CN111488498A - Node-graph cross-layer graph matching method and system based on graph neural network - Google Patents

Node-graph cross-layer graph matching method and system based on graph neural network Download PDF

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CN111488498A
CN111488498A CN202010282856.8A CN202010282856A CN111488498A CN 111488498 A CN111488498 A CN 111488498A CN 202010282856 A CN202010282856 A CN 202010282856A CN 111488498 A CN111488498 A CN 111488498A
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纪守领
凌祥
王赛卓
陈建海
吴春明
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Zhejiang University ZJU
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Abstract

The invention discloses a node-graph cross-layer graph matching system based on a graph neural network, which comprises a graph node embedded vector coding module, a node-graph cross-layer graph matching network module, a graph vector coding module, a similarity calculation module and the like; in addition, the invention also discloses a 'node-graph' cross-layer graph matching method based on the graph neural network, and the method learns the cross-layer interaction information of each node and another graph in one graph in a fine-grained manner based on the graph neural network, so that the embedded information of each node can be effectively updated, and a cross-layer graph matching system based on the method can be obtained based on end-to-end training, so that the similarity between any two graph data can be quickly and accurately calculated.

Description

Node-graph cross-layer graph matching method and system based on graph neural network
Technical Field
The invention relates to the field of graph data mining, in particular to a node-graph cross-layer graph matching method and system based on a graph neural network.
Background
With the continuous development of the big data age, graph data not only shows exponential growth in number, but also is ubiquitous in the current big data environment. The graph data has a wide range of application scenarios, for example, in the fields of bioinformatics, chemical drugs, recommendation systems, social networks, static program analysis, and the like.
The calculation of the similarity between graph data is a basic problem in the graph data application process, namely, given a specific graph data, one or a plurality of similar graph data needs to be searched from a database containing a large amount of graph data. Therefore, to measure the similarity between graph data, two common metrics are mainly proposed at present: graph edit distance and maximum common subgraph. However, graph edit distance and maximum common subgraph are both known NP-hard problems, and graph edit distance and maximum common subgraph between two graphs cannot be accurately calculated within a reasonable time frame even with the most advanced algorithms. Therefore, the graph similarity calculation represented by the graph edit distance and the maximum common subgraph does not generally calculate the accurate value of the similarity directly, but calculates the approximate value of the similarity rapidly through a heuristic algorithm, thereby reducing the cost of the graph data similarity calculation. At present, the method is mainly realized by designing a very complex heuristic algorithm or a discrete combination optimization algorithm, and the time complexity is still polynomial time or even sub-exponential power time of the number of graph nodes.
Recently, the graph neural network model has proven to be a powerful model that can efficiently learn the embedded vectors of nodes in graph data. There are a number of graphical neural network models available today: 1) learning the embedded vectors of the nodes to solve the node classification problem; 2) aggregating the embedded vectors of all nodes in the graph data to obtain a graph vector representation to solve the graph classification problem; 3) the distribution of the graph data is learned to solve the graph generation problem.
However, few studies have been made to calculate the similarity of graph data using a graph neural network model. A simple and straightforward method is to encode two map data separately into two map vectors and then compare the map vectors of the two map data for similarity calculation. Although the graph vectors of the two graph data respectively contain important information of each graph in the calculation method, finer-grained mutual information between the embedded vectors of different levels of the two graphs cannot be sensed.
In summary, the current method for calculating the similarity of graph data by using a neural network has the following problems: 1) no consideration is given to interaction information at low levels between graph data, 2) no consideration is given to interaction information at different levels (global and local) between two graphs at the same time; 3) cross-hierarchy interaction information of part of nodes in data of one graph and the whole of another graph is not considered.
Disclosure of Invention
Aiming at the defects of the existing method for calculating the similarity of graph data by using a neural network, the invention provides a 'node-graph' cross-layer graph matching method based on the neural network, which learns the cross-layer interaction information of each node in one graph and the whole other graph in a fine-grained manner based on the neural network, not only can effectively update the embedded information of each node, but also can obtain a cross-layer graph matching system based on the method based on an end-to-end mode training so as to realize the quick and accurate calculation of the similarity between any two graph data.
In order to achieve the above object of the invention: the invention provides the following technical scheme: a node-graph cross-layer graph matching method based on a graph neural network comprises the following steps:
(1) learning an embedded vector of each node in each graph data in the database by using a graph convolutional neural network and a twin network architecture;
(2) obtaining a cross-layer interaction feature vector of each node by comparing the embedded vector of each node in one graph with the whole graph vector of the other graph, and finally taking the cross-layer interaction feature vector as a new embedded vector of each node in the graph;
(3) aggregating the embedded vectors of all nodes in each graph data by using a pooling method to respectively obtain graph vector representations of the two graph data;
(4) and calculating the similarity of the graph vectors after the two graph data are aggregated.
Preferably, in step (1), the learning of the embedded vector of each node in the graph data by acting on a set of input graph data (typically 2) includes:
(1-1) defining the calculation problem of the similarity of the graph data as follows: given two graph data (G)1，G2) The similarity value s of the two graphs is calculated. Wherein
Figure BDA0002447368190000031
By N nodes vi∈V1And several edges ei，j＝(vi，vj)∈E1It is shown that,
Figure BDA0002447368190000032
by M nodes vi∈V2And several edges ei，j＝(vi，vj)∈E2Represents;
(1-2) initializing graph G respectively by using feature information on nodes and edges of graph data1And G2G can be obtained from the feature matrix X and the adjacency matrix A1＝(X1，A1)，X1∈RN×d，X1∈RN×N；G2＝(X2，A2)，X2∈RM×d，X2∈RM×MWhere d is the initial dimension of the node feature vector;
(1-3) using twin network architecture and graph convolution neural network to compare graph G1And G2Updating the feature vector of each node to obtain a new feature matrix H1And H2。
Further preferably, in the steps (1-3), the graphs G are respectively matched1And G2Updating the feature vector of each node, including:
(1-3a) the graph G is updated simultaneously with the same twin graph convolutional neural network, respectively1And G2The embedded vector of each node in the system is updated according to the formula:
Figure BDA0002447368190000041
1, 2 represents diagram G1Or G2The value of the index of (a) is,
Figure BDA0002447368190000042
shows diagram GlNormalized Laplace matrix, W(i)And i ═ {0, 1, 2} respectively represents the training parameters of the three-layer graph convolutional network.
(1-3b) obtaining a graph G by updating node embedded vectors in the three-layer graph convolution neural network1And G2Updated feature matrix
Figure BDA0002447368190000043
And
Figure BDA0002447368190000044
Figure BDA0002447368190000045
wherein
Figure BDA0002447368190000046
l ═ {1, 2} represents graph G, respectively1And G2And d' represents the updated dimension of the node feature vector.
Preferably, in the step (2), the step of calculating the cross-layer interaction feature vector of each node by comparing the embedded vector of each node in one graph with the whole graph vector of another graph is a key part of the present invention, and comprises:
(2-1) in order to obtain fine-grained mutual information of the node-graph cross-hierarchy, the attention coefficient of each node in the graph and all nodes in another graph is calculated respectively. Using a diagram G1Middle node
Figure BDA0002447368190000048
For example, compute node viAnd graph G2Attention coefficient values of all nodes in the system
Figure BDA0002447368190000047
(2-2) attention coefficient α calculated using step (2-1)i，jAs a graph G2The weight of each node in the graph G is calculated2Vector of (2)
Figure BDA0002447368190000051
(2-3) are directed to FIG. G, respectively1Middle node viEmbedded vector of
Figure BDA0002447368190000052
And FIG. G in step (2-2)2Vector of (2)
Figure BDA0002447368190000053
Performing linear transformation, and calculating cosine similarity of the two-dimensional matrix after linear transformation
Figure BDA0002447368190000054
The mutual information of 'node-graph' cross-hierarchy matching can be obtained, wherein linear transformation is W1∈R1×D，
Figure BDA0002447368190000055
(2-4) repeating the steps (2-1) to (2-3) to obtain the graph G1And G2After all nodes in the tree are updated by node-graph cross-layer graph matching operation
Figure BDA0002447368190000056
And
Figure BDA0002447368190000057
preferably, in step (3), calculating a graph vector representation for each graph datum comprises:
(3-1) Using training parameters
Figure BDA0002447368190000058
Respectively comparing the graphs G obtained in the step (2)1And G2Performing linear transformation on the medium characteristic matrix to obtain
Figure BDA0002447368190000059
And
Figure BDA00024473681900000510
(3-2) performing element-by-element pooling operation on the linearly transformed feature matrices to respectively obtain a graph G1And G2Vector of (2)
Figure BDA00024473681900000511
And
Figure BDA00024473681900000512
Figure BDA00024473681900000513
wherein pooling stands for pooling operation.
Preferably, in step (4), two graph data G are calculated1And G2The similarity value of (a) includes:
(4-1) drawing G calculated in step (3)1And G2The graph vectors are connected to obtain a merged vector
Figure BDA00024473681900000514
(4-2) carrying out multiple times of standard fully-connected neural networks on the merged vector, and gradually reducing the output dimension to 1;
(4-3) adopting sigmoid activation function to limit the range of the output scalar value to 0,1]Within the range, the normalized graph similarity is finally obtained
Figure BDA0002447368190000061
Figure BDA0002447368190000062
Another object of the invention is: the invention also provides a node-graph cross-layer graph matching system based on the graph neural network, which comprises a graph node embedded vector coding module, a node-graph cross-layer graph matching network module, a graph vector coding module, a similarity calculation module and the like,
(1) the graph node embedded vector coding module updates the embedded vector of each node in each graph data by using a parameter-shared twin graph neural network;
(2) the node-graph cross-layer graph matching network module calculates the cross-layer interaction characteristic vector of each node by using a node-graph cross-layer graph matching method and updates the cross-layer interaction characteristic vector into a new embedded vector of each node;
(3) the graph vector coding module is used for aggregating the embedded vectors of all nodes in each graph data to obtain the graph vector representation of each graph data;
(4) and the similarity calculation module is used for calculating the similarity of the two graph data.
Compared with the prior art, the invention has the beneficial effects that:
1) the invention obtains the characteristic vector of each node at cross-layer fine granularity by comparing the whole graph vector of each node embedded in one graph with that of another graph, thereby effectively capturing the low-level information matched with the node;
2) the invention is a learning system of the similarity of the calculation graph obtained by training in an end-to-end mode, avoids using a complex heuristic or discrete combination optimization method, can effectively reduce the calculation time and improve the calculation efficiency of the similarity of the graph;
3) the graph similarity learning framework constructed based on the graph neural network is suitable for most of graph similarity calculation methods based on deep learning and has universality.
Drawings
FIG. 1 is a schematic diagram of a graph similarity calculation system based on a cross-layer graph matching network according to the present invention;
FIG. 2 is a schematic flow diagram of a graph node embedding vector encoding module;
FIG. 3 is a schematic flow diagram of a "node-graph" cross-layer graph matching network module;
FIG. 4 is a flow diagram of the vector encoding module;
FIG. 5 is a schematic flow chart of a similarity calculation module;
FIG. 6 is a diagram of error variations during network training;
fig. 7 shows the test result obtained by inputting the molecular diagram data into the trained network for testing 40000.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
As shown in FIG. 1, the graph similarity calculation system based on the cross-layer graph matching network comprises a graph node embedding vector encoding module, a "node-graph" cross-layer graph matching network module, a graph vector encoding module and a similarity calculation module 4 modules.
The role of the graph node embedded vector coding module is to initialize the feature matrix and the adjacency matrix of the two graphs and learn the feature vector of each node in the graphs. The working flow is shown in fig. 2, and the specific steps are as follows:
(1) given a set of graph data (G)1，G2) Respectively initializing a feature matrix X and an adjacent matrix A of the two graphs by utilizing feature information of nodes and edges in the graphs;
(2) respectively calculating degree matrix D and normalized Laplace matrix of two graphs
Figure BDA0002447368190000081
(3) Training parameters W for respectively initializing three-layer graph convolutional neural network(i)，i＝{0，1，2}；
(4) According to equation (1), the feature matrix X and the normalized Laplace matrix of each graph are used
Figure BDA0002447368190000082
And respectively calculating the embedded vector of each point in the graph to obtain the updated feature matrix H of each graph.
The role of the node-graph cross-layer graph matching network module is to generate a feature matrix of cross-layer interaction of each graph by comparing the embedded vector of each node in one graph with the graph vector of another graph. The working flow is shown in fig. 3, and the specific steps are as follows:
(1) respectively calculating attention coefficients of each node embedding vector in the two graphs and all node embedding vectors in the other graph;
(2) calculating an overall graph vector corresponding to another graph by using the attention coefficient calculated by each node as a weight;
(3) initializing a linear variation matrix W in a node-graph cosine distance1；
(4) And respectively calculating cosine similarity values of graph vectors of each node and the other graph in the two graphs, wherein the cosine similarity values serve as feature vectors after node-graph matching.
The image vector coding module is used for aggregating the feature matrix of each image through a pooling method to respectively obtain the image vector of each image. The working flow is shown in fig. 4, and the specific steps are as follows:
(1) initializing a linear transformation matrix W2；
(2) Performing linear transformation on the feature matrix of each graph;
(3) and performing maximum pooling operation on the transformed feature matrix to obtain a graph vector of each graph.
The similarity calculation module is used for connecting the graph vectors of the two graphs to calculate the similarity. The working flow is shown in fig. 5, and the specific steps are as follows:
(1) connecting the graph vectors of the two graphs to obtain a connected graph vector;
(2) initializing three layers of standard fully-connected neural networks, gradually reducing output dimension, and setting the output dimension of the last layer as 1;
(3) carrying out three-layer full-connection neural network operation on the connected graph vectors;
(4) and (3) adopting a sigmoid activation function to limit the range of the output scalar value within the range of [0,1], and finally obtaining the normalized graph similarity.
The effect of the present invention will be described in further detail with reference to simulation experiments.
Simulation experiment conditions are as follows:
the data set used in the simulation experiment of the invention is 700 molecular map structural data of AIDS antiviral screening compounds of national cancer institute of America, and is used for calculating the map editing distance between the two medicine molecular map structural data. Because the graph edit distance is calculated in pairs, a total of 700 pieces of drug molecular graph structure data can be divided into 500 × 500 ═ 250,000 bisection graph data for training, 200 × 200 ═ 40,000 bisection graph data for testing, and the accurate graph edit distance of each pair of molecular graph data is calculated by a traditional accurate calculation method.
The experiment was run on a computer equipped with 2 intel Xeon CPUs, a 128G memory, and one intevada GTX 1080Ti GPU. The experiment set batch size is 128 and iterations are stopped 10000 times.
Experimental contents and results:
the simulation laboratory inputs 250,000 pairs of medicine molecular graph data for training into the node-graph cross-layer graph matching network based on the graph neural network stated in the invention, utilizes the weight of the Gaussian random initialization network, and utilizes the mean square error loss to train the graph matching network until the model converges or the iteration maximum times is reached, and the mean square error convergence process in the network training process is shown in FIG. 6.
Finally, 40000 fractal graph data for testing is input into a trained network for testing, the test result is measured by a spearman grade correlation coefficient rho (the stronger the correlation is, the larger the correlation coefficient rho is, the maximum value is 1) and the number precision @ k of correlation results in the first k recommendations, and the test result is shown in fig. 7.
As can be seen from FIG. 7, the model of the present invention has a high correlation coefficient on the test data, and the average spearman rank correlation coefficient reaches 0.901; meanwhile, precision of precision @10 and precision @20 of the invention are quite high and respectively reach 0.455 and 0.636. In addition, compared with the traditional graph editing distance calculation method, the calculation time of each sample in the test stage is greatly shortened, and the average calculation time of each test sample is only 9.302 milliseconds.

Claims (8)

1. A node-graph cross-layer graph matching method based on a graph neural network is characterized by comprising the following steps:
(1) learning an embedded vector of a node of each of the two graph data by using a graph convolutional neural network and a twin network architecture;
(2) obtaining a cross-layer interaction feature vector of each node by comparing the embedded vector of each node in one graph with the whole graph vector of the other graph, and finally taking the cross-layer interaction feature vector as a new embedded vector of each node in the graph;
(3) aggregating the embedded vectors of all nodes in each graph data by using a pooling method to respectively obtain graph vector representations of the two graph data;
(4) and calculating the similarity of the graph vectors after the two graph data are aggregated.
2. The node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 1, wherein the step (1) comprises the following steps:
(1-1) acting on a set of drawing data G1、G2，
(1-2) Using G1And G2Respectively initializing G with characteristic information of respective node and edge1And G2The feature matrix X, the adjacency matrix a;
(1-3) utilizing twin network architecture and graph convolution neural network to respectively pair G1And G2Updating the feature vector of each node to obtain a new feature matrix H1And H2；
The step (2) comprises the following steps:
(2-1) calculating attention coefficients of each node of one graph and all nodes in the other graph respectively;
(2-2) calculating an overall graph vector corresponding to another graph by using the attention coefficient calculated by each node as a weight;
(2-3) initializing a linear change matrix W in the cosine distance of the node-graph1；
(2-4) respectively calculating the cosine similarity value of each node of one graph and the graph vector of the other graph, wherein the cosine similarity value is used as a feature vector after the node-graph matching;
the step (3) comprises the following steps:
(3-1) initializing the Linear transformation matrix W2；
(3-2) performing linear transformation on the feature matrix of each graph;
(3-3) performing maximum pooling operation on the transformed feature matrix to obtain a graph vector of each graph;
the step (4) comprises the following steps:
(4-1) connecting the graph vectors of the two graphs to obtain a connected graph vector;
(4-2) initializing three layers of standard fully-connected neural networks, gradually reducing output dimensions, and setting the output dimension of the last layer as 1;
(4-3) carrying out three-layer full-connection neural network operation on the connected graph vectors;
and (4-4) limiting the range of the output scalar value to the range of [0,1] by adopting a sigmoid activation function, and finally obtaining the normalized graph similarity.
3. The node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 2, wherein: in the step (1), G is respectively initialized by utilizing the characteristic information of the nodes and the edges of the respective graph data1And G2G can be obtained from the feature matrix X and the adjacency matrix A1＝(X1，A1)，X1∈RN×d，X1∈RN×N；G2＝(X2，A2)，X2∈RM×d，X2∈RM×MWherein d is the initial dimension of the node feature vector; wherein,
Figure FDA0002447368180000038
by N nodes vi∈V1And several edges ei，j＝(vi，vj)∈E1Represents;
Figure FDA0002447368180000039
by M nodes vi∈V2And several edges ei，j＝(vi，vj)∈E2And (4) showing.
4. The node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 2, wherein: in the step (1-3), first, G is updated simultaneously by using the same twin map convolutional neural networks respectively1And G2The embedded vector of each node in the system is updated according to the formula:
Figure FDA0002447368180000031
l ═ {1, 2} represents G1Or G2The value of the index of (a) is,
Figure FDA0002447368180000032
represents GlNormalized Laplace matrix, W(i)And i ═ {0, 1, 2} respectively represents training parameters of the three-layer graph convolutional neural network;
secondly, obtaining G by updating node embedded vectors in the three-layer graph convolutional neural network1And G2Updated feature matrix
Figure FDA0002447368180000033
And
Figure FDA0002447368180000034
wherein
Figure FDA0002447368180000035
Each represents G1And G2And d' represents the updated dimension of the node feature vector.
5. The node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 2, wherein: in the step (2), the step (2-1) respectively calculates attention coefficients of each node in one graph and all nodes in another graph, and G is used1Middle node
Figure FDA00024473681800000310
For example, compute node viAnd G2Attention coefficient values of all nodes in the system
Figure FDA0002447368180000036
Step (2-1), attention coefficient α is usedi，jAs G2The weight of each node in G is calculated2Vector of (2)
Figure FDA0002447368180000037
Step (2-3), for G respectively1Middle node viEmbedded vector of
Figure FDA0002447368180000041
And G in step (2-2)2Vector of (2)
Figure FDA0002447368180000042
Performing linear transformation, and calculating cosine similarity of the two-dimensional matrix after linear transformation
Figure FDA0002447368180000043
Mutual information of the node-graph matching across the levels can be obtained,wherein the linear transformation is W1∈R1×D，
Figure FDA0002447368180000044
(2-4) repeating the steps (2-1) to (2-3) to obtain G1And G2After all nodes in the tree are updated by node-graph cross-layer graph matching operation
Figure FDA0002447368180000045
And
Figure FDA0002447368180000046
6. the node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 2, wherein: in the step (3), the step (c),
(3-1) Using training parameters
Figure FDA0002447368180000047
Respectively comparing G obtained in the step (2)1And G2Performing linear transformation on the medium characteristic matrix to obtain
Figure FDA0002447368180000048
And
Figure FDA0002447368180000049
(3-2) performing element-by-element pooling operation on the linearly transformed feature matrices to respectively obtain G1And G2Vector of (2)
Figure FDA00024473681800000410
And
Figure FDA00024473681800000411
Figure FDA00024473681800000412
Figure FDA00024473681800000413
wherein pooling stands for pooling operation.
7. The node-graph cross-layer graph matching method based on the graph neural network as claimed in claim 2, wherein: in the step (4), the step of (C),
(4-1) G calculated in the step (3)1And G2The graph vectors are connected to obtain a merged vector
Figure FDA00024473681800000414
(4-2) carrying out multiple times of standard fully-connected neural networks on the merged vector, and gradually reducing the output dimension to 1;
(4-3) adopting sigmoid activation function to limit the range of the output scalar value to 0,1]Within the range, the normalized graph similarity is finally obtained
Figure FDA0002447368180000051
Figure FDA0002447368180000052
8. A node-graph cross-layer graph matching system based on a graph neural network is characterized by comprising the following components:
the graph node embedded vector coding module is used for updating the embedded vector of each node in each graph data;
the node-graph cross-layer graph matching network module is used for acquiring a cross-layer interaction feature vector of each node so as to acquire a new embedded vector of each node;
the graph vector coding module is used for aggregating the embedded vectors of all nodes in each graph data to obtain the graph vector representation of each graph data;
and the similarity calculation module is used for obtaining the similarity of the two graph data.
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