A graph neural network node classification method integrating local topological structure

Abstract

The present invention provides a graph neural network node classification method integrating local topological structure, and the steps are as follows: the node feature information is first based on the self-attention mechanism and the Laplacian matrix is ​​used as the position encoding information to obtain the useful information of the farther nodes on the graph to update the node feature itself. After that, a local structure with the central node as the starting point is defined, and information is extracted from the local structure. Then, a recurrent neural network is used to add the input node feature to the latest node feature. The output of the recurrent neural network is used as input, and the adjacency matrix based on the self-attention mechanism is used as a mask matrix to update the feature according to the neighboring nodes. Finally, a softmax operation is used to obtain a one-hot vector representing the node label and compare it with the true label vector. The trained network model is used to obtain the prediction result on the test set. This method can classify nodes when the node relationship and node features are known.

Description

Technical Field

[0001] The present invention relates to deep learning and graph neural networks, and in particular to a graph neural network node classification method integrating local structures. Background Art

[0002] Graphs are non-Euclidean data that are more complex and expressive than commonly used data with regular arrangements (e.g., text, audio, video). Networks or graphs are ubiquitous data structures that are widely used in biology, neuroscience, engineering, and social sciences to capture the interactions (i.e., edges) between units (i.e., nodes) of complex systems. For example, in the social media industry, users link and interact with other users (e.g., friends, colleagues) through their profile information, and the entire social media network is modeled as an attribute graph of product / friend / community recommendations; in medicine and pharmacology, molecules and chemical bonds can be constructed as graphs to potentially discover new drugs by identifying their biological activities; in academic citation networks, papers are connected through citations, and titles, authors, locations, and keywords form graph features for automatic classification and image classification.

[0003] In various complex networks, entities are abstracted into "points" that are independent of their size and shape, and the lines connecting entities are abstracted into "edges", and the relationship between these points and lines is then represented in the form of a graph. The structure of the graph reflects the structural relationship of the network and also contains a lot of important information. For example, if an article is cited by many articles, it means that the article has a great influence, but the category of the literature citing it may not be the same as it (the physics literature will be cited by the neural network literature for its formula), which takes into account the out-degree size of a node. How to define the local structure of the graph and obtain rich node information from the local structure of the graph has always been considered a challenging task.

[0004] Defining a universal local structure is a necessary condition for obtaining node information from the structure. Traditional neural networks are inherently local propagation updates, which naturally excludes some effective global interactions and the extraction of local structural information, which is not conducive to large-scale graphs or dense graph structures. Measuring the importance of nodes in a graph is usually a good way to understand the graph, which has not been considered in previous literature studies. This requires a graph neural network node classification algorithm that incorporates local structure. Summary of the invention

[0005] The technical problem to be solved by the present invention is that the current graph neural network only focuses on the feature information of adjacent nodes, ignores some distant but very important node information, and also fails to capture the information provided by the local structure of the graph.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a fusion graph attention network that characterizes the spatial relationship between data by calculating the different importance between nodes and a graph neural network node classification method that characterizes the local structure based on three basic relationships between nodes.

[0007] This method divides the entire data set into three parts: training, verification, and testing. First, part of the feature data set (training set) is selected to train the deep neural network model. Then, the trained network model is used to test part of the data set (verification set). After all batches are trained, the best model is used to test the final test set to verify the predictive performance of the deep neural network model obtained through training.

[0008] The specific steps include:

[0009] A graph neural network node classification method integrating local structure, characterized by comprising the following steps:

[0010] Step 1) Input node features, incidence matrix and adjacency matrix; use directed graph to represent the spatial relationship between nodes;

[0011] Step 2) Use the first self-attention mechanism to calculate the importance between different nodes, and use the Laplacian matrix as the position information encoding to extract useful information from the farther nodes in the directed graph to update the features of its own node;

[0012] Step 3) inputting the new representation of the node feature obtained in step 2) into the local structure network to obtain a new node feature;

[0013] Step 4) Use a recurrent neural network to add the node features input in step 1) and the latest node features in step 3) and output them;

[0014] Step 5) takes the output of step 4) as input, and uses the adjacency matrix based on the self-attention mechanism as a mask matrix to update the node features according to the neighboring nodes;

[0015] Step 6) Perform a softmax operation on the output of step 5) to obtain a one-hot vector representing the node label;

[0016] Step 7) The output of step 6) is used to determine whether it belongs to the training stage and determine the subsequent operation process;

[0017] Step 8) Use the one-hot vector directly for prediction;

[0018] Step 9) The one-hot vector is compared with the true label vector to calculate the loss value predicted by the network model;

[0019] Use the loss value to judge the classification effect of the current model, continue to adjust the weight parameters in the network, and optimize the network model; when the loss value of the network model converges to the minimum or the training reaches the specified number of iterations, the training ends and the trained network model is output;

[0020] Step 10) Use the trained network model to test its performance on the test set;

[0021] Step 11) Compare the prediction results of the test set obtained in step 10) with the real data and return the accuracy to reflect the quality of the model;

[0022] In the step 3), the central node information is considered from the three most basic relationships among the three nodes, and the node information is converted into edge information according to the association matrix to consider the influence of the central node on the neighboring nodes, that is, the correlation between pairs of nodes; the weight of the edge adjacency matrix is ​​updated according to the defined local structure to update the edge features and thus update the node features.

[0023] The method of the present invention combines deep learning and node local structure to classify nodes of graph neural network. First, the information of distant nodes and neighboring nodes is obtained according to the self-attention mechanism, and then useful information is extracted according to the local structure. The information of distant nodes is combined with the information of neighboring nodes, and the node structure information is combined with the node feature information, so as to improve the classification ability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1a The overall algorithm framework flow chart of the present invention is

[0025] Figure 1b This is a module diagram of the self-attention mechanism of the present invention;

[0026] Figure 2 A flowchart of graph neural network node classification provided by an embodiment of the present invention;

[0027] Figure 3a to Figure 3c There are three basic node relationships used in the present invention. DETAILED DESCRIPTION

[0028] The present invention is a graph neural network node classification method integrating local structure, for node feature information:

[0029] First, based on the self-attention mechanism, the Laplacian matrix is ​​used as the position encoding information to obtain useful information of distant nodes on the graph to update the characteristics of its own nodes.

[0030] Afterwards, a local structure starting from the central node is defined, and information is extracted from the local structure.

[0031] Then, a recurrent neural network is used to add the input node features to the latest node features. In graph neural networks, the information of neighbor nodes is the most important and provides a large amount of information. Therefore, the output of the recurrent neural network is used as input, and the adjacency matrix based on the self-attention mechanism is used as a mask matrix to update the features according to the neighbor nodes.

[0032] Finally, a softmax operation is used to obtain the one-hot vector representing the node label and compare it with the true label vector.

[0033] Use the trained network model to obtain the prediction results on the test set.

[0034] In order to better understand the technical solution of the present invention, the embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be clear that the described embodiments and all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] The embodiment of the present invention provides a graph neural network node classification method integrating local structure, referring to Figure 2 , the method comprises the following steps:

[0036] Step 101, input node features and adjacency matrix;

[0037] Step 102, use the self-attention mechanism to calculate the importance between different nodes (the formula is as follows) and use the Laplacian matrix as the position information encoding to extract the useful information of the farther nodes to update the node features;

[0038]

[0039] Step 103, input the new representation of the node features obtained in step 102 into the local structure network. The present invention considers the central node information from the three most basic relationships of the three nodes, and converts the node information into edge information to consider the influence of the central node on the neighboring nodes (the correlation between paired nodes). The three basic node relationships are shown in Figure 3a to Figure 3c As shown. The weight of the edge adjacency matrix is ​​updated according to the defined local structure, so as to update the edge features and thus update the node features;

[0040] Step 104, recurrent neural network output. Add the latest node feature obtained in step 103 to the input node feature;

[0041] Step 105: The adjacent node information is more important. The node features output from step 104 are input into another self-attention mechanism. The adjacency matrix is ​​used as a mask matrix to update the node features through the adjacent nodes.

[0042] Step 106, a softmax operation is performed on the output of step 105 to obtain a one-hot vector representing the node label;

[0043] Step 107 is used to determine whether it belongs to the training stage and determine the subsequent operation process.

[0044] In this embodiment, 60% of the data set is used to train the model, and then the model is used to verify 20% of the data. After the training is completed, the obtained network model is used to test the other 20% of the data set. In the testing phase, all the data in the test set are processed through steps 101 to 107, just like the data in the training phase;

[0045] Step 108, the one-hot vector obtained after softmax in step 106 is directly used for prediction;

[0046] Step 109, based on the above-calculated classification results and the corresponding real data, the loss value predicted by the network model is calculated, and the following formula is listed:

[0047]

[0048] The network model determines the classification effect of the current model based on the calculated loss value, and continues to adjust the weight parameters in the network to optimize the network model. When the loss value of the network model converges to the minimum or the training reaches the specified number of iterations, the training ends and the trained network model is output;

[0049] Step 110, using the trained network model to test its performance on the test set.

[0050] In the testing phase, the above steps are repeated using the test set data, except that no training is required and the trained network model parameters are directly used;

[0051] Step 111, compare the prediction results of the test set with the real data to return the accuracy, thereby reflecting the quality of the model.

[0052] Further references Figure 1a Further explanation of the above method:

[0053] The network topology is constructed based on the entities in the complex network and the lines connecting the entities. A directed graph G = {V, E, A} is used to represent the spatial relationship between nodes, where V = {1, ..., N} represents n nodes with connection relationships, and E = {e ij |i, j∈V} represents the set of edges between nodes. In addition, Represents the adjacency matrix of graph G. If there is a connection between nodes i and j ((i, j)∈V), then a ij =1 otherwise a ij= 0. We use I N represents the N×N identity matrix, D represents the degree matrix, where D ii =Σ j A ij represents the degree of node i;

[0054] Clarify the data format and prediction problem definition. Assume that the label of each node in the attribute graph G = {V, E, A} belongs to one of C labels, which can be expressed as y i ∈{0, 1} C We will have a label matrix Y∈{0,1} N×C , where yi is the i-th row of Y. X=(x1,x2,...,x N )∈R N×F It is represented by all the feature values ​​of all nodes, N is the number of nodes, and F is the number of features of each node. According to the defined network structure, the label matrix Y′∈{0,1} of all nodes will be predicted N×C And compare with the Y matrix to get the model effect;

[0055] refer to Figure 1b , in step 102:

[0056] The node features are represented and learned by the self-attention mechanism, and the Laplacian matrix is ​​used as the position encoding information to obtain the information of distant nodes. The formula is listed as follows:

[0057] A lp =ID -1 / 2 AD -1 / 2 =U T ΛU (1)

[0059] I represents the identity matrix, U represents the eigenvector, and U T represents the transpose of the eigenvector and Λ represents the eigenvalue.

[0060] The Laplacian matrix is ​​used in the self-attention mechanism module to obtain position information, which is defined as follows:

[0061] Q=XW Q , K = XW K , V = XW V (2)

[0062]

[0063] A soft =softmax(A·A lp ) (4)

[0064] X attn =A soft V (5)

[0065] Where X = [x1,…,x n ]∈R n×d represents the input of the single-head attention mechanism, and d represents the node feature dimension. According to the self-attention mechanism, Q represents the query vector, which will be matched with each key later. d Q represents the feature dimension of vector Q; K represents the key vector, which will be matched by querry later. d K Represents the feature dimension of vector K, K T represents the transpose of the key vector; V represents the information extracted from the input feature X, d V Represents the characteristic dimension of vector V; the matching process of Q and K can be understood as calculating the correlation between the two. The greater the correlation, the greater the weight of V.

[0066] where A is a matrix that captures the similarity between queries and keys. attn Represents the output of a single-head self-attention module;

[0067] In step 103:

[0068] Define the local structure. If the out-degree and in-degree of a node are both large, the present invention defines it as a central node. The present invention considers the central node information from the three most basic relationships of the three nodes, and converts the node information into edge information to consider the impact of the central node on the neighboring nodes (the correlation between paired nodes). The new node feature value obtained in the previous step is used as input X to convert it into edge feature information Z:

[0069] Z=MTXW a (6)

[0070] Where M∈R |V|×|E| represents the association matrix encoding the connections between nodes and edges. a is a learnable projection matrix.

[0071] If the connection relationship between the three nodes is: node i points to node j, node j points to node k, then node j is the central node. If the central node j has many neighboring nodes (node ​​j has a large degree), then the correlation between (i->j) and (j->k) will be weakened due to the influence of other neighboring nodes, and the edge matrix A e The weight of is defined as:

[0072]

[0073] Among them, deg- (j) and deg + (j) denotes the in-degree and out-degree of node j, respectively. σ is the standard deviation of node degree.

[0074] If the connection relationship between the three nodes is: node i points to node j, node k points to node j, then node j is the central node. The central node j is affected by nodes i and k. The correlation between (i->j) and (k->j) is determined by the out-degree of nodes i and k. The edge matrix A e The weight of is defined as:

[0075]

[0076] If the connection relationship between the three nodes is: node j points to node i, node j points to node k, then node j is the central node. The correlation between (j->i) and (j->k) cannot be determined only by the degree of the central node j, but by the in-degree of nodes i and k. The edge matrix A e The weight of is defined as:

[0077]

[0078] Update the feature information of the edge and thus the feature information of the node according to the defined local structure information, which is defined as follows:

[0079] z (1) =A e W b z (10)

[0080] x stru =M z (1) (11)

[0081] Among them, W b is a learnable parameter, z (1) is the feature information of the edge extracted according to the defined local structure, x stru It converts edge information into the latest node feature information based on the association matrix M.

[0082] In step 104:

[0083] RNN output. Add the node features of the previous step output and input.

[0084] In step 105:

[0085] Neighbor node information is the most important in the graph neural network. The output of the recurrent neural network in the previous step is used as input into the self-attention mechanism, and the neighbor node information is used to update the own feature information. Similar to step 102, the difference is that in this step, the adjacency matrix is ​​used as the position encoding information, which is equivalent to a mask matrix, and only the information of the neighbor nodes is paid attention to.

[0086] In step 106:

[0087] Node classification is performed after softmax operation.

[0088] According to the comparison between the obtained one-hot vector and the true label vector, the predicted loss value is output according to the loss value calculation formula in the neural network model; by analyzing the change trend of the loss value, according to the gradient descent algorithm, the weight parameters in the network model are adjusted to reduce the loss value of the next prediction, thereby achieving the purpose of further optimizing the network model;

[0089] In step 109:

[0090] Determine whether the loss value of the current network model converges to the minimum, or whether it reaches the specified number of iterations; if not, return to continue training the model; if it has been reached, end the training and output the trained model;

[0091] In step 110:

[0092] The trained network model is used to test the data to be verified, and the verification method is the same as steps 102) to 109). If the effect is better, the model will be saved.

[0093] In step 111:

[0094] The best saved model is used to test the test set and the model effect is returned.

[0095] The effective combination of step 102 and step 105 of the present invention uses the Laplace regularization matrix and the adjacency matrix as the position encoding information of the graph respectively. Different from the existing node attention feature information extraction, the present invention not only pays attention to the adjacent node information but also pays attention to the useful information of the distant nodes, which is conducive to some effective global interactions and also obtains important information from important adjacent nodes.

[0096] Step 103 of the present invention defines a local structure about the central node, considers the central node information from the three most basic relationships of the three nodes, and converts the node information into edge information to consider the influence of the central node on the neighboring nodes (correlation between paired nodes). According to this local structure, useful information is extracted to update the characteristics of the node.

[0097] The present invention effectively integrates the attention mechanism with the local structure. When updating the features of graph nodes, it not only combines the information of distant nodes with the information of neighboring nodes, but also combines the structural information and feature information of the nodes, and classifies the nodes according to the latest node features.

[0098] The above-described embodiment is only a preferred solution of the present invention and does not limit the present invention in any form. There are other variations and modifications without exceeding the technical solution described in the claims.

Claims

1. A graph neural network node classification method that integrates local topological structures is applied in academic citation networks. Papers are connected through citations, and titles, authors, locations, and keywords form graphical features for image classification; its characteristics are The graph neural network node classification method includes the following steps: Step 1) Input node features, incidence matrix and adjacency matrix; use directed graph to represent the spatial relationship between nodes; Step 2) Use the first self-attention mechanism to calculate the importance between different nodes, and use the Laplacian matrix as the position encoding information to extract useful information from the farther nodes in the directed graph to update the features of its own nodes; Step 3) inputting the new representation of the node feature obtained in step 2) into the local structure network to obtain a new node feature; Among them, a local structure with the central node as the starting point is defined, the central node information is obtained from the three most basic relationships of the three nodes, and the central node information is converted into edge feature information according to the association matrix, so as to obtain the influence of the central node and the neighboring nodes, and then determine the correlation between paired nodes; the weight of the edge adjacency matrix is ​​updated according to the defined local structure, so as to update the edge features and thus update the node features; The central node refers to a node whose out-degree and in-degree are greater than a threshold, in which case it is defined as a central node. When j is the central node, the three most basic relationships among the three nodes are: node i points to node j, node j points to node k; node i points to node j, node k points to node j; node j points to node i, node j points to node k; Step 4) Use a recurrent neural network to add the node features input in step 1) and the latest node features in step 3) and output them; Step 5) inputting the node features outputted from step 4) into the second self-attention mechanism, and using the neighbor node information to update the own feature information; wherein the adjacency matrix is ​​used as the position encoding information; Step 6) Perform a softmax operation on the output of step 5) to obtain a one-hot vector representing the node label; Step 7) The output of step 6) is used to determine whether it belongs to the training stage; if it does not belong to the training stage, proceed to step 8); if it belongs to the training stage, proceed to step 9); Step 8) Use the one-hot vector directly for prediction; Step 9) Compare the one-hot vector with the true label vector and calculate the loss value predicted by the network model; Use the loss value to judge the classification effect of the current model, continue to adjust the weight parameters in the network, and optimize the network model; when the loss value of the network model converges to the minimum or the training reaches the specified number of iterations, the training ends and the trained network model is output; Step 10) Use the trained network model to test its performance on the test set; Step 11) compares the prediction results of the test set obtained in step 10) with the real data, and returns the accuracy to reflect the quality of the model.

2. The method for node classification of a graph neural network integrating local topological structure according to claim 1 is characterized in that The network topology is constructed based on the entities in the complex network and the lines connecting the entities, and the spatial relationship between the nodes is represented by a directed graph G = {V, E, A}; where: V = {1, ..., N} represents N connected nodes; E={e ij |i, j∈V} represents the set of edges between nodes, e ij represents the edge between node i and node j; Represents the adjacency matrix of the directed graph G. If there is a connection between nodes i and j, then a ij =1, otherwise a ij =0,(i,j)∈V}; Assume that the label of each node in the directed graph G = {V, E, A} belongs to one of C labels, and the label of the node is denoted by y i ∈{0, 1} C , then we get the label matrix Y∈{0,1} N×C , where y i is the i-th row of Y; The label matrix Y′∈{0, 1} of all nodes is predicted through the defined network model N×C , and compare it with Y to get the model effect.

3. The graph neural network node classification method according to claim 1, characterized in that the entire The dataset is divided into three parts: training, validation, and testing; This method uses 60% of the data set as a training set to train the network model; then uses this network model to verify the 20% data set as a validation set; After training is completed, the obtained network model is used to test the other 20% of the data set as the test set; In the testing phase, all the data in the test set and the data in the training phase are processed through steps 1) to 7).

4. The graph neural network node classification method integrating local topological structure according to claim 2 is characterized by: In step 2): The node features are represented by self-attention mechanism learning, and the Laplacian matrix A is used lp As position encoding information to obtain distant node information; list the formula: A lp =I-D -1 / 2 AD -1 / 2 =U T ΛU (1) I represents the identity matrix, D represents the degree matrix; U represents the eigenvector, U T represents the transpose of the eigenvector, and Λ represents the eigenvalue; The Laplacian matrix is ​​used in the self-attention mechanism to obtain the position encoding information, which is defined as follows: Q=XW Q ,K=XW K ,V att =XW V (2) A soft =softmax(A att ·A lp ) (4) X attn =A soft V att (5) Where X = (x1, x2, ..., x N ,)∈R N×F Represents all feature values ​​of all nodes, used as the input of the single-head attention mechanism, N is the number of nodes, and F represents the number of features of each node; In the formula, Q represents the query vector, which will be matched with each key later. d Q Represents the characteristic dimension of vector Q; In the formula, K represents the key vector, which will be matched by the query later. d K Represents the feature dimension of vector K, K T Represents the transpose of the key vector; Where V att Represents the information extracted from the input feature X, d V Represents vector V att The characteristic dimension of The process of matching Q and K is to calculate the correlation between the two. The greater the correlation, the higher the corresponding V att The greater the weight; The matrix Aatt is used to capture the similarity between Q and K; X attn Represents the output of the single-head self-attention mechanism module.

5. The method for node classification of a graph neural network integrating local topological structures according to claim 4 is characterized in that In the step 3): The new node feature value obtained in step 2) is used as input X' to transform it into edge feature information Z: Z=M T X’W a Where M∈R |V|×|E| represents the association matrix encoding the connections between nodes and edges; W a is a learnable projection matrix; If the connection relationship between three nodes is: node i points to node j, node j points to node k, then node j is the central node; if the number of neighbor nodes of central node j is greater than a threshold, that is, the degree of node j is greater than a threshold, then the correlation between (i->j) and (j->k) becomes weaker due to the influence of other neighbor nodes, and the weight of the edge adjacency matrix Ae is defined as: Among them, deg - (j) and deg + (j) represents the in-degree and out-degree of node j, respectively; σ is the standard deviation of node degree; If the connection relationship between the three nodes is: node i points to node j, node k points to node j, then node j is the central node; the central node j is affected by nodes i and k, and the correlation between (i->j) and (k->j) is determined by the out-degree of nodes i and k. The edge adjacency matrix A e The weight of is defined as: If the connection relationship between the three nodes is: node j points to node i, node j points to node k, then node j is the central node; the correlation between (j->i) and (j->k) cannot be determined by the degree of the central node j alone, but is determined by the in-degree of nodes i and k. The edge adjacency matrix A e The weight of is defined as: Update the feature information of the edge according to the defined local structure information, thereby updating the feature information of the node; the definition is as follows: With (1) =A e IN b WITH x stru =Mz (1) Among them, W b is a learnable parameter, z (1) is the feature information of the edge updated according to the defined local structure, x stru The feature information of the edge is converted into the latest node feature information based on the association matrix M.

6. The method for node classification of a graph neural network integrating local topological structures according to claim 1 is characterized in that In the step 6), a one-hot vector is obtained by performing node classification through a softmax operation; based on the comparison between the one-hot vector and the true label vector, a predicted loss value is output according to the loss value calculation formula in the neural network model; by analyzing the changing trend of the loss value, the weight parameters in the network model are adjusted according to the gradient descent algorithm, so that the loss value of the next prediction is reduced, thereby achieving the purpose of further optimizing the network model.

7. The method for node classification of a graph neural network integrating local topological structures according to claim 1 is characterized by: In the step 9): determine whether the current network model loss value converges to a minimum, or whether a specified number of iterations is reached; If it is not reached, return to continue training the model; if it is reached, end the training and output the trained model; In the step 10), the trained network model is used to test the data to be verified, and the verification method is the same as that of steps 2) to 9); If the effect is better, save the network model; In the step 11), the best saved network model is used to test the test set and the model effect is returned.

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