Graph network information measurement method, robust graph representation learning method and graph data analysis method

Abstract

The invention provides a graph network information measurement method, a robust graph representation learning method and a graph data analysis method. The method mainly comprises the following steps: acquiring an adjacent matrix of a graph network topology; calculating an edge curvature of the graph network topology based on the adjacent matrix; and taking the edge curvature as graph network information measurement, and judging whether the related sub-topology has topology defects or not according to a network information measurement theory. According to the method, the edge curvature is used as network information measurement, and graph topology defect detection can be accurately realized. According to the robust graph representation learning method, the feature representations of the network topology after modification and the network topology before modification are extracted respectively, and the feature representations are integrated to obtain a representation learning result of the network topology, so that the stability and the accuracy of graph representation learning based on the graph neural network can be remarkably improved; the over-compression phenomenon of graph representation in the message passing process is reduced, and the representation learning performance is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of graph representation learning, and in particular to a graph network information metric, a robust graph representation learning and a graph data analysis method. Background Art

[0002] In recent years, graph neural networks (GNNs) have attracted widespread attention due to their excellent performance in processing graph-structured data. Unlike traditional neural network models, graph neural networks capture the relationship of data by passing information between nodes in the graph structure, which makes it particularly outstanding in fields such as social network analysis, recommendation systems, and bioinformatics. In graph neural networks, message passing networks (MPNs), as a mainstream technical means, have been widely used in different types of graph data processing tasks. Message passing networks achieve graph representation learning by exchanging and updating information between nodes. The core idea is to capture the complex dependencies between nodes through a local message passing mechanism. However, message passing networks are often affected by topological defects in practical applications. For example, Alon et al. published "On The Bottleneck of Graph Neural Networks and its Practical Implications" in the 2021 International Conference on Learning Representations, which shows that there is an over-compression problem in graph representation learning, which will lead to the loss or distortion of important structural information during information transmission, resulting in the performance degradation of graph neural networks.

[0003] To solve these problems, researchers need to measure and optimize the graph topology appropriately to ensure that the graph representation learning model can accurately capture the key information in the graph and improve its robustness. In recent years, for example, Topping et al. published "Understanding Over-Squashing and Bottlenecks on Graphs via Curvature" at the 2022 International Conference on Learning Representations, which proposed using Graph Ricci Curvature as a measure of local topological over-compression, and explored how to alleviate the problems in graph representation learning by changing the topology. However, the theoretical basis has not yet fully explained the relationship between Ricci curvature and over-compression. Karhadkar et al. published "FoSR: First-Order Spectral Rewiring for Addressing Oversquashing in GNNs" at the 2023 International Conference on Learning Representations, which proposed to optimize the graph topology inspired by the spectral gap, but it lacks sufficient measurement tools and cannot effectively locate the location of bottlenecks and defective topologies.

[0004] Therefore, there is currently no effective and reasonable tool that can overcome problems such as over-compression in graph learning and obtain stable representation learning results. Although existing tools and methods have improved the practical application of graph representation learning, they still face challenges in theory and it is difficult to accurately and efficiently measure information compression in graph topology. Existing methods still lack effective metrics to detect and deal with defects in graph topology. It is necessary to propose new graph network information metrics and methods to improve the robustness and stability of graph learning models. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a graph network information measurement method, as well as a graph representation learning method and system based on the graph network information measurement method, which can stably and efficiently realize representation learning of graph data.

[0006] One aspect of the present invention provides a graph network information measurement method, comprising:

[0007] Get the adjacency matrix of the graph network topology;

[0008] Calculating the edge curvature of the graph network topology based on the adjacency matrix;

[0009] The edge curvature is used as a graph network information metric, and the network information metric theory is used to determine whether a related sub-topology has a topological defect.

[0010] Preferably, the calculating the edge curvature of the graph network topology based on the adjacency matrix includes:

[0011] If the graph network structure contains transition probability information, the transition probability information is organized into a transition probability matrix P, that is, any element P of the matrix ij represents the transition probability p from node i to node j ij ; Otherwise, the transition probability matrix of the graph network topology is calculated by normalizing the degree, that is, for any pair of adjacent edges i, j, where d i represents the degree of node i;

[0012] Repeat the following steps for each edge in the graph network topology:

[0013] Calculate the adjacent triangle transition probability and the adjacent 4-ring transition probability of the edge based on the transition probability matrix and the adjacency matrix;

[0014] Calculate the number of adjacent triangle transition paths and the number of adjacent 4-ring transition paths of the edge based on the adjacency matrix;

[0015] Determine the message gain: If the graph representation learning model parameter matrix is ​​known, calculate the 1-norm of the model parameter matrix as an estimate of the message gain, otherwise replace the message gain with a constant;

[0016] The edge curvature is obtained by making a polynomial combination of the adjacent triangle transition probability, the adjacent 4-ring transition probability, the adjacent triangle transition path number, the adjacent 4-ring transition path number, the message gain and the degree of the node.

[0017] Preferably, the topological defect includes the over-compression phenomenon of the graph, which is expressed as follows: for any edge s~i in the graph, s,i represents its two end nodes, and the target node i represents h i For the feature x of the source node s s The first-order partial derivative mode length

[0018] The network information measurement theory refers to: using edge curvature to measure the noise from the defect graph topology during the learning process, the edge curvature and the expected upper bound of noise resistance have a probability approximation relationship; wherein, the noise refers to the noise caused by the characteristic representation of the neighboring nodes on the target path information transmission path squeezing the target information, and the noise resistance is the representation h of the target node i. i For the feature x of the source node s s The first-order partial derivative mode length measure.

[0019] Preferably, the step of using the edge curvature as a graph network information metric to determine whether a related sub-topology has a topological defect includes:

[0020] Set the minimum threshold κ of edge curvature;

[0021] For each edge in the graph network topology, make a judgment:

[0022] For edges with edge curvature less than κ, the edge is judged as a defective edge;

[0023] For an edge whose edge curvature is greater than or equal to κ, the edge is determined to be a non-defective edge.

[0024] According to a second aspect of the present invention, a robust graph representation learning method is provided, comprising:

[0025] Using any of the graph network information measurement methods described above, the defective edges of the graph network topology are obtained;

[0026] Modifying the defective edge of the graph network topology to obtain a new topology with stability;

[0027] Feature representations of the modified graph network topology and the graph network topology before and after modification are extracted and integrated to obtain a graph representation.

[0028] Preferably, the modifying the defective edge of the graph network topology to obtain a new topology with stability includes:

[0029] For each defective edge, connect all nodes in the 1-neighborhood of one neighboring node i and another neighboring node j of the defective edge;

[0030] Or: randomly add connections in the neighborhood of two nodes of the defective edge;

[0031] Or: Delete edges whose curvature exceeds the set value.

[0032] Preferably, extracting the feature representations of the graph network topology after modification and the graph network topology before modification and integrating them to obtain the graph representation comprises:

[0033] Initialize two graph neural networks with a message passing network architecture and The two message passing network architectures have the same number of layers L and the same weight parameter distribution;

[0034] For each layer of the message passing network l=1…L, repeat the following:

[0035] use Get the lth layer hidden representation of the original topology use Obtain the l-th layer hidden representation of the new topology

[0036] Adopt the sum of the two hidden representations As the hidden representation output of this layer;

[0037] If l < L, this output serves as the common input for the next layer of the two message passing networks;

[0038] If l = L, then H L Is the final output of the message passing network and serves as the graph representation.

[0039] According to the third aspect of the present invention, there is provided a graph data analysis method, including:

[0040] If the graph data to be analyzed is social network user interaction data, in each graph network topology, nodes represent different users, and edges represent the relationships between users; adopt the robust graph representation learning method described in any one of claims 5-7 to obtain the graph representation of each social network graph, and identify community structures or important nodes from the graph representation for determining user behavior patterns and network propagation characteristics;

[0041] If the graph data to be analyzed is biomolecules, in each graph, nodes represent different biomolecules, and edges represent the interactions between molecules; adopt the robust graph representation learning method described in any one of claims 5-7 to obtain the graph representation of each biomolecule graph, and identify key molecules or potential biological pathways from the graph representation to judge the functions and influences of molecules.

[0042] According to the fourth aspect of the present invention, there is provided a terminal, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it can be used to execute the graph network information measurement method described in any one of items 3, or the graph representation learning method described in any one of them, or the graph data analysis method described in any one of them.

[0043] According to the fifth aspect of the present invention, there is provided a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it can be used to execute the graph network information measurement method described in any one of them, or the graph representation learning method described in any one of them, or the graph data analysis method described in any one of them.

[0044] Compared with the prior art, the embodiments of the present invention have at least one of the following beneficial effects:

[0045] For the graph network information measurement information in the embodiments of the present invention, using edge curvature as the network information measurement can accurately detect graph topology defects.

[0046] The graph network information measurement method in the embodiment of the present invention uses the adjacency matrix of the graph as topological information, can directly obtain the information measurement on each edge, and has a lower time complexity than Ricci curvature; no additional computing resources such as neural networks are required.

[0047] The graph network information measurement method in the embodiment of the present invention adopts the curvature measurement that takes into account the node transition probability. By analyzing the neighborhood topological properties and transition probability law of the edge in the graph, it approaches the expectation of over-compression of the edge. It can accurately realize the detection of graph topological defects and can be applied to the performance improvement of graph representation learning.

[0048] The robust graph representation learning method in the embodiment of the present invention can significantly improve the stability and accuracy of graph representation learning based on graph neural network, reduce the over-compression phenomenon of graph representation during message transmission, and ensure the representation learning performance.

[0049] The robust graph representation learning method in the embodiment of the present invention can reduce the impact of over-compression while retaining the original topological information, thereby enhancing the robustness of representation learning.

[0050] Based on the above-mentioned graph network information metric and robust graph representation learning method, the embodiment of the present invention can detect, locate and correct defective topology for any graph topology, and enhance the performance and stability of graph representation learning. It has extremely strong practical application value, especially in actual graph data analysis applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0052] Figure 1 The present invention is a flowchart of a graph network information measurement method in one embodiment of the present invention.

[0053] Figure 2 The flowchart is a method for calculating edge curvature metrics edge by edge in one embodiment of the present invention.

[0054] Figure 3 The flowchart of the robust graph representation learning method in one embodiment of the present invention is shown.

[0055] Figure 4 The present invention is a flowchart for obtaining learning results based on the graph topology before and after modification in one embodiment of the present invention.

[0056] Figure 5 The present invention is a flowchart of using a robust graph representation learning method for graph data analysis in one embodiment of the present invention.

[0057] Figure 6 This is a diagram showing the implementation effect of graph network information measurement in one embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0059] Figure 1 The figure is a flow chart of a method for measuring network information in one embodiment of the present invention.

[0060] Reference Figure 1 As shown, the network information measurement method in this embodiment includes the following steps:

[0061] S100, obtaining an adjacency matrix of the graph network topology;

[0062] S200, calculating the edge curvature of the graph network topology based on the adjacency matrix;

[0063] S300, using the edge curvature as a graph network information metric, and determining whether a related sub-topology has a topological defect based on network information metric theory.

[0064] In S100, the graph network topology refers to a structure composed of nodes and edges, where the nodes represent entities, the edges represent the relationship between entities, and the degree of the nodes represents the number of edges connected to the nodes. The graph (network) used for measurement can be any natural graph data. In a preferred embodiment, the graph topology in the Cora data set can be used as the graph network topology to be measured. Based on this graph topology, its adjacency matrix is ​​obtained: first, the topological relationship of the network is clarified, including the relationship between nodes and edges. Then, according to the determined network topology, an initial adjacency matrix is ​​constructed. The adjacency matrix is ​​a square matrix that represents the connection relationship between nodes in the graph. If there is an edge between nodes i and j, the corresponding position in the adjacency matrix is ​​1; if there is no edge, it is 0. Further, for directed networks (ie, edges have directions), the adjacency matrix is ​​asymmetric; while for undirected networks (ie, edges have no directions), the adjacency matrix is ​​symmetric. If there are multiple edges or self-edges, the elements corresponding to the multiple edges can be set to a value greater than 1, and the diagonal elements corresponding to the self-edges can be set to 1.

[0065] Of course, in other embodiments, various programming languages ​​and tools can also be used to generate an adjacency matrix. For example, in MATLAB, a built-in function can be used to generate an adjacency matrix for a complex network. In Python, the adjacency_matrix function in the networkx library can be used to obtain an adjacency matrix.

[0066] Based on this adjacency matrix, the edge curvature is calculated. A preferred embodiment of the present invention provides a preferred scheme of S200, which calculates the edge curvature of each edge in the topology based on the network information metric theory and uses the edge curvature as the information metric on the graph network.

[0067] In this step, the network information metric theory refers to a related theory that shows that the edge curvature metric has a mathematical relationship with the actual topological defect. In this embodiment, the topological defect can be an over-compression phenomenon of the graph, which is expressed as follows: for any edge s~i in the graph, s,i represents its two end nodes, and the target node i represents h i For the feature x of the source node s s The first-order partial derivative mode length The theory is that the curvature and the expected upper bound of the overcompression phenomenon in a node neighborhood exist in a probabilistic approximation relationship, that is, Where C is a constant related to the overall statistics of graph neural networks and graph topology, independent of i and j, and S1(j)\{i} represents the 1-neighborhood of node j excluding node i.

[0068] Furthermore, Figure 2 FIG. 1 is a flow chart of calculating edge curvature measurement edge by edge in a preferred embodiment of the present invention. Figure 2 FIG. 4 illustrates a process of calculating edge curvature in an embodiment of the present invention. In this embodiment, the edge curvature calculation may specifically include the following steps:

[0069] S210, obtaining a transition probability matrix P of the graph.

[0070] In this step, if the graph contains node transition probability information, the information is processed into a transition probability matrix. Otherwise, the transition probability matrix of the graph is calculated by normalizing the degree.

[0071] Repeat the following steps for each edge i~j of the graph:

[0072] S220, calculating the adjacent triangle transition probability P of the edge based on the graph transition probability matrix and the graph adjacency matrix Δ (i,j) and the adjacent 4-ring transition probability P □j (i,j);

[0073] In this step, in represents the set of vertices that form a triangle with edges i~j, P jk represents the transition probability from node j to node k;

[0074] In this step, in represents the set of neighbor nodes of j among the vertices that form a 4-ring with edges i~j;

[0075] S230, calculating the number of adjacent triangle transfer paths of the edge based on the graph adjacency matrix Number of adjacent 4-ring transition paths

[0076] In this step, Represents the number of two-hop paths from i to adjacent triangle nodes that do not pass through j.

[0077] In this step, Represents the number of two paths from i to adjacent 4-ring nodes that do not pass through j.

[0078] S240, obtaining a message gain constant β;

[0079] In this step, if the parameter matrix W of each layer of the graph network model used to represent learning is known (1) …W (L) , then calculate the message gain constant Otherwise, let the message gain constant be a suitable real number. In this embodiment, let β=10.

[0080] S250, a polynomial combination is used to combine the adjacent triangle transition probability, the adjacent four-ring transition probability, the adjacent triangle transition path number, the adjacent four-ring transition path number, the message gain and the degree of the node to obtain the edge curvature calculation result Curv(i, j).

[0081] In this step, Among them, d i represents the degree of node i, P ji represents the transition probability from node j to node i, P □j and P Δ They are P □j (i,j) and P Δ Simplified representation of (i,j)

[0082] The above embodiment adopts a curvature metric based on a graph random walk model, and approaches the expectation of over-compression of the edge by analyzing the neighborhood topological properties and transition probability law of the edge in the graph. This can accurately realize graph topological defect detection and can be applied to performance improvement of graph representation learning.

[0083] After calculating the curvature of each edge, a topological defect judgment is performed (the judgment of defective topology refers to determining the defective edge based on the edge curvature). In a preferred embodiment of the present invention, a threshold judgment method is adopted, that is, a minimum threshold κ of the edge curvature is set, and for an edge with a curvature less than κ, the edge is judged to be a defective edge, and for an edge with a curvature greater than or equal to κ, the edge is judged to be a non-defective edge.

[0084] Of course, in some other embodiments, other judgment rules may also be used, such as selecting n edges with the lowest curvature as defective edges and the remaining edges as non-defective edges.

[0085] The graph network information measurement method of the above embodiment of the present invention can efficiently detect information over-compression caused by topological defects in the graph representation learning process, and is applicable to actual graph representation learning scenarios. It is also versatile and can be used in various message-passing graph neural networks.

[0086] The graph network information measurement method in the above embodiment of the present invention has extremely strong practical application value, especially in the graph representation learning method based on the graph message passing network in the actual graph representation learning application. In the actual graph message passing representation learning scenario, the graph node representation is transmitted on the network topology, and the existence of defective topology inevitably causes the node representation to be compressed and distorted in this process. In this actual application scenario, the current graph representation learning model based on the graph message passing network produces serious loss of expressive ability as the message transmission distance increases. In order to solve this problem, based on the same technical concept, the present invention further provides a robust graph representation learning method, based on the local topology defect degree measurement obtained by the graph network information measurement in the above embodiment, and further uses the following method to improve the topology and model structure, which can greatly improve the graph representation learning performance in such actual scenarios.

[0087] Specifically, Figure 3 Flow chart of a robust graph representation learning method according to an embodiment of the present invention. Figure 3 As shown, this embodiment provides a robust graph representation learning method, which specifically includes the following steps:

[0088] S400, modifying the network topology according to the edge curvature to obtain a new topology with stability; wherein the calculation of the edge curvature and the identification of defective edges can be performed using the graph network information measurement method described in S100-S300;

[0089] In this step, modifying the network topology refers to a method of appropriately changing the connections between nodes under the premise of fixing the network nodes, thereby increasing the curvature of the defective edge in the new topology. For example, in this embodiment, for any edge i~j determined as a defective edge according to S300, all neighbor nodes connecting i and j are added to obtain a new graph topology.

[0090] Of course, in some other implementations, the topology can also be modified by randomly adding connections in the neighborhood of two nodes of the defective edge, or deleting some edges with excessive curvature.

[0091] S500, respectively extracting the graph feature representations before and after the topology is modified, and integrating them to obtain the representation learning result.

[0092] Figure 4 A flowchart showing learning results obtained based on the graph topology before and after modification in one embodiment of the present invention.

[0093] Reference Figure 4 As shown, in this embodiment, the process of obtaining the graph representation learning result may include the following steps:

[0094] S510, initialize two graph neural networks with message passing network architecture (such as graph convolutional network GCN or graph attention network GIN, etc.) and

[0095] In this step, the two message passing networks should have the same number of network layers L and consistent weight parameter distribution. Mainly used for message passing on unedited topologies to obtain graph representations. Mainly used for message passing to obtain graph representation on the edited topology;

[0096] For each layer of the message passing network l=1…L, the following operations are performed layer by layer:

[0097] S520, using Message passing on the original topology to obtain the l-th layer hidden representation use Message passing on the modified topology obtains the lth layer hidden representation

[0098] In this step, the inputs used by the two networks to obtain the hidden representation are the same. If l = 1, the input is the node feature matrix X, and if l > 1, the input is the hidden representation output H of the previous layer. l ;

[0099] S530, sum the two implicit representations As the hidden representation output of this layer.

[0100] S540, output the representation of the last layer H L As a result of graph representation learning, the result can be used for graph data analysis.

[0101] The graph representation learning method provided in this embodiment uses a stable rewiring method to adjust the topology of the detected defective sub-topology, which can significantly improve the stability of the graph representation learning model based on the message passing network and ensure the feature expression capability.

[0102] Possible applications of graph data analysis in this embodiment include social network analysis, biological information prediction, etc. The robust graph representation learning method used in this embodiment can enhance the in-depth understanding and related research of relevant graph data.

[0103] Based on the same inventive concept, in other embodiments of the present invention, a graph data analysis method is provided, a robust graph representation learning method obtains a graph representation, and the graph representation is used for data analysis.

[0104] Figure 5 FIG. 1 is a flowchart of obtaining graph data and applying the robust graph representation learning method to graph data analysis in an embodiment of the present invention. Figure 5 As shown, in this embodiment, the process of using the robust graph representation learning method for graph data analysis may include the following steps:

[0105] If you analyze social network data, the following steps are involved:

[0106] S610, nodes represent different users, and edges represent the relationships between users.

[0107] S620: Represent the social network user interaction data as a graph structure.

[0108] S630, using the robust graph representation learning method in the above embodiment to obtain the node representation of each social network graph, and a clustering algorithm can be used to identify community structures or important nodes to implement graph data analysis.

[0109] If you analyze bioinformatics data, the following steps are involved:

[0110] S640, nodes represent different biomolecules, and edges represent the interactions between molecules.

[0111] S650, representing the interaction relationship between biomolecules as a graph structure.

[0112] S660, using the robust graph representation learning method in the above embodiment to obtain the node representation of each biomolecule graph, and using a community detection algorithm to identify key molecules or potential biological pathways to achieve graph data analysis.

[0113] In order to verify the feasibility and effectiveness of the graph network information measurement method in the above embodiment, in a specific embodiment, the graph network information measurement method in the above embodiment is used to measure the degree of over-compression in the graph representation learning process.

[0114] Specifically, the over-compression scenario in metric graph representation learning is described as follows: For any two nodes s,i in the graph, the representation h of the target node i is i For the feature x of the source node s s The first-order partial derivative mode length (called influence score) indicates the fidelity of the message transmission between the two nodes. If the influence score between the two nodes is too low during the actual message transmission representation learning process, it is considered that the message transmission between the two nodes is over-compressed. Using appropriate metrics to predict the size of the influence score during message transmission can be called measuring over-compression in graph representation learning.

[0115] In this application scenario:

[0116] First, generate a random graph topology of 20 to 100 nodes (generated by algorithms including watts_trogatz, powerlaw and gnp). For each graph topology, select all two-hop neighbor nodes as sample node pairs, and use a certain metric to predict the upper bound P of the influence score of each pair of nodes i. i , and then obtain the upper bound S of the actual impact score of the pair of samples through actual message transmission i ,by As the average prediction error of the entire image.

[0117] Implementation effect:

[0118] In the above embodiment, the graph network information measurement method provided by the embodiment of the present invention is used to measure the degree of compression in a random graph topology of 20 to 100 nodes. The results are as follows: Figure 6 As shown. Figure 6 As shown in (a), the metric method provided by the present invention can predict the influence score with a relative error of 30% to 100% and the error does not increase with the increase of the number of nodes. For comparison, Figure 6 As shown in (b), Topping et al. used the Balanced Forman Ricci Curvature as a metric, which has an error of at least 750%. Figure 6 As shown in (c), Nguyen et al. used the Ollivier Ricci Curvature as a metric, which has an error of at least 200%. Figure 6 As shown in (d), Black et al. use effective resistance as a metric, which has an error of at least 200%. In addition, except for the graph network information metric proposed by the present invention, the average errors of other metrics increase with the increase of the number of nodes.

[0119] Therefore, the present invention can achieve stable over-compression measurement on graph topologies with different numbers of nodes and different forms, and has extremely strong practical application value, especially in actual graph representation learning applications.

[0120] In another specific embodiment, the robust graph representation learning method in the above-mentioned embodiment of the present invention is used for graph data analysis applications.

[0121] Specifically, the scenario of graph data analysis is described as follows: social network user interaction data is represented as a graph structure. In each graph, nodes represent different users, and edges represent the relationship between users, such as friends, attention, or message exchanges. The graph representation learning method is used to obtain the node representation of each social network graph, and the community structure or important nodes are identified based on algorithms such as clustering, or the interaction relationship between biological molecules is represented as a graph structure. In each graph, nodes represent different biological molecules, and edges represent the interaction between molecules, such as binding or reaction. The graph representation learning method is used to obtain the node representation of each biological molecule graph, and key molecules or potential biological pathways are identified based on algorithms such as community detection. This scenario can be called "graph data analysis."

[0122] In this application scenario:

[0123] First, the method in the above embodiment is used to obtain a graph data analysis data set, and then a graph neural network classification model is used to classify the graph samples. The node features and structural information of the graph samples are input into the model, and the model predicts the category labels of the graph samples based on this information.

[0124] Implementation effect:

[0125] In the above embodiment, the graph representation learning method provided by the present invention and the graph representation learning method proposed in the papers of Nyugen et al. and Topping et al. are used to compare the classification accuracy of the graph representation learning method on the datasets based on 6 different graph classification datasets including chemical biology, social network, image and computer vision provided by TUDatasets. Table 1 shows the classification accuracy results. Compared with the papers of Nyugen and Topping et al., the present invention can obtain better classification results in most cases.

[0126] Table 1

[0127]

[0128] Therefore, the method of the embodiment of the present invention can achieve stable graph representation learning on different graphs collected in different scenarios, and has extremely strong practical application value, especially the graph representation learning method based on the graph message passing network in actual graph data analysis applications.

[0129] Based on the same inventive concept, in other embodiments of the present invention, a terminal is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor can be used to execute the above-mentioned method or to run the above-mentioned system when executing the program.

[0130] Optionally, the memory is used to store programs; the memory may include volatile memory (English: volatile memory), such as random-access memory (English: random-access memory, abbreviated: RAM), such as static random-access memory (English: static random-access memory, abbreviated: SRAM), double data rate synchronous dynamic random access memory (English: Double Data Rate Synchronous Dynamic Random Access Memory, abbreviated: DDR SDRAM), etc.; the memory may also include non-volatile memory (English: non-volatile memory), such as flash memory (English: flash memory). The memory is used to store computer programs (such as applications, functional modules, etc. that implement the above method), computer instructions, etc., and the above-mentioned computer programs, computer instructions, etc. can be partitioned and stored in one or more memories.

[0131] The processor is used to execute the computer program stored in the memory to implement the various steps in the method involved in the above embodiment. For details, please refer to the relevant description in the above method embodiment.

[0132] The processor and the memory may be independent structures or integrated structures. When the processor and the memory are independent structures, the memory and the processor may be coupled and connected via a bus.

[0133] Based on the same inventive concept, in other embodiments of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, it can be used to execute the above method, or run the above system.

[0134] Among them, computer-readable media include computer storage media and communication media, wherein the communication media include any media that facilitates the transmission of computer programs from one place to another. The storage medium can be any available medium that can be accessed by a general or special-purpose computer. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and the storage medium can be located in an ASIC. In addition, the ASIC can be located in a user device. Of course, the processor and the storage medium can also be present in a communication device as discrete components.

[0135] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0137] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0138] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0139] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A graph network information measurement method, characterized in that: Including: Obtain the adjacency matrix of the graph network topology; Calculate the edge curvature of the graph network topology based on the adjacency matrix; Use the edge curvature as a graph network information metric, and determine whether there are topological defects in the relevant sub-topology according to the network information metric theory.

2. The graph network information measurement method according to claim 1, characterized in that: The calculating the edge curvature of the graph network topology based on the adjacency matrix includes: If the graph network structure contains transition probability information, the transition probability information is organized into a transition probability matrix P, that is, any element P of the matrix ij represents the transition probability p from node i to node j ij ; Otherwise, the transition probability matrix of the graph network topology is calculated by normalizing the degree of the nodes of the graph network topology, that is, for any pair of adjacent edges i, j, where d i represents the degree of node i; Repeat the following steps for each edge in the graph network topology: Calculate the adjacent triangle transition probability and the adjacent 4-cycle transition probability of the edge based on the transition probability matrix and the adjacency matrix; Calculate the number of adjacent triangle transition paths and the number of adjacent 4-cycle transition paths of the edge based on the adjacency matrix; Determine the message gain: If the parameter matrix of the graph representation learning model is known, calculate the 1-norm of the model parameter matrix as an estimate of the message gain, otherwise replace the message gain with a constant; Perform a polynomial combination of the adjacent triangle transition probability, the adjacent 4-cycle transition probability, the number of adjacent triangle transition paths, the number of adjacent 4-cycle transition paths, the message gain, and the degree of the node to obtain the edge curvature.

3. The graph network information measurement method according to claim 1, characterized in that: The topological defects include the over-compression phenomenon of the graph, which is expressed as follows: for any edge s~i in the graph, s,i represents its two end nodes, and the target node i represents h i For the feature x of the source node s s The first-order partial derivative mode length The network information measurement theory refers to: using edge curvature to measure the noise from the defect graph topology during the learning process, the edge curvature and the expected upper bound of noise resistance have a probability approximation relationship; wherein, the noise refers to the noise caused by the characteristic representation of the neighboring nodes on the target path information transmission path squeezing the target information, and the noise resistance is the representation h of the target node i. i For the feature x of the source node s s The first-order partial derivative mode length measure.

4. The graph network information measurement method according to claim 1, characterized in that: The using the edge curvature as a graph network information metric and determining whether there are topological defects in the relevant sub-topology according to the network information metric theory includes: Set the lowest threshold κ of the edge curvature; For each edge in the graph network topology, make a judgment: For an edge with an edge curvature less than κ, determine that the edge is a defective edge; For an edge with an edge curvature greater than or equal to κ, determine that the edge is a non-defective edge.

5. A robust graph representation learning method, characterized in that: Including: Adopt the graph network information metric method described in any one of claims 1-4 to obtain the defective edges of the graph network topology; Modify the defective edges of the graph network topology to obtain a new topology with stability; Extract the feature representations of the modified graph network topology and the pre-modified graph network topology, and integrate them to obtain a graph representation.

6. The robust graph representation learning method according to claim 5, characterized in that The modifying the defective edges of the graph network topology to obtain a new topology with stability includes: For each defective edge, connect all the nodes within the 1-neighborhood of one adjacent node i and another adjacent node j of the defective edge; Or: Randomly add connections in the neighborhoods of the two nodes of the defective edge; Or: Delete the edges with curvatures exceeding the set value.

7. The robust graph representation learning method according to claim 5, characterized in that The extracting the feature representations of the modified graph network topology and the pre-modified graph network topology and integrating them to obtain a graph representation includes: Initialize two graph neural networks with a message passing network architecture and The two message passing network architectures have the same number of layers L and the same weight parameter distribution; For each layer of message passing network l = 1…L, repeat the following operations: use Get the lth layer hidden representation of the original topology use Get the lth layer hidden representation of the new topology Using the sum of the two implicit representations As the hidden representation output of this layer; If l < L, the output is used as the common input for the next layer of the two message passing networks; If l = L, then H L is the final output of the message passing network, represented as a graph.

8. A graph data analysis method, characterized in that: Including: If the graph data to be analyzed is social network user interaction data, in each graph network topology, nodes represent different users, and edges represent the relationships between users; adopt the robust graph representation learning method described in any one of claims 5-7 to obtain the graph representation of each social network graph, and identify community structures or important nodes from the graph representation for determining user behavior patterns and network propagation characteristics; If the graph data to be analyzed is a biological molecule, in each graph, the nodes represent different biological molecules, and the edges represent the interactions between molecules; the robust graph representation learning method described in any one of claims 5-7 is used to obtain the graph representation of each biological molecule graph, identify key molecules or potential biological pathways from the graph representation, and determine the function and impact of the molecule.

9. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it can be used to execute the graph network information measurement method described in any one of claims 1-4, or the graph representation learning method described in any one of claims 5-7, or the graph data analysis method described in claim 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, it can be used to execute the graph network information measurement method described in any one of claims 1-4, or the graph representation learning method described in any one of claims 5-7, or the graph data analysis method described in claim 8.

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