron. y (z) represents a category-aware projection network that maps node representations to a subspace associated with that category. λ is the contrast intensity coefficient, which controls the participation of negative samples. Where p(u,v) represents the probability that there is a citation relationship between two citation nodes, and ε represents the citation edge in the undirected graph of the citation network.

5. The citation network node classification method based on implicit isometric manifold according to claim 2, characterized in that, In step (2), the degree of matching between the predicted node degree of the paper and the original node degree in the mask citation graph is calculated to reflect the importance of the paper in the citation relationship; Furthermore, the node attribute reconstruction error from the paper is introduced to measure the ability of the embedding representation to recover node text features, resulting in a comprehensive degree regression loss. in, z represents the number of nodes in the citation network. v It is encoder f E The output node representation, deg mask (v) represents the degree of the paper node in the masked citation graph, x v It is the d-dimensional feature vector of node v, ‖·‖ F Let F represent the norm, and θ∈(0,1] represent the hyperparameters that control the weights of the node attribute reconstruction loss.

6. The citation network node classification method based on implicit isometric manifold according to claim 2, characterized in that, In step (2), an equidistant regularization loss is constructed. To ensure that the Euclidean distance in the latent space corresponds to the citation network distance in the observation space, the following specific representation is made: Among them, z mix Let G(z) represent the linear interpolation points in the latent space for two nodes. mix ) indicates that the local coordinate is z mix The Riemann metric of the Riemannian manifold, J denotes the Jacobian matrix, H(f) D (z mix )) indicates that the local coordinates are f D (z mix The Riemann metric of the Riemannian manifold, H(f) D (z mix Euclidean distance is defined as a distance metric, where I = 1. Among them, P D (x i ,x j ) is the empirical distribution of node pairs in the citation network dataset. It is an approximate posterior distribution. It is the average scaling factor across all dimensions, and m is the scaling factor of G(z). mix ) dimension, Denotes mathematical expectation, |·| F Let F denote the F norm, I denote the identity matrix, and tr denote the trace operation of the matrix.

7. The citation network node classification method based on implicit isometric manifold according to claim 1, characterized in that, In step (3), cross-entropy is used as the loss function. The specific formula for training the model is as follows: Y pred =f cls (z v ) Among them, z v It is encoder f E The output node representation, f cls Y represents the classification function, crossEntropy(·) is the cross-entropy function, and Y... pred It is a predicted label, Y label It's a real label.

8. A computer system comprising a memory, a processor, and computer programs / instructions stored in the memory and executable on the processor, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the citation network node classification method for implicit isometric manifolds according to any one of claims 1-7.

9. A computer-readable storage medium storing a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the citation network node classification method for implicit isometric manifolds according to any one of claims 1-7.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the citation network node classification method for implicit isometric manifolds according to any one of claims 1-7.

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