Semi-supervised node classification method based on graph convolution network and probabilistic inference model

Abstract

The present application relates to the technical field of image node classification, and especially relates to a semi-supervised node classification method based on a graph convolution network and a probabilistic inference model, solves the technical problems in the background art, the method utilizes an edge complete tree to divide a graph, and lets a message propagation mechanism of the graph convolution network interactively execute inside and between subgraphs, integrates the similarity between nodes into the graph convolution network, so that the node state matrix in each layer satisfies the similarity constraint, in order to perform node classification, the method utilizes a conditional random field to model the correlation between node labels, and deeply fuses it with the graph convolution network fusing the node similarity. The method uses a kind of local first-order approximation in frequency domain graph convolution to realize convolution architecture, can learn the information of graph on hidden layer, also uses fast approximate convolution, can quickly, scalablely complete semi-supervised classification task based on point, can efficiently semi-supervised learning on large-scale graph data.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image node classification, and particularly relates to a semi-supervised node classification method based on a graph convolutional network and a probabilistic inference model. BACKGROUND

[0002] In recent years, with the rapid development of deep learning, many scholars have begun to use the powerful feature extraction capability of deep learning to process graph data. This requires embedding the nodes, edges and even subgraphs of the graph into a low-dimensional vector space, and requires the embedding vector to capture the local and global structure information of the graph. Graph data is different from picture, text and other data with regular structure, and has complex non-regular structure. In addition, graph data has diversified connection modes (directed and undirected, weighted and unweighted, homogeneous and heterogeneous, dynamic and static) and task types (node classification, graph classification, link prediction). Therefore, the deep learning model facing massive complex graph structure data still faces many challenges.

[0003] In order to cope with the above challenges, the graph neural network (GNN) emerges as the times require, and the graph convolutional network (GCN) as the most typical GNN model has attracted particular attention. Generally, the GCN model includes two categories: (1) GCN model based on spectral method; (2) GCN model based on local spatial structure. The GCN model can encode the structure information of the graph in the low-dimensional representation vector of the node or edge through the message passing mechanism. The message passing mechanism has scalability limitations on large graphs. Therefore, it is necessary to divide the large graph data into several small graphs, and then integrate the messages on the small graphs. In addition, the traditional graph convolutional network does not consider the similarity between nodes and the correlation between node labels in the message passing process, which will affect the accuracy of classification. Therefore, it is necessary to integrate the node similarity and node label correlation into the graph convolutional network. SUMMARY

[0004] In order to overcome the technical defects that the traditional graph convolutional network does not consider the similarity between nodes and the correlation between node labels in the message passing process, resulting in poor classification accuracy, the present application provides a semi-supervised node classification method based on a graph convolutional network and a probabilistic inference model.

[0005] The present application provides a semi-supervised node classification method based on a graph convolutional network and a probabilistic inference model, comprising the following steps:

[0006] Step one, the large graph is divided into several small graphs by using graph partitioning algorithm, the edge complete tree which can preserve all edge information in the graph is obtained by enhancing the spanning tree, then the edge complete tree is segmented, and each subtree is divided into several subgraphs according to its nodes, in order to ensure the message propagation between nodes, and save the coarsening graph composed of the connection relationship between subgraphs;

[0007] Step two, message propagation is carried out on the subgraph and the coarsening graph respectively by using graph convolution network, the message propagation mechanism of the graph convolution network is:

[0008]

[0009] Among them, represents the adjacent matrix with self-loop, represents the row and column of ;

[0010] The objective function of node classification is:

[0011]

[0012] Among them, W is the weight, X is the feature matrix of the node, A is the adjacency matrix, Y is the node label, H l is the node feature matrix of the lth layer graph convolution network, represents the F norm, γ is a random variable, R(·) represents the regularization function added to realize the similarity constraint between nodes, in order to ensure the flexibility of the regularization function, the conditional random field is used to model the similarity between node features, and

[0013]

[0014] Among them, X l = F(A, H l-1 , W l ), E(H l , X l ) represents the energy function which can not only strengthen the feature representation of the node, but also capture the similarity between the feature of the node and its adjacent nodes, Z(X l ) represents the partition function; the average field variational inference is used to approximate the calculation of P(H l |X l ), that is, to minimize KL(Q(H l )||P(H l |X l )); finally, the similarity P(H l |X l), i.e. to obtain a conditional random field operator that can be embedded into the graph convolution network; performing the graph convolution network with the conditional random field operator on each subgraph and the coarse graph respectively to obtain the representation vector of the corresponding node in the subgraph and the coarse graph; in order to ensure the message passing between the subgraph and the coarse graph, the representation information of the node in the subgraph is converged by a global pooling operator and is passed to the corresponding node in the coarse graph; the representation of the node in the coarse graph is obtained by the message passing in the coarse graph, and the representation is passed to the node in the corresponding subgraph;

[0015] Step three, the graph convolution network with the conditional random field operator encodes the graph structure information in the feature vector without considering the correlation between the node labels, so the correlation between the node labels is calculated next, for the observable node, the log likelihood function of the label of the observable node is φ (Y label |H l ); the label Y unlabel of the unknown node is taken as a hidden variable, and by using variational inference, the evidence lower bound ELBO of the log likelihood function is obtained, i.e.

[0016]

[0017] The parameters φ and θ are updated interactively by using the variational EM algorithm, in the variational E step, the graph convolution network with the conditional random field layer is used to represent the variational distribution, i.e.

[0018]

[0019] In the variational M step, the graph convolution network with the conditional random field layer is used to represent the conditional probability, i.e.

[0020]

[0021] Finally, the label of the unlabeled node is predicted by using the variational distribution , i.e. the node classification is realized.

[0022] The method divides the graph by using the edge complete tree, and makes the message passing mechanism of the graph convolution network execute interactively between the subgraphs and the subgraphs, in addition, the method fuses the similarity between the nodes into the graph convolution network, so that the node state matrix in each layer satisfies the similarity constraint, in order to perform the node classification, the method models the correlation between the node labels by using the conditional random field, and deeply fuses the graph convolution network with the fused node similarity.

[0023] Compared with the prior art, the technical scheme provided by the application has the following advantages: for large graph node classification problems, graph partitioning, probabilistic inference model and graph convolution network are used for node classification, which not only ensures the scalability of the model, but also fully considers the similarity between nodes and the correlation between labels; the method can perform efficient semi-supervised learning on large-scale graph data, the method uses a local first-order approximation in the frequency domain graph convolution to realize the convolution architecture, which can learn the information of the graph on the hidden layer, in addition, the method also uses fast approximate convolution, which can quickly and scalable complete the point-based semi-supervised classification task. BRIEF DESCRIPTION OF DRAWINGS

[0024] The accompanying drawings, which are incorporated herein and constitute part of the specification, illustrate embodiments consistent with the application and, together with the description, serve to explain the principles of the application.

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments or prior art description will be briefly introduced hereinafter. Obviously, for those skilled in the art, other drawings can also be obtained based on these drawings without any creative effort.

[0026] Figure 1 A schematic diagram of the semi-supervised node classification method based on the graph convolution network and the probabilistic inference model. DETAILED DESCRIPTION

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments or prior art description will be briefly introduced hereinafter. Obviously, for those skilled in the art, other drawings can also be obtained based on these drawings without any creative effort.

[0028] In the description, it should be noted that the terms "first", "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance. It should be noted that, unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connecting" should be understood in a broad sense, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0029] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein; obviously, the examples in the specification are only a part of the embodiments of the present application, not all the embodiments.

[0030] The specific embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0031] In one embodiment, as shown in Figure 1 the semi-supervised node classification method based on graph convolution network and probabilistic inference model includes the following steps:

[0032] Step one, since the large graph data contains a large number of nodes and edges, the large graph is divided into several small graphs by using graph partitioning algorithm. Considering the complexity of graph partitioning problem and the good properties of tree structure, the edge complete tree which can preserve all edge information in the graph is obtained by enhancing the generated tree, and then the edge complete tree is segmented, and each subtree is divided into several subgraphs according to its nodes, that is, induced subgraphs, in order to ensure the message propagation between nodes and save the coarse graph composed of the connection relationship between subgraphs;

[0033] Step two, message propagation is carried out on the subgraph and the coarse graph by using the graph convolution network. The message propagation mechanism of the graph convolution network is:

[0034]

[0035] wherein, denotes the adjacent matrix with self-loop, denotes the row of ; in order to consider the similarity between nodes, the state matrix H l ∈R n×d is regarded as a row random vector, and then the conditional random field (CRF) is used to model the similarity between nodes; wherein the objective function of node classification is changed to:

[0036]

[0037] wherein, W is the weight, X is the feature matrix of the node, A is the adjacent matrix, Y is the node label, H l is the node feature matrix of the lth layer graph convolution network, denotes the F norm, γ is a random variable, and R(·) represents the regularization function added to realize the similarity constraint between nodes. In order to ensure the flexibility of the regularization function, the conditional random field is used to model the similarity between node features, and

[0038]

[0039] wherein X l = F(A, H l-1 , W l ), E(H l , X l) is an energy function that represents both the feature representation of the node and the similarity between the node and its neighbors, Z(X l ) is a partition function; since the partition function Z(X l ) is difficult to compute, the mean-field variational inference is used to approximate the computation of P(H l |X l ), i.e., to minimize the KL(Q(H l )||P(H l |X l )); finally, the similarity between the node features P(H l |X l ) is computed, i.e., a conditional random field operator that can be embedded into a graph convolutional network is obtained; the graph convolutional network with the conditional random field operator is executed on each subgraph and the coarse graph, respectively, to obtain the representation vectors of the corresponding nodes in the subgraph and the coarse graph; in order to ensure the message passing between the subgraph and the coarse graph, the representation information of the nodes in the subgraph is aggregated by a global pooling operator and is passed to the corresponding nodes in the coarse graph; the representation of the nodes in the coarse graph is obtained through the message passing in the coarse graph, and the representation is passed to the nodes in the corresponding subgraph;

[0040] Step three, the graph convolutional network with the conditional random field operator encodes the graph structure information in the feature vector without considering the correlation between the node labels, so the correlation between the node labels is calculated next, for the observable nodes, the log-likelihood function of the label of the observable node is log p φ (Y label |H l ); the label Y unlabel of the unknown node is taken as a hidden variable, and the evidence lower bound ELBO of the log-likelihood function is obtained by using variational inference, i.e.,

[0041]

[0042] The variational EM algorithm is used to interactively update the parameters φ and θ, in the variational E step, the variational distribution is represented by using the graph convolutional network with the conditional random field layer, i.e.,

[0043]

[0044] In the variational M step, the conditional probability is represented by using the graph convolutional network with the conditional random field layer, i.e.,

[0045]

[0046] Finally, the label of the unlabeled node is predicted by using the variational distribution , i.e., the node classification is realized.

[0047] The above description is merely one specific implementation of the application, and thus the technical solutions recorded in the foregoing embodiments can be modified or some or all of the technical features can be substituted equivalently by those skilled in the art, without departing from the scope of the technical solutions of the embodiments, and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the embodiments, and should be included in the protection scope of the claims.

Claims

1. A semi-supervised node classification method based on graph convolutional networks and probabilistic inference models, characterized in that, Includes the following steps: Step 1: Use a graph partitioning algorithm to divide the large graph into several smaller graphs. By enhancing the spanning tree, we obtain an edge-complete tree that can retain all edge information in the graph. Then, we partition the edge-complete tree and obtain several subgraphs for each subtree based on its nodes. In order to ensure message propagation between nodes, we also save the coarsened graph composed of the connection relationships between the subgraphs. Step 2: Use a graph convolutional network to perform message propagation on the subgraph and the coarsened graph respectively. The message propagation mechanism of the graph convolutional network is as follows: in, This represents an adjacency matrix with self-loops. express The lines and; The objective function for node classification is: Where W is the weight, X is the feature matrix of the node, A is the adjacency matrix, Y is the node label, and H is the node label. l Let be the node feature matrix of the l-th layer graph convolutional network. Let F denote the F-norm, γ be a random variable, and R(·) denote the regularization function added to implement the similarity constraint between nodes. To ensure the flexibility of the regularization function, we propose to use conditional random fields to model the similarity between node features, letting Where X l =F(A,H) l-1 W l ), E(H l ,X l Z(X) represents an energy function that both enhances the feature representation of a node and captures the similarity between its features and those of its neighboring nodes. l P(H) is represented as the partitioning function; P(H) is approximated using mean-field variational inference. l |X l That is, minimizing KL(Q(H)). l )||P(H l |X l Finally, the similarity P(H) between node features is calculated. l |X l This process yields a Conditional Random Field (CRF) operator that can be embedded into a graph convolutional network. A graph convolutional network with the CRF operator is then executed on each subgraph and coarsened graph to obtain the representation vectors of the corresponding nodes in the subgraph and coarsened graph. To ensure message passing between the subgraph and coarsened graph, the representation information of nodes in the subgraph is aggregated using a global pooling operator and passed to the corresponding nodes in the coarsened graph. The representation of the nodes in the coarsened graph is obtained through message passing within the coarsened graph, and this representation is then passed to the nodes in the corresponding subgraph. Step 3: The graph convolutional network with conditional random field operators encodes graph structure information in feature vectors. Since it doesn't consider the correlation between node labels, we then calculate the correlation between node labels. For observable nodes (which are labeled nodes), the log-likelihood function of their labels is log p. φ (Y label |H l ); Label the unknown node Y unlabel As a hidden variable, using variational inference, we can obtain the evidence lower bound ELBO of the log-likelihood function, i.e. The variational EM algorithm is used to interactively update parameters φ and θ. In the variational E-step, a graph convolutional network with conditional random field layers is used to represent the variational distribution, i.e. In the variational M-step, a graph convolutional network with conditional random field layers is used to represent the conditional probabilities, i.e. Finally, using variational distribution By predicting the labels of unlabeled nodes, node classification can be achieved.

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