A semi-supervised graph node classification method based on personalized web page ranking

Abstract

The present invention discloses a semi-supervised graph node classification method based on personalized web page ranking: Step 1: For a given graph, the personalized web page ranking value of the node in the graph is calculated by a personalized web page ranking algorithm, thereby obtaining the sorting distribution vector corresponding to each label, and the dependency vector of the node is obtained according to the sorting distribution vector, and the dependency vector is regularized to obtain the dependency matrix. Step 2: By performing multi-layer stacking calculation on the hidden layer of the graph neural network, the hidden layer matrix output by the graph neural network after the multi-layer hidden layer is stacked is obtained; Step 3: The dependency matrix is ​​added to the last hidden layer matrix of the graph neural network to obtain a new global hidden matrix, and then a new graph neural network is obtained; Step 4: The new graph neural network is used for node classification. The present invention finally uses the newly constructed graph neural network for node classification, achieving a better node classification effect.

Description

Technical Field

[0001] The invention belongs to the field of data mining, and in particular relates to a graph node classification method under semi-supervised conditions based on personalized web page ranking. Background Art

[0002] In recent years, with the development of information technology, a large amount of data and information has been pouring into people's learning and life. Many data are expressed as irregular non-Euclidean data like topological networks. Many social software commonly used by people, such as Tencent QQ, WeChat, Weibo, etc., are representatives of the application field of non-Euclidean data. The massive unstructured data generated by these software has a certain topological structure, consisting of nodes and edges, which is what we often call graphs. Graphs are closely related to our lives and have practical uses in many fields. One of the important research hotspots is the graph node classification problem. On a graph, its nodes are divided into labeled nodes and unlabeled nodes. By propagating the information of labeled nodes to unlabeled nodes, the category of unlabeled nodes is predicted. This is the node classification process. The graph node classification problem has many applications in real life, such as web page classification in citation networks, community member identification in social networks, page recommendation in the World Wide Web, protein prediction in protein relationship networks, etc. The common method to solve the graph node classification problem is graph neural network, which includes graph convolutional network, graph attention network and other network models extended on this basis, such as the Markov network.

[0003] Although graph neural networks have shown strong effectiveness in graph node classification, there are still some shortcomings. Existing graph neural network models generally consist of a set of hidden layers and a set of soft max layers after the hidden layers. The hidden layers are used to obtain high-order information of the nodes, and the soft max layers are used to obtain the approximate probability of the nodes. The high-order information of the nodes is composed of the node representation vectors obtained by the node representation learning. The soft max layer only uses the representation information of the nodes when classifying the nodes, ignoring the dependency between labeled nodes and unlabeled nodes, resulting in inaccurate node classification results. Summary of the invention

[0004] In view of the defects or shortcomings existing in the above-mentioned prior art, the present invention provides a semi-supervised graph node classification method based on personalized web page ranking, which can obtain the dependency relationship between labeled nodes and unlabeled nodes, and further quantify the dependency relationship in the form of dependency vectors, and obtain the dependency matrix on this basis. The dependency matrix is ​​then added to the last hidden layer of the graph neural network to form a new graph neural network, and finally the newly constructed graph neural network is used to perform node classification to achieve better node classification effect.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A semi-supervised graph node classification method based on personalized web page ranking includes the following steps:

[0007] Step 1: For a given graph, the personalized web page ranking value of the node in the graph is calculated by the personalized web page ranking algorithm, so as to obtain the sorting distribution vector corresponding to each label, and the dependency vector of the node is obtained according to the sorting distribution vector. After regularizing the dependency vector, the dependency matrix is ​​obtained.

[0008] Step 2: By performing multi-layer stacking calculation on the hidden layers of the graph neural network, the hidden layer matrix output by the graph neural network after the multi-layer hidden layers are stacked is obtained, where each hidden layer contains the propagation and output parts of the node representation learning;

[0009] Step 3: Add the dependency matrix obtained in step 1 to the last hidden layer matrix of the graph neural network obtained in step 2 to obtain a new global hidden matrix H. At this time, the hidden layer matrix of the graph neural network becomes H, and the graph neural network is transformed into a new graph neural network.

[0010] Step 4: Use the softmax layer of the new graph neural network to classify nodes.

[0011] Furthermore, the step 1 specifically includes the following sub-steps:

[0012] Step 11, define a graph G = (V, E), where V is a set of n nodes, n = |V|, E is a set of m edges, E = {(i, j) | i∈V, j∈V}; V L is the set of training set nodes, Y L is the label set of the training set nodes, C represents the number of categories or labels contained in the graph G, C = {0, 1, 2…C-1};

[0013] Step 12: traverse the training set node set V L and the label set Y of the training set nodes L , and obtain the node set V with label c in the training set in turn c ; and c∈{0,1,2,…,C-1}, where Y c Indicates that the labels of all nodes are the label set of c; X is the feature matrix of graph G k is the dimension of the feature vector of each node in the node set V;

[0014] Step 13: construct a personalized web page ranking value PR(i,Vc ) of formula (1):

[0015]

[0016] Among them, PR(i, V c ) represents the personalized web page ranking value of node i in V; λ represents the attenuation factor, which is 0.85; |V c | represents the node set V with label c in the training set c In(i) is the number of nodes in the graph; In(i) is the set of adjacent nodes pointing to node i; node j∈In(i) is the adjacent node of i; |Out(j)| is the number of edges leading from node j; PR(j,V c ) represents the personalized webpage ranking value of the neighboring node j of i. In formula 1, the initial a+b represents the degree of node i, and its value is equal to the out-degree a and the added degree b of node i;

[0017] Step 14: Set V obtained in step 12 c The whole is taken as the input of formula 1, and the personalized webpage ranking value of node i in V is calculated by formula 1; then the personalized webpage ranking values ​​of n nodes calculated are used to form a sorting distribution vector It is expressed by formula 2:

[0018]

[0019] Step 15: Repeat step 14 to obtain C sort distribution vectors Then, the C personalized web page ranking values ​​corresponding to node i are extracted from the C sorting distribution vectors in turn. The extraction process is Indicates that the function Indicates obtaining the sort distribution vector of node i when category is c The personalized web page ranking value PR(i,V c ), which constitutes the dependency vector d of node i i , It is expressed by formula 3:

[0020]

[0021] in, Represents node i in the sorted distribution vector The personalized web page ranking value in;

[0022] Step 16: Dependency vector d on node i i Regularize to get R_d i ;

[0023] Step 17, calculate the dependency matrix D,

[0024] Furthermore, the specific operations of step 16 are as follows:

[0025] Using Equation 4, the dependency vector d of node i is i The ranking values ​​of C personalized web pages are added together to obtain sum(d i ), and then use the C personalized web page ranking values ​​to divide by sum(d i ), and get the regularized dependency vector R_d i :

[0026] sum(d i )=PR(i,V 0 )+PR(i,V 1 )+R(i,V 2 )+…+PR(i,V C-1 ) (4)

[0027]

[0028] Furthermore, the step 2 specifically includes the following sub-steps:

[0029] Step 21, the representation learning of node i includes a propagation part and an output part, wherein the representation learning vector of the propagation part of the first hidden layer is The representation learning vector of the output part is

[0030]

[0031] in, is the representation learning vector of the propagation part of the first hidden layer, X i The feature vector X representing node i i ∈X,X j The feature vector X represents the neighboring node j of i j ∈X, represents the representation learning vector of node j in the propagation part of the first hidden layer, X (i,j) represents the eigenvector of edge (i, j), and f is the propagation function used to transform The dimension of becomes q is the representation learning vector obtained after the representation learning propagation function f The dimension of the propagation part is the representation learning matrix, that is, the hidden layer matrix h is the n propagation part representation learning vector obtained by passing the propagation function of the representation learning of the n nodes through the first hidden layer The nodes are stacked and stored in order to form a matrix with n rows and q columns. That is, the feature vector X of node j j .

[0032]

[0033] in, is the representation learning vector of the output part of the first hidden layer, is the representation learning vector of the propagation part of the first hidden layer, X i The feature vector X representing node i i ∈X, g is the propagation function used to The dimension of f is output by becomes t is the representation learning vector obtained after the representation learning propagation function g The dimension of the output part is the representation learning matrix, that is, the hidden layer matrix

[0034] Step 22, when the number of hidden layers is l, the propagation function output of the representation learning of the l-1th layer is used as the input of the lth layer, and the output of the representation learning of the lth layer is used as the input of the l+1th layer. At this time, the propagation and output process of the representation learning can be expressed as Equation 8, Equation 9 and Equation 10:

[0035]

[0036]

[0037]

[0038] in are the representation learning vectors of the propagation parts of the lth layer and the l+1th layer respectively, are the representation learning vectors of the output part of the l-1th layer and the lth layer respectively. At this time, the representation learning matrix of the propagation part of the lth layer is the hidden layer matrix The representation learning matrix of the output part of the l+1 layer is the hidden layer matrix

[0039] Stack L hidden layers to get the final hidden layer matrix C is the number of categories in the dataset.

[0040] Furthermore, in step 3, the dependency matrix obtained in step 1 is added to the last hidden layer matrix of the graph neural network obtained in step 2 using formula 11 to obtain a new global hidden matrix H:

[0041]

[0042] Among them, the function Represents the dependency matrix D added to the hidden layer matrix h (L) The specific method is to combine the dependency matrix D with the hidden layer matrix h (L) The value of the bitwise multiplication of the elements in is used as the element value of the corresponding position. n is the number of nodes in the graph, and C is the number of label categories.

[0043] Furthermore, the specific operations of step 4 are as follows:

[0044] Use the soft max layer of the new graph neural network to classify the nodes in the test set, which is expressed by formula 12, where z is the final node classification probability, n is the number of nodes in the graph, and C is the number of label categories;

[0045] z = soft max(H) (12).

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] (1) The present invention utilizes a personalized web page ranking algorithm to aggregate the multi-hop neighborhood information of a node and the topological structure information of a graph. This information is represented by a dependency vector of a node, and a dependency matrix is ​​further constructed based on the dependency vector.

[0048] (2) The present invention adds the dependency matrix to the last hidden layer of the graph neural network to construct a new graph neural network, and uses the newly constructed graph neural network to achieve better node classification effect.

[0049] (3) The method of constructing a new graph neural network is highly versatile and can be applied to a variety of graph neural network models, such as graph convolutional neural networks, graph attention networks, graph Markov networks, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of the semi-supervised graph node classification method based on personalized web page ranking of the present invention.

[0051] Figure 2 It is a flowchart of the module for calculating the dependency matrix. DETAILED DESCRIPTION

[0052] The technical terms involved in this invention are:

[0053] Personalized web page ranking algorithm: Personalized PageRank algorithm, PageRank algorithm is a web page ranking algorithm proposed by Google. PageRank algorithm determines the approximate value of the importance of the website's page by calculating the number and quality of page links. The basic assumption is that more important websites may receive more links from other websites.

[0054] The present invention is a semi-supervised graph node classification method based on personalized web page ranking, which can be implemented based on any software language. The basic implementation idea of ​​the method is: first calculate the dependency relationship between nodes through a personalized web page ranking algorithm, and then further obtain the dependency matrix on this basis, and then calculate the global hidden layer matrix by stacking multiple hidden layers of the graph neural network, wherein each hidden layer contains two parts of the propagation and output of the representation learning of the node, and then add the dependency matrix to the global hidden layer matrix to construct a new graph neural network model, and finally use the new graph neural network model for node classification. The method of the present invention is a general tool for graph neural networks, and the construction of the invention is described below using the graph neural network (GNN) as an example. Then in the experimental part, the graph convolutional neural network (GCN), the graph attention network (GAT), and the graph Markov network (GMNN) are used as examples for experimental verification. The model naming mode of the method of the present invention is to add D in front of the original graph neural network model, and the above three models are changed to DGCN, DGAT, and DGMNN accordingly.

[0055] The following is a detailed discussion of the present invention using Python language and the public data set Pubmed as an example in conjunction with the accompanying drawings. The Pubmed data set has 19717 nodes, 44338 edges, and 3 classes. The characteristic dimension of each node is 500, and the node label rate is 0.003, that is, there are 60 training set nodes, 20 training set nodes for each category, and 1000 test set nodes. All evaluation algorithms in the experiment use the complex network tool processing package Networkx (v1.11) and Python (v3.6). The computer information used in the experiment is: processor AMD Ryzen 5 1500X 3.50GHz, memory 32.0GB, operating system Windows10.

[0056] like Figure 1 As shown, the semi-supervised graph node classification method based on personalized web page ranking provided by the present invention specifically includes the following steps:

[0057] Step 1: For a given graph, the personalized web page ranking value of the node in the graph is calculated by the personalized web page ranking algorithm, so as to obtain the sorting distribution vector corresponding to each label, and the dependency vector of the node is obtained according to the sorting distribution vector. The dependency vector is regularized to obtain the dependency matrix. The main purpose of this step is to find the dependency relationship between the labeled node and the node to be classified, and to obtain the global information of the graph, that is, the multi-hop neighborhood node information of the node. Figure 2 As shown, it includes the following sub-steps:

[0058] Step 11, given a graph G = (V, E), where V is defined as a set of n nodes, n = |V|, E is a set of m edges, E = {(i, j) | i∈V, j∈V}; V L is the set of training set nodes, Y L is the label set of the training set nodes, C represents the number of categories contained in the graph G (i.e. the number of different labels), C = {0, 1, 2…C-1}. Taking the Pubmed dataset as an example, there are 19717 nodes, i.e. n = 19717, 44338 edges, i.e. m = 44338, and 3 categories, i.e. C = 3;

[0059] Step 12: traverse the training set node set V L and the label set Y of the training set nodes L , and obtain the node set V with label c in the training set in turn c ; and c∈{0,1,2,…,C-1}, where Y c Indicates that the labels of all nodes are the label set of c; X is the feature matrix of graph G k is the dimension of the feature vector of each node in the node set V.

[0060] The purpose of this step is to find the training set node set for each category in the training set, so as to support the subsequent use of the personalized web page ranking algorithm. Taking the Pubmed dataset as an example, the purpose of this step is to obtain the training set V L The node sets V corresponding to the three categories 0 , V 1 ,V 2 ,.

[0061] Step 13: construct a personalized web page ranking value PR(i,V c ) of formula (1):

[0062]

[0063] Among them, PR(i, V c) represents the personalized web page ranking value of node i in V; λ represents the attenuation factor (taken as 0.85); |V c | represents the node set V with label c in the training set c In(i) is the number of nodes in the graph; In(i) is the set of adjacent nodes pointing to node i; node j∈In(i) is the adjacent node of i; |Out(j)| is the number of edges leading from node j; PR(j,V c ) represents the personalized webpage ranking value of the neighboring node j of i. In formula 1, the initial a+b represents the degree of node i, and its value is equal to the out-degree a and the added degree b of node i;

[0064] The purpose of this step is to provide a method for calculating the personalized web page ranking value of the node, laying the foundation for subsequent calculations. Taking the Pubmed dataset as an example, |V c |=|V 0 |+|V 1 |+|V 2 |=60,|V 0 |=|V 1 |=|V 2 |=20;

[0065] Step 14: Set V obtained in step 12 c The whole is taken as the input of formula 1, and the personalized webpage ranking value of node i in V is calculated by formula 1; then the personalized webpage ranking values ​​of n nodes calculated are used to form a sorting distribution vector It is expressed by formula 2. Taking the Pubmed dataset as an example That is, the sort distribution vector is a one-dimensional row vector with a size of 19717. This step is used to calculate the personalized web page ranking value of the node and temporarily store it for subsequent use.

[0066]

[0067] Step 15: Repeat step 14 to obtain C sort distribution vectors Then, the C personalized web page ranking values ​​corresponding to node i are extracted from the C sorting distribution vectors in turn. The extraction process is Indicates that the function Indicates obtaining the sort distribution vector of node i when category is c The personalized web page ranking value PR(i,V c ), such as the personalized webpage ranking value of node 5 in the Pubmed dataset when category is 2 The dependency vector d that constitutes node i i , It is expressed in Formula 3, taking the Pubmed dataset as an example That is, the dependency vector of a node is a one-dimensional row vector of size 3:

[0068]

[0069] in, Represents node i in the sorted distribution vector The personalized web page ranking value in .

[0070] Step 16: Dependency vector d on node i i Regularize to get R_d i .

[0071] Specifically, for d i The idea of ​​regularization is as follows: First, use Equation 4 to calculate the dependency vector d of node i. i The ranking values ​​of C personalized web pages are added together to obtain sum(d i ), and then use the C personalized web page ranking values ​​to divide by sum(d i ), and get the regularized dependency vector R_d i , the regularization process is expressed by Equation 4 and Equation 5:

[0072] sum(d i )=PR(i,V 0 )+PR(i,V 1 )+R(i,V 2 )+…+PR(i,V C-1 ) (4)

[0073]

[0074] In order to standardize the evaluation of the effect of node dependencies on node classification, this step deliberately regularizes the node dependency vector.

[0075] Step 17, calculate the dependency matrix D, D = {R_d 0 ,R_d 1 ,…,R_d n-1}, It can be seen that D is the regularized dependency vector of n nodes stacked in the order of the nodes, and finally forms a matrix with n rows and c columns. Take the Pubmed dataset as an example That is, a matrix with 19717 rows and 3 columns.

[0076] Step 2: By performing multi-layer stacking calculations on the hidden layers of the graph neural network, the hidden layer matrix output by the graph neural network after multiple hidden layers are stacked is obtained, where each hidden layer contains two parts: the propagation and output of the node representation learning.

[0077] The purpose of this step is to obtain high-order information representation of nodes through multi-layer iteration of hidden layers, aggregate information between nodes and adjacent nodes, and graph topology information. Assuming that the graph neural network has L hidden layers, L = {1, 2, ... l-1, l, l+1, ... L}, the specific operation of the stacking process of the graph neural network hidden layer is as follows:

[0078] Step 21, the representation learning of node i includes a propagation part and an output part, wherein the representation learning vector of the propagation part of the first hidden layer is The representation learning vector of the output part is

[0079]

[0080] in, is the representation learning vector of the propagation part of the first hidden layer, X i The feature vector X representing node i i ∈X,X j The feature vector X represents the neighboring node j of i j ∈X, represents the representation learning vector of node j in the propagation part of the first hidden layer, X (i,j) represents the eigenvector of edge (i, j), and f is the propagation function used to transform The dimension of becomes q is the representation learning vector obtained after the representation learning propagation function f The dimension of the propagation part is the representation learning matrix, that is, the hidden layer matrix h (1) The n propagation part representation learning vectors are obtained by passing the propagation function of the representation learning of the n nodes through the first hidden layer The nodes are stacked and stored in order to form a matrix with n rows and q columns. That is, the feature vector X of node j j .

[0081]

[0082] in, is the representation learning vector of the output part of the first hidden layer, is the representation learning vector of the propagation part of the first hidden layer, X i The feature vector X representing node i i ∈X, g is the propagation function used to The dimension of f is output by becomes t is the representation learning vector obtained after the representation learning propagation function g The dimension of the output part is the representation learning matrix, that is, the hidden layer matrix

[0083] Step 22, when the number of hidden layers is l, the propagation function output of the representation learning of the l-1th layer is used as the input of the lth layer, and the output of the representation learning of the lth layer is used as the input of the l+1th layer. At this time, the propagation and output process of the representation learning can be expressed as Equation 8, Equation 9 and Equation 10:

[0084]

[0085]

[0086]

[0087] in are the representation learning vectors of the propagation parts of the lth layer and the l+1th layer respectively, are the representation learning vectors of the output part of the l-1th layer and the lth layer respectively. At this time, the representation learning matrix of the propagation part of the lth layer is the hidden layer matrix The representation learning matrix of the output part of the l+1 layer is the hidden layer matrix Here the hidden layer matrix h (l) and h (l+1) and the hidden layer matrix h in step 21 (1) Store in the same manner.

[0088] Stack L hidden layers to get the final hidden layer matrix Here the hidden layer matrix h (L) and the hidden layer matrix h in step 21 (1) Store in the same way, where C is the number of categories in the data set. This step obtains the high-order information representation of the node through L layers of hidden layers.

[0089] Step 3: Using formula 11, add the dependency matrix D obtained in step 1 to the last hidden layer matrix h of the graph neural network obtained in step 2. (L) In the above example, we get a new global hidden matrix H. Then the hidden layer matrix of the original graph neural network becomes H, and then the original graph neural network is transformed into a new graph neural network DGNN:

[0090]

[0091] Among them, the function Indicates that D joins h (L) The specific method is to convert matrices D and h of the same dimension into(L) The value of the bitwise multiplication of the elements in is used as the element value of the corresponding position.

[0092] It can be seen that through steps 1 to 3, a new graph neural network DGNN that is different from other graph neural networks is obtained, that is, a node dependency matrix representing the dependency relationship between nodes is added to the last layer of the hidden layer of the original graph neural network, making the original graph neural network become a DGNN with more powerful classification effect. This step combines the dependency matrix with the graph neural network, which is the key to achieving superior node classification effect.

[0093] Step 4. The graph neural network is an end-to-end deep learning model consisting of a set of hidden layers and a soft max layer behind the hidden layers. The hidden layer is used to obtain the high-order representation of the node, and the soft max layer uses the information output by the hidden layer to obtain the direct approximate probability distribution of the node. Therefore, the soft max layer of the new graph neural network is used to classify the nodes. The specific operations are as follows:

[0094] Use the soft max layer of DGNN to classify the nodes in the test set, expressed as formula 12, where Z is the final node classification probability Taking the Pubmed dataset as an example, Z represents the probability that the node to be tested belongs to category 0, category 1, and category 2 respectively.

[0095] z = soft max(H) (12).

[0096] The following are the test results of the method of the present invention:

[0097] Table 1 is a comparison of the overall performance of the new graph neural network proposed by the present invention after adding the node dependency matrix and other existing algorithms, and the comparison indicator is the node classification accuracy. The experiment highlights the effectiveness of the present invention as a whole. From the data in Table 1, it can be seen that the models DGCN, DGAT, and DGMNN after adding the node dependency matrix are 0.4, 0.6, and 2.1 higher than their original models, respectively. At the same time, the experimental effect of GMNN is also significantly higher than other models.

[0098] Table 1. Overall performance comparison of algorithms

[0099]

[0100]

[0101] Table 2 is a performance comparison of the algorithm of the present invention with other existing algorithms under low label rates of Pubmed dataset. Compared with the original label rate of Pubmed dataset of 0.003, the training set has 60 nodes, and each category has 20 training set nodes. In this experiment, the label rates are set to 0.0003, 0.0005, 0.001, and 0.002, that is, the nodes of each category in the training set are changed to 2, 4, 7, and 14 respectively to compare the superiority of the present invention under low label rates. The comparison index is the node classification accuracy. It can be seen from the experimental results of Table 2 that, under the premise of reducing the number of nodes in the same training set, the experimental results of DGMNN with the node dependency matrix added are significantly higher than other models. At the same time, as the number of nodes in the training set increases, the increase of DGMNN is also better than other models.

[0102] Table 2 Performance comparison of Pubmed low label rate algorithms

[0103]

[0104] Table 3 is a robustness comparison of the algorithms of the Pubmed dataset. The effect of enhancing the robustness of the node dependency distribution matrix on the algorithm is studied by using a random attack method to generate an interference graph. Random attack disturbs the graph structure by adding false edges. False edges are edges that do not originally exist. In this experiment, the proportions of false edges added are 2%, 6%, 10%, and 15% of the original edges, respectively, that is, the number of false edges added is 887, 2660, 4434, and 6651, respectively. The interference graph is a graph with false edges added to the original graph. The comparison index is the node classification accuracy. It can be seen from the experimental results in Table 3 that with the increase in the proportion of false edges, the node classification accuracy of all models is decreasing, but the node classification accuracy of the models DGCN, DGAT, and DGMNN with the node dependency matrix added is higher than that of the original model. At the same time, the node classification accuracy of DGMNN is the highest among all models, which further proves the effectiveness of the invention.

[0105] Table 3 Robustness comparison of algorithms on Pubmed dataset

[0106]

Claims

1. A semi-supervised graph node classification method based on personalized web page ranking, characterized in that: This node classification method is applied to network classification in citation networks, and the dataset sequences are selected from PubMed, CiteSeer or Cora; The specific steps include: Step 1: For a given graph, the personalized web page ranking value of the node in the graph is calculated by the personalized web page ranking algorithm, so as to obtain the sorting distribution vector corresponding to each label, and the dependency vector of the node is obtained according to the sorting distribution vector, and the dependency vector is regularized to obtain the dependency matrix; Step 2: Obtain the output hidden layer matrix by stacking multiple hidden layers of the graph neural network, where each hidden layer contains the propagation and output parts of the node representation learning; Step 3: Add the dependency matrix obtained in step 1 to the last hidden layer matrix of the graph neural network obtained in step 2 to obtain a new global hidden matrix , then the hidden layer matrix of the graph neural network becomes , and then the graph neural network is transformed into a new graph neural network; Step 4: Use the new graph neural network softmax The layer performs node classification; The step 1 specifically includes the following sub-steps: Step 11, define a graph , where the definition yes n A collection of nodes, , yes m The collection of edges, ; is the set of training set nodes, , is the label set of the training set nodes, express G The number of categories contained in is the number of different labels. ; Step 12: Traverse the training set node set And the label set of the training set nodes , and the labels in the training set are c A collection of nodes ; and ,in, Indicates that all nodes have labels c The tag collection of for The characteristic matrix , For a node collection The dimension of the feature vector of each node in; Step 13: Construct a personalized web page ranking value for computing the node Formula (1): （1） in, express V Midpoint Personalized web page ranking value; represents the attenuation factor, which is 0.85; Indicates that the label in the training set is Node set The number of midpoints; Indicates that the node The set of adjacent nodes of yes The adjacent nodes of Represented by the node The number of outgoing edges; express The adjacent nodes of The personalized web page ranking value, in formula 1, the initial , Representation Node The degree of the node is equal to Out-degree Join Degree ; Step 14: The set obtained in step 12 The whole is taken as the input of formula 1 and calculated by formula 1 V Midpoint The personalized web page ranking value of n The personalized web page ranking values ​​of nodes constitute the sorting distribution vector , , expressed by formula 2: （2） Step 15, repeat step 14 to get sorted distribution vector , then from Extract nodes from the sorted distribution vector Corresponding Personalized web page ranking values, the extraction process uses Indicates that the function Indicates that a node is obtained In the category Time sort distribution vector Personalized web page ranking value in , which constitutes the node The dependency vector , , expressed by Formula 3: （3） in, Representation Node In sorted distribution vector The personalized web page ranking value in; Step 16: Node The dependency vector Regularize to get ; Step 17: Calculate the dependency matrix , .

2. The semi-supervised graph node classification method based on personalized web page ranking according to claim 1, characterized in that: The specific operation of step 16 is as follows: Using the formula 4 for nodes The dependency vector of The personalized web page ranking values ​​are added together to obtain , then use The ranking values ​​of personalized web pages are divided by , and get the regularized dependency vector : （4） （5）。 3. The semi-supervised graph node classification method based on personalized web page ranking according to claim 1, characterized in that: The step 2 specifically includes the following sub-steps: Step 21, Node The representation learning of includes the propagation part and the output part; among them, the representation learning vector of the propagation part of the first hidden layer is , the representation learning vector of the output part is : （6） in, is the representation learning vector of the propagation part of the first hidden layer, Representation Node The eigenvector of , express The adjacent nodes of The eigenvector of , Representation Node The representation learning vector of the propagation part in the first hidden layer, Represents edge The characteristic vector of is the propagation function, which is used to The dimension of becomes , is the propagation function learned through representation The representation learning vector obtained later The dimension of the propagation part is the representation learning matrix, that is, the hidden layer matrix , For the general The nodes are obtained by the propagation function of the representation learning of the first hidden layer. The propagation part represents the learning vector A stack of nodes is formed by stacking them in order. OK A matrix of columns; where the initial Node The eigenvector of ; （7） in, is the representation learning vector of the output part of the first hidden layer, is the representation learning vector of the propagation part of the first hidden layer, Representation Node The eigenvector of , is the propagation function, which is used to The dimension of Output becomes , is the propagation function learned through representation The representation learning vector obtained later The dimension of the output part is the representation learning matrix, that is, the hidden layer matrix ; Step 22, when the number of hidden layers is layer, at this time with the first The propagation function output of the representation learning of the layer is used as the The input of the layer, The output part of the layer representation learning is used as the The input of the layer, then the propagation and output process of representation learning can be expressed as Equation 8, Equation 9 and Equation 10: （8） （9） （10） in , Respectively Layer, The representation learning vector of the propagation part of the layer, , Respectively Layer, The representation learning vector of the output part of the layer, then l The representation learning matrix of the layer propagation part is the hidden layer matrix , No. l +1 layer output part representation learning matrix is ​​the hidden layer matrix ; Will The hidden layers are stacked to get the final hidden layer matrix , is the number of categories in the dataset.

4. The semi-supervised graph node classification method based on personalized web page ranking according to claim 1, characterized in that: In step 3, the dependency matrix obtained in step 1 is added to the last hidden layer matrix of the graph neural network obtained in step 2 using formula 11 to obtain a new global hidden matrix H: （11） Among them, the function Represents the dependency matrix Add hidden layer matrix The method is to convert the dependency matrix of the same dimension into With the hidden layer matrix The value of the bitwise multiplication of the elements in is used as the element value of the corresponding position. , is the number of nodes in the graph, is the number of label categories.

5. The semi-supervised graph node classification method based on personalized web page ranking according to claim 1, characterized in that: The specific operation of step 4 is as follows: Using new graph neural network The layer classifies the nodes of the test set, which is expressed by formula 12, where is the final node classification probability, , is the number of nodes in the graph, is the number of label categories; （12）。

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