Link prediction method and device, computer equipment, storage medium and product

Abstract

The invention relates to a link prediction method and device, computer equipment, a storage medium and a product. The method comprises the following steps: acquiring target feature information of each network node in a network structure chart of a target power system in a current time period; wherein the target feature information of each network node comprises node attribute information and link connection information of the network node; determining link connection information of each network node in a future time period according to the target feature information of each network node based on a network link prediction model; wherein the network link prediction model is obtained by training a dual-order graph attention auto-encoder according to historical feature information of each network node in a reference time period and link connection information between the network nodes in a comparison time period; wherein the comparison time period is a time period after the reference time period. By adopting the method, the accuracy of the predicted link connection information can be ensured.

Description

Technical Field

[0001] The present application relates to the field of smart grid technology, and in particular to a link prediction method, device, computer equipment, storage medium and product. Background Art

[0002] Link prediction in power systems involves estimating the probability of forming a connection between two nodes in a network structure. It can improve grid management, cloud computing resource scheduling, and complete knowledge graphs in smart grids. In smart grid research, link prediction is particularly important because it affects the allocation and scheduling of resources within the power system.

[0003] Traditional link prediction methods can be divided into three categories: heuristic methods, latent feature methods, and content-based methods. Heuristic methods calculate node similarity scores based on some heuristic rules. Latent feature methods involve decomposing the matrix representation of the network to learn low-dimensional node embeddings. However, during the encoding process, feature extraction based solely on the adjacency matrix faces the difficulty of capturing node features affected by diverse neighborhood factors, both locally and globally, which in turn reduces the efficiency of the link prediction process and the accuracy of the link prediction results of the power system. Summary of the invention

[0004] Based on this, it is necessary to provide a link prediction method, device, computer equipment, storage medium and product to address the above technical problems, which can improve the efficiency of the link prediction process of the power system and the accuracy of the link prediction results.

[0005] In a first aspect, the present application provides a link prediction method, comprising:

[0006] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0007] Based on the network link prediction model, according to the target feature information of each of the network nodes, determining the link connection information of each of the network nodes in a future period;

[0008] The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

[0009] In one of the embodiments, the network link prediction model includes an attention network and an encoding network;

[0010] The determining, based on the network link prediction model and according to the target feature information of each of the network nodes, the link connection information of each of the network nodes in a future period includes:

[0011] Based on the attention network, determining the attention feature between two adjacent network nodes according to the link connection information of each network node in the current time period;

[0012] Based on the coding network, the link connection information of each of the network nodes in the future time period is determined according to the node attribute information of each of the network nodes in the current time period and the attention characteristics between two adjacent network nodes.

[0013] In one embodiment, determining the attention feature between two adjacent network nodes according to the link connection information of each network node in the current time period includes:

[0014] Determining correlation information between the two adjacent network nodes according to link connection information of each of the network nodes in the current time period;

[0015] For any two adjacent network nodes, determining a common neighbor node between the two adjacent network nodes according to correlation information between the two adjacent network nodes;

[0016] Based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

[0017] In one embodiment, the determining the attention feature between the two adjacent network nodes based on the cosine similarity function according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes includes:

[0018] Determining a common neighbor value between the two adjacent network nodes according to the node feature information of the common neighbor node;

[0019] Determining a neighbor feature between the two adjacent network nodes according to the common neighbor value and correlation information between the two adjacent network nodes;

[0020] Based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the neighbor feature between the two adjacent network nodes.

[0021] In one embodiment, the determining the attention feature between the two adjacent network nodes based on the neighbor feature between the two adjacent network nodes based on the cosine similarity function includes:

[0022] Based on the cosine similarity function, according to the neighbor characteristics between the two adjacent network nodes, determining the cosine similarity between the two adjacent network nodes;

[0023] Based on a preset exponential function, determining an attention coefficient between the two adjacent network nodes according to the cosine similarity between the two adjacent network nodes;

[0024] Based on the activation function, the attention feature between the two adjacent network nodes is determined according to the attention coefficient between the two adjacent network nodes.

[0025] In one embodiment, the network link prediction model is constructed in the following manner:

[0026] Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system during a reference period, and link connection information between each network node in the network structure diagram of the target power system during a comparison period;

[0027] Constructing an adjacency matrix of the network structure graph according to the historical feature information;

[0028] Inputting the historical feature information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram;

[0029] Based on the cosine similarity function, a first loss function is constructed according to the predicted connection information between the network nodes in the network structure diagram and the mean square error between the link connection information between the network nodes in the network structure diagram in the sample data;

[0030] Based on a preset logarithmic function and according to the adjacency matrix, construct a second loss function;

[0031] Constructing a target loss function according to the sum of the first loss function and the second loss function;

[0032] The target loss function is used to train the initial network link prediction model to obtain the network link prediction model.

[0033] In a second aspect, the present application also provides a link prediction device, including:

[0034] An information acquisition module, used to acquire target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0035] A link prediction module, used to determine the link connection information of each of the network nodes in a future period based on the network link prediction model and the target feature information of each of the network nodes;

[0036] The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

[0037] In a third aspect, the present application further provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0038] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0039] Based on the network link prediction model, according to the target feature information of each of the network nodes, determining the link connection information of each of the network nodes in a future period;

[0040] The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

[0041] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the following steps are implemented:

[0042] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0043] Based on the network link prediction model, according to the target feature information of each of the network nodes, determining the link connection information of each of the network nodes in a future period;

[0044] The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

[0045] In a fifth aspect, the present application further provides a computer program product, including a computer program, which implements the following steps when executed by a processor:

[0046] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0047] Based on the network link prediction model, according to the target feature information of each of the network nodes, determining the link connection information of each of the network nodes in a future period;

[0048] The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

[0049] The link prediction method, device, computer equipment, storage medium and product obtain the target feature information of each network node in the network structure diagram of the target power system in the current period; wherein the target feature information of each network node includes the node attribute information and link connection information of the network node; based on the network link prediction model, according to the target feature information of each network node, the link connection information of each network node in the future period is determined; wherein the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; wherein the comparison period is the period after the reference period. The above scheme, by introducing the dual-order graph attention autoencoder, utilizes the applicability of the dual-order graph attention autoencoder, and trains the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period, comprehensively considers the link connection information between each network node, ensures the accuracy of the obtained network link prediction model, and further ensures the accuracy of the predicted link connection information. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the related technologies, the drawings required for use in the embodiments or the related technical descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0051] Figure 1 A schematic diagram of a link prediction method in an embodiment;

[0052] Figure 2 A schematic diagram of a process for determining link connection information in an embodiment;

[0053] Figure 3 A schematic diagram of a process for determining attention features in one embodiment;

[0054] Figure 4 A schematic diagram of a flow chart for determining attention features in another embodiment;

[0055] Figure 5 A schematic diagram of a process for determining attention features in yet another embodiment;

[0056] Figure 6 A schematic diagram of a process for training a network link prediction model in one embodiment;

[0057] Figure 7 is a flow chart of a link prediction method in another embodiment;

[0058] Figure 8 is a structural block diagram of a link prediction device in one embodiment;

[0059] Fig. 9 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0061] The link prediction method provided in the embodiment of the present application can be applied in an application environment for predicting the network structure of a power system. The link prediction method provided in the embodiment of the present application can be executed by a computer device, which can be a server or a terminal with powerful computing capabilities.

[0062] In one embodiment, Figure 2 As shown, a link prediction method is provided, which is described by taking the method applied to a server as an example, and specifically includes the following steps:

[0063] S101, obtaining target characteristic information of each network node in a network structure diagram of a target power system in a current period.

[0064] The target characteristic information of each network node includes node attribute information and link connection information of the network node. The link connection information of each network node represents the link relationship between the network node and other network nodes.

[0065] Optionally, the node attribute information and link connection information of each network node in the network structure diagram of the target power system in the current period can be obtained from the management system of the target power system as the target characteristic information of each network node in the current period.

[0066] S102, based on the network link prediction model and according to the target feature information of each network node, determining the link connection information of each network node in the future period.

[0067] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; the comparison period is the period after the reference period.

[0068] The network link prediction model includes an attention network and an encoding network. The attention network is a network used to extract the attention features of each network node and its corresponding adjacent nodes from the target feature information of each network node; in the embodiment of the present application, the attention network can be used as an attention module and embedded in the network link prediction model based on a dual-order graph attention autoencoder; the encoding network can be constructed by a graph convolutional network.

[0069] Optionally, the target feature information of each network node can be input into the network link prediction model, so that the attention network and encoding network in the network link prediction model calculate the target feature information of each network node, and use the output results of the network link prediction model as the link connection information of each network node in the future time period.

[0070] In the above link prediction method, the target feature information of each network node in the network structure diagram of the target power system in the current period is obtained; wherein, the target feature information of each network node includes the node attribute information and link connection information of the network node; based on the network link prediction model, the link connection information of each network node in the future period is determined according to the target feature information of each network node; wherein, the network link prediction model is obtained by training the double-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; wherein, the comparison period is the period after the reference period. The above scheme, by introducing the double-order graph attention autoencoder, utilizes the applicability of the double-order graph attention autoencoder, and trains the double-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period, comprehensively considers the link connection information between each network node, ensures the accuracy of the obtained network link prediction model, and further ensures the accuracy of the predicted link connection information.

[0071] Optionally, in one embodiment, Figure 2 As shown, a method for determining link connection information of a network node is provided, which specifically includes the following steps:

[0072] S201, based on the attention network, determine the attention features between two adjacent network nodes according to the link connection information of each network node in the current time period.

[0073] Among them, two adjacent network nodes refer to two network nodes that have a connection relationship in the network structure diagram. The attention feature between two adjacent network nodes refers to the importance feature between two adjacent network nodes.

[0074] Optionally, the link connection information of each network node in the current time period can be input into the attention network, so that the attention network can calculate and analyze the link connection information of each network node in the current time period according to the network parameters, and use the output result of the attention network as the attention feature between two adjacent network nodes.

[0075] S202, based on the coding network, according to the node attribute information of each network node in the current time period, and the attention characteristics between two adjacent network nodes, determine the link connection information of each network node in the future time period.

[0076] Optionally, the node attribute information of each network node in the current time period and the attention features between two adjacent network nodes can be input into the coding network, so that the coding network calculates the node attribute information of each network node in the current time period and the attention features between two adjacent network nodes according to the network parameters, and uses the output result of the coding network as the link connection information of each network node in the future time period.

[0077] In this embodiment, by introducing the attention network and the encoding network, the target feature information of each network node is combined with the encoding process, ensuring the accuracy of the link connection information of each network node in the determined future time period and the efficiency of the determination process.

[0078] Optionally, in one embodiment, Figure 3 As shown, a method for determining the attention feature between two adjacent network nodes is provided, which specifically includes the following steps:

[0079] S301, determining correlation information between two adjacent network nodes according to link connection information of each network node in a current period.

[0080] Among them, the correlation information between two adjacent network nodes represents the mutual relationship and degree of dependence between the two adjacent network nodes.

[0081] Optionally, the Pearson product-moment correlation coefficient between two adjacent network nodes may be calculated based on the link connection information of each network node in the current period to characterize the correlation between the two adjacent network nodes and constitute correlation information.

[0082] S302: For any two adjacent network nodes, determine a common neighbor node between the two adjacent network nodes according to correlation information between the two adjacent network nodes.

[0083] The common neighbor node between two adjacent network nodes is a node that has a connection relationship with both adjacent network nodes.

[0084] Optionally, for any two adjacent network nodes, a basic graph analysis algorithm may be used to calculate all common neighbor network nodes between the two adjacent network nodes according to correlation information between the two adjacent network nodes, as common neighbor nodes.

[0085] S303, based on the cosine similarity function, according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes, determine the attention feature between the two adjacent network nodes.

[0086] In this embodiment, by introducing the correlation information and common neighbors between two adjacent network nodes, it is equivalent to comprehensively considering the common neighbor nodes of the two adjacent network nodes, further ensuring the accuracy of the determined attention features between the two adjacent network nodes.

[0087] Optionally, in one embodiment, Figure 4 As shown, a method for determining the attention feature between two adjacent network nodes is provided, which specifically includes the following steps:

[0088] S401, determining a common neighbor value between two adjacent network nodes according to node feature information of a common neighbor node.

[0089] Among them, the common neighbor value between two adjacent network nodes is an indicator used to measure the similarity or correlation between two adjacent network nodes in the graph.

[0090] Optionally, the common neighbor value between two adjacent network nodes may be calculated based on the node feature information of the common neighbor nodes and in combination with the number of the common neighbor nodes.

[0091] S402: Determine a neighbor feature between two adjacent network nodes according to a common neighbor value and correlation information between the two adjacent network nodes.

[0092] The neighbor features between two adjacent network nodes represent the features of the common neighbor nodes between the two adjacent network nodes.

[0093] Optionally, a two-order attention network can be introduced. According to the common neighbor value and correlation information between two adjacent network nodes, the process of determining the neighbor features between two adjacent network nodes can be expressed by the following formula (1):

[0094] (1)

[0095] Among them, the subscript It is Quantity, and are two vectors determined according to the common neighbor value and correlation information between two adjacent network nodes.

[0096] S403, based on the cosine similarity function and according to the neighbor features between the two adjacent network nodes, determining the attention features between the two adjacent network nodes.

[0097] Optionally, the definition of the cosine similarity function can be expressed by the following formula:

[0098] (2)

[0099] in, and are learnable weights, It is The eigenvector of It is The feature vector of It is the measure of attention; It is a multi-layer perceptron consisting of a single layer, using the Sigmoid activation function to avoid the vanishing gradient of the cosine similarity function.

[0100] Furthermore, based on the cosine similarity function defined above, according to a preset calculation procedure, the attention feature between two adjacent network nodes is automatically determined according to the neighbor feature between the two adjacent network nodes.

[0101] In this embodiment, by introducing the common neighbor value, neighbor features and cosine similarity function between two adjacent network nodes, the similarity between two adjacent network nodes is calculated from different dimensions, thereby ensuring the accuracy of the attention features determined between two adjacent network nodes.

[0102] Optionally, in one embodiment, Figure 5 As shown, a method for determining the attention feature between two adjacent network nodes is provided to refine S403, specifically comprising the following steps:

[0103] S501 , based on a cosine similarity function and according to neighbor features between two adjacent network nodes, determining the cosine similarity between two adjacent network nodes.

[0104] Among them, the cosine similarity between two adjacent network nodes is used to measure the similarity between two adjacent network nodes, which is generally between 0 and 1.

[0105] Optionally, based on the expression of the cosine similarity function defined in formula (2) in the above embodiment, the neighbor features between two adjacent network nodes are introduced to obtain the cosine similarity between two adjacent network nodes.

[0106] S502, based on a preset exponential function, according to the cosine similarity between the two adjacent network nodes, determine the attention coefficient between the two adjacent network nodes.

[0107] Among them, the attention coefficient between two adjacent network nodes is used to measure the weight coefficient of the importance of different information contained in the two adjacent network nodes.

[0108] Optionally, based on a preset exponential function, according to the cosine similarity between two adjacent network nodes, the process of determining the attention coefficient between two adjacent network nodes can be expressed by the following formula (3):

[0109] (3)

[0110] in, Is a node and The attention coefficient between .

[0111] S503, based on the activation function and according to the attention coefficient between the two adjacent network nodes, determining the attention feature between the two adjacent network nodes.

[0112] Optionally, based on the activation function, according to the attention coefficient between two adjacent network nodes, the process of determining the attention feature between two adjacent network nodes can be expressed by the following formula (4):

[0113] (4)

[0114] in, is the attention feature between two adjacent network nodes; is the weight.

[0115] It should be noted that based on the above formula (4), the attention module can be constructed as:

[0116] (5)

[0117] It should be noted that when calculating the neighborhood on a small scale After the attention features are obtained, in the embodiment of the present application, the attention features of the two-order neighbors are calculated. Specifically, the embodiment of the present application considers two different orders: 1st order and 2nd order, where 2nd order is the 2nd order neighbor of the current node. The two-order feature embedding can be expressed by formula (6):

[0118] (6)

[0119] in, is the second-order weight.

[0120] In this embodiment, by introducing the cosine similarity and attention coefficient between two adjacent network nodes, a method for quickly and accurately calculating the attention features between two adjacent network nodes is provided.

[0121] Optionally, in one embodiment, Figure 6 As shown, a training method for a network link prediction model is provided, which specifically includes the following steps:

[0122] S601, obtaining sample data.

[0123] Among them, the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system in a reference period, and link connection information between each network node in the network structure diagram of the target power system in a comparison period, and the comparison period is the period after the reference period.

[0124] S602: construct an adjacency matrix of the network structure graph according to the historical feature information.

[0125] Among them, the adjacency matrix represents the matrix of adjacent relationships between network nodes in the network structure graph.

[0126] Optionally, the number of network nodes and the number of links in the network structure diagram can be determined based on the link connection information between each network node in the network structure diagram in the historical feature information. Furthermore, according to the adjacency matrix construction rules, the adjacency matrix of the network structure diagram is constructed according to the number of network nodes and the number of links in the network structure diagram and the link connection relationship between each network node.

[0127] S603, inputting the historical feature information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram.

[0128] Among them, the initial network link prediction model is an untrained neural network model constructed based on a two-order graph attention autoencoder; the predicted connection information is the link connection information of each network node in the comparison period predicted by the initial network link prediction model.

[0129] Optionally, the historical feature information in the sample data may be input into an initial network link prediction model, and the output of the initial network link prediction model may be used as the predicted connection information between the network nodes in the network structure diagram.

[0130] S604, constructing a first loss function based on the cosine similarity function and the predicted connection information between the network nodes in the network structure diagram and the mean square error between the link connection information between the network nodes in the network structure diagram in the sample data.

[0131] The cosine similarity function is a function used to measure the similarity between two vectors. The first loss function is a function that characterizes the distance between node similarity and the corresponding node edge, and the learned node features are constrained by minimizing this distance.

[0132] Optionally, the heuristic information (i.e., the common neighbor information between two adjacent network nodes) and the node feature information of the two-order embedding can be integrated to construct a first loss function, and the first loss function can be expressed in the form of a mean square error. Specifically, based on the cosine similarity function, according to the predicted connection information between each network node in the network structure diagram, and the mean square error between the link connection information between each network node in the network structure diagram in the sample data, the process of constructing the first loss function can be expressed by the following formula (7):

[0133] (7)

[0134] in, represents the cosine similarity function; and They represent the embedded features of network nodes and the actual node features, respectively, which can be determined based on the predicted connection information. It is heuristic information and can be determined based on the link connection information between each network node.

[0135] S605: Based on a preset logarithmic function and the adjacency matrix, a second loss function is constructed.

[0136] Among them, the second loss function represents the loss of link prediction.

[0137] Optionally, based on a preset logarithmic function and according to the adjacency matrix, the process of constructing the second loss function can be expressed by the following formula (8):

[0138] (8)

[0139] (9)

[0140] in, is the adjacency matrix, the positive edge ( ) is weighted as ,in, is the negative side ( ) to the positive edges. The purpose of this is to balance the contribution of positive and negative edges to the loss. Otherwise, due to the sparsity of actual networks, the loss may be dominated by negative edges. To predict the link ( ) probability. It is the node representation (embedding) matrix output by the network link prediction model on the node feature matrix of the network structure graph. No. Rows are network nodes Representation ; is the sigmoid function.

[0141] S606: construct a target loss function according to the sum of the first loss function and the second loss function.

[0142] Optionally, the process of constructing the target loss function according to the sum of the first loss function and the second loss function can be expressed by the following formula (10):

[0143] (10)

[0144] S607, using the target loss function to train the initial network link prediction model to obtain the network link prediction model.

[0145] In this embodiment, by introducing the first loss function and the second loss function, the accuracy and comprehensiveness of the constructed target loss function are guaranteed, and the accuracy of the network link prediction model trained by using the target loss function is further guaranteed.

[0146] Figure 7 FIG. 2 is a flow chart of a link prediction method in another embodiment. Based on the above embodiment, this embodiment provides an optional example of a link prediction method. Figure 7 The specific implementation process is as follows:

[0147] S701, obtaining link connection information and node attribute information of each network node in the network structure diagram of the target power system in the current period.

[0148] The target characteristic information of each network node includes node attribute information and link connection information of the network node.

[0149] S702, based on the attention network in the network link prediction model, according to the link connection information of each network node in the current time period, determine the correlation information between two adjacent network nodes.

[0150] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; among them, the comparison period is the period after the reference period.

[0151] S703, based on the attention network, for any two adjacent network nodes, according to the correlation information between the two adjacent network nodes, determine the common neighbor nodes between the two adjacent network nodes.

[0152] S704, based on the attention network, determine the common neighbor value between two adjacent network nodes according to the node feature information of the common neighbor node.

[0153] S705, based on the attention network, determine the neighbor features between two adjacent network nodes according to the common neighbor value and correlation information between the two adjacent network nodes.

[0154] S706, based on the attention network and the cosine similarity function, determine the attention feature between two adjacent network nodes according to the neighbor feature between the two adjacent network nodes.

[0155] Optionally, based on the cosine similarity function, the cosine similarity between two adjacent network nodes is determined according to the neighbor characteristics between the two adjacent network nodes; based on a preset exponential function, the attention coefficient between two adjacent network nodes is determined according to the cosine similarity between two adjacent network nodes; based on the activation function, the attention characteristics between two adjacent network nodes are determined according to the attention coefficient between two adjacent network nodes.

[0156] S707, based on the coding network in the network link prediction model, according to the node attribute information of each network node in the current time period, and the attention characteristics between two adjacent network nodes, determine the link connection information of each network node in the future time period.

[0157] The specific process of the above S701-S707 can be found in the description of the above method embodiment. The implementation principle and technical effect are similar and will not be repeated here.

[0158] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0159] Based on the same inventive concept, the embodiment of the present application also provides a link prediction device for implementing the link prediction method involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in one or more link prediction device embodiments provided below can refer to the limitations on the link prediction method above, and will not be repeated here.

[0160] In one embodiment, Figure 8 As shown, a link prediction device 800 is provided, including: an information acquisition module 810 and a link prediction module 820, wherein:

[0161] The information acquisition module 810 is used to obtain the target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes the node attribute information and link connection information of the network node.

[0162] The link prediction module 820 is used to determine the link connection information of each network node in the future period based on the network link prediction model and the target feature information of each network node;

[0163] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; among them, the comparison period is the period after the reference period.

[0164] The link prediction device obtains the target feature information of each network node in the network structure diagram of the target power system in the current period; wherein the target feature information of each network node includes the node attribute information and link connection information of the network node; based on the network link prediction model, according to the target feature information of each network node, the link connection information of each network node in the future period is determined; wherein the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; wherein the comparison period is the period after the reference period. The above scheme, by introducing the dual-order graph attention autoencoder, utilizes the applicability of the dual-order graph attention autoencoder, and trains the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period, comprehensively considers the link connection information between each network node, ensures the accuracy of the obtained network link prediction model, and further ensures the accuracy of the predicted link connection information.

[0165] In one embodiment, the network link prediction model includes an attention network and an encoding network; the link prediction module 820 includes:

[0166] The first prediction unit is used to determine the attention features between two adjacent network nodes based on the attention network and according to the link connection information of each network node in the current time period.

[0167] The second prediction unit is used to determine the link connection information of each network node in the future time period based on the coding network, according to the node attribute information of each network node in the current time period, and the attention characteristics between two adjacent network nodes.

[0168] In one embodiment, the first prediction unit includes:

[0169] The information determination subunit is used to determine the correlation information between two adjacent network nodes according to the link connection information of each network node in the current period.

[0170] The node determination subunit is used to determine, for any two adjacent network nodes, the common neighbor node between the two adjacent network nodes according to the correlation information between the two adjacent network nodes.

[0171] The feature determination subunit is used to determine the attention feature between two adjacent network nodes based on the cosine similarity function, according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

[0172] In one embodiment, the feature determination subunit comprises:

[0173] The first determining slave unit is used to determine the common neighbor value between two adjacent network nodes according to the node characteristic information of the common neighbor node.

[0174] The second determining slave unit is used to determine the neighbor characteristics between two adjacent network nodes according to the common neighbor value and correlation information between the two adjacent network nodes.

[0175] The feature determination slave unit is used to determine the attention feature between two adjacent network nodes based on the neighbor features between the two adjacent network nodes based on the cosine similarity function.

[0176] In one embodiment, the feature determination slave unit is specifically configured to:

[0177] Based on the cosine similarity function, the cosine similarity between two adjacent network nodes is determined according to the neighbor characteristics between the two adjacent network nodes; based on the preset exponential function, the attention coefficient between the two adjacent network nodes is determined according to the cosine similarity between the two adjacent network nodes; based on the activation function, the attention characteristics between the two adjacent network nodes are determined according to the attention coefficient between the two adjacent network nodes.

[0178] In one embodiment, the link prediction device 800 is further configured to:

[0179] Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system in a reference period, and link connection information between each network node in the network structure diagram of the target power system in a comparison period; construct an adjacency matrix of the network structure diagram based on the historical characteristic information; input the historical characteristic information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram; based on the cosine similarity function, construct a first loss function according to the predicted connection information between each network node in the network structure diagram and the mean square error between the link connection information between each network node in the network structure diagram in the sample data; based on the preset logarithmic function, construct a second loss function according to the adjacency matrix; construct a target loss function according to the sum of the first loss function and the second loss function; use the target loss function to train the initial network link prediction model to obtain the network link prediction model.

[0180] Each module in the above-mentioned link prediction device can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0181] In an exemplary embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in FIG. Fig. 9 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a link prediction method is implemented.

[0182] Those skilled in the art will understand that Fig. 9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0183] In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented:

[0184] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0185] Based on the network link prediction model, the link connection information of each network node in the future period is determined according to the target feature information of each network node;

[0186] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; among them, the comparison period is the period after the reference period.

[0187] In one embodiment, the network link prediction model includes an attention network and an encoding network; when the processor executes the computer program to determine the link connection information of each network node in the future time period based on the network link prediction model and the target feature information of each network node, the following steps are also implemented:

[0188] Based on the attention network, the attention features between two adjacent network nodes are determined according to the link connection information of each network node in the current time period; based on the encoding network, the link connection information of each network node in the future time period is determined according to the node attribute information of each network node in the current time period and the attention features between two adjacent network nodes.

[0189] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes according to the link connection information of each network node in the current period, the processor further implements the following steps:

[0190] According to the link connection information of each network node in the current time period, the correlation information between two adjacent network nodes is determined; for any two adjacent network nodes, the common neighbor node between the two adjacent network nodes is determined according to the correlation information between the two adjacent network nodes; based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

[0191] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes, the following steps are also implemented:

[0192] According to the node feature information of the common neighbor nodes, the common neighbor value between two adjacent network nodes is determined; according to the common neighbor value and correlation information between two adjacent network nodes, the neighbor features between two adjacent network nodes are determined; based on the cosine similarity function, according to the neighbor features between two adjacent network nodes, the attention features between two adjacent network nodes are determined.

[0193] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function and the neighbor feature between the two adjacent network nodes, the processor further implements the following steps:

[0194] Based on the cosine similarity function, the cosine similarity between two adjacent network nodes is determined according to the neighbor characteristics between the two adjacent network nodes; based on the preset exponential function, the attention coefficient between the two adjacent network nodes is determined according to the cosine similarity between the two adjacent network nodes; based on the activation function, the attention characteristics between the two adjacent network nodes are determined according to the attention coefficient between the two adjacent network nodes.

[0195] In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

[0196] Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system in a reference period, and link connection information between each network node in the network structure diagram of the target power system in a comparison period; construct an adjacency matrix of the network structure diagram based on the historical characteristic information; input the historical characteristic information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram; based on the cosine similarity function, construct a first loss function according to the predicted connection information between each network node in the network structure diagram and the mean square error between the link connection information between each network node in the network structure diagram in the sample data; based on the preset logarithmic function, construct a second loss function according to the adjacency matrix; construct a target loss function according to the sum of the first loss function and the second loss function; use the target loss function to train the initial network link prediction model to obtain the network link prediction model.

[0197] In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

[0198] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0199] Based on the network link prediction model, the link connection information of each network node in the future period is determined according to the target feature information of each network node;

[0200] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; among them, the comparison period is the period after the reference period.

[0201] In one embodiment, the network link prediction model includes an attention network and an encoding network; when the processor executes the computer program to determine the link connection information of each network node in the future time period based on the network link prediction model and the target feature information of each network node, the following steps are also implemented:

[0202] Based on the attention network, the attention features between two adjacent network nodes are determined according to the link connection information of each network node in the current time period; based on the encoding network, the link connection information of each network node in the future time period is determined according to the node attribute information of each network node in the current time period and the attention features between two adjacent network nodes.

[0203] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes according to the link connection information of each network node in the current period, the processor further implements the following steps:

[0204] According to the link connection information of each network node in the current time period, the correlation information between two adjacent network nodes is determined; for any two adjacent network nodes, the common neighbor node between the two adjacent network nodes is determined according to the correlation information between the two adjacent network nodes; based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

[0205] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes, the following steps are also implemented:

[0206] According to the node feature information of the common neighbor nodes, the common neighbor value between two adjacent network nodes is determined; according to the common neighbor value and correlation information between two adjacent network nodes, the neighbor features between two adjacent network nodes are determined; based on the cosine similarity function, according to the neighbor features between two adjacent network nodes, the attention features between two adjacent network nodes are determined.

[0207] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function and the neighbor feature between the two adjacent network nodes, the processor further implements the following steps:

[0208] Based on the cosine similarity function, the cosine similarity between two adjacent network nodes is determined according to the neighbor characteristics between the two adjacent network nodes; based on the preset exponential function, the attention coefficient between the two adjacent network nodes is determined according to the cosine similarity between the two adjacent network nodes; based on the activation function, the attention characteristics between the two adjacent network nodes are determined according to the attention coefficient between the two adjacent network nodes.

[0209] In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

[0210] Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system in a reference period, and link connection information between each network node in the network structure diagram of the target power system in a comparison period; construct an adjacency matrix of the network structure diagram based on the historical characteristic information; input the historical characteristic information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram; based on the cosine similarity function, construct a first loss function according to the predicted connection information between each network node in the network structure diagram and the mean square error between the link connection information between each network node in the network structure diagram in the sample data; based on the preset logarithmic function, construct a second loss function according to the adjacency matrix; construct a target loss function according to the sum of the first loss function and the second loss function; use the target loss function to train the initial network link prediction model to obtain the network link prediction model.

[0211] In one embodiment, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the following steps:

[0212] Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node;

[0213] Based on the network link prediction model, the link connection information of each network node in the future period is determined according to the target feature information of each network node;

[0214] Among them, the network link prediction model is obtained by training the dual-order graph attention autoencoder according to the historical feature information of each network node in the reference period and the link connection information between each network node in the comparison period; among them, the comparison period is the period after the reference period.

[0215] In one embodiment, the network link prediction model includes an attention network and an encoding network; when the processor executes the computer program to determine the link connection information of each network node in the future time period based on the network link prediction model and the target feature information of each network node, the following steps are also implemented:

[0216] Based on the attention network, the attention features between two adjacent network nodes are determined according to the link connection information of each network node in the current time period; based on the encoding network, the link connection information of each network node in the future time period is determined according to the node attribute information of each network node in the current time period and the attention features between two adjacent network nodes.

[0217] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes according to the link connection information of each network node in the current period, the processor further implements the following steps:

[0218] According to the link connection information of each network node in the current time period, the correlation information between two adjacent network nodes is determined; for any two adjacent network nodes, the common neighbor node between the two adjacent network nodes is determined according to the correlation information between the two adjacent network nodes; based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

[0219] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes, the following steps are also implemented:

[0220] According to the node feature information of the common neighbor nodes, the common neighbor value between two adjacent network nodes is determined; according to the common neighbor value and correlation information between two adjacent network nodes, the neighbor features between two adjacent network nodes are determined; based on the cosine similarity function, according to the neighbor features between two adjacent network nodes, the attention features between two adjacent network nodes are determined.

[0221] In one embodiment, when the processor executes the computer program to determine the attention feature between two adjacent network nodes based on the cosine similarity function and the neighbor feature between the two adjacent network nodes, the processor further implements the following steps:

[0222] Based on the cosine similarity function, the cosine similarity between two adjacent network nodes is determined according to the neighbor characteristics between the two adjacent network nodes; based on the preset exponential function, the attention coefficient between the two adjacent network nodes is determined according to the cosine similarity between the two adjacent network nodes; based on the activation function, the attention characteristics between the two adjacent network nodes are determined according to the attention coefficient between the two adjacent network nodes.

[0223] In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

[0224] Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system in a reference period, and link connection information between each network node in the network structure diagram of the target power system in a comparison period; construct an adjacency matrix of the network structure diagram based on the historical characteristic information; input the historical characteristic information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram; based on the cosine similarity function, construct a first loss function according to the predicted connection information between each network node in the network structure diagram and the mean square error between the link connection information between each network node in the network structure diagram in the sample data; based on the preset logarithmic function, construct a second loss function according to the adjacency matrix; construct a target loss function according to the sum of the first loss function and the second loss function; use the target loss function to train the initial network link prediction model to obtain the network link prediction model.

[0225] It should be noted that the data involved in this application (including but not limited to data used for analysis, stored data, displayed data, etc.) are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0226] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0227] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0228] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A link prediction method, characterized in that: The method comprises: Obtain target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node; Based on the network link prediction model, according to the target feature information of each of the network nodes, determining the link connection information of each of the network nodes in a future period; The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

2. The method according to claim 1, characterized in that The network link prediction model includes an attention network and an encoding network; The determining, based on the network link prediction model and according to the target feature information of each of the network nodes, the link connection information of each of the network nodes in a future period includes: Based on the attention network, determining the attention feature between two adjacent network nodes according to the link connection information of each network node in the current time period; Based on the coding network, the link connection information of each of the network nodes in the future time period is determined according to the node attribute information of each of the network nodes in the current time period and the attention characteristics between two adjacent network nodes.

3. The method according to claim 2, characterized in that The determining, according to the link connection information of each of the network nodes in the current time period, the attention feature between two adjacent network nodes includes: Determining correlation information between the two adjacent network nodes according to link connection information of each of the network nodes in the current time period; For any two adjacent network nodes, determining a common neighbor node between the two adjacent network nodes according to correlation information between the two adjacent network nodes; Based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes.

4. The method according to claim 3, characterized in that: The method of determining the attention feature between the two adjacent network nodes based on the cosine similarity function according to the node attribute information of the common neighbor node and the correlation information between the two adjacent network nodes includes: Determining a common neighbor value between the two adjacent network nodes according to the node feature information of the common neighbor node; Determining a neighbor feature between the two adjacent network nodes according to the common neighbor value and correlation information between the two adjacent network nodes; Based on the cosine similarity function, the attention feature between the two adjacent network nodes is determined according to the neighbor feature between the two adjacent network nodes.

5. The method according to claim 4, characterized in that The step of determining the attention feature between the two adjacent network nodes based on the cosine similarity function and the neighbor feature between the two adjacent network nodes includes: Based on the cosine similarity function, according to the neighbor characteristics between the two adjacent network nodes, determining the cosine similarity between the two adjacent network nodes; Based on a preset exponential function, determining an attention coefficient between the two adjacent network nodes according to the cosine similarity between the two adjacent network nodes; Based on the activation function, the attention feature between the two adjacent network nodes is determined according to the attention coefficient between the two adjacent network nodes.

6. The method according to claim 1, characterized in that The network link prediction model is constructed in the following way: Acquire sample data; wherein the sample data includes historical characteristic information of each network node in the network structure diagram of the target power system during a reference period, and link connection information between each network node in the network structure diagram of the target power system; Constructing an adjacency matrix of the network structure graph according to the historical feature information; Inputting the historical feature information in the sample data into the initial network link prediction model to obtain the predicted connection information between each network node in the network structure diagram; Based on the cosine similarity function, a first loss function is constructed according to the predicted connection information between the network nodes in the network structure diagram and the mean square error between the link connection information between the network nodes in the network structure diagram in the sample data; Based on a preset logarithmic function and according to the adjacency matrix, construct a second loss function; Constructing a target loss function according to the sum of the first loss function and the second loss function; The target loss function is used to train the initial network link prediction model to obtain the network link prediction model.

7. A link prediction device, characterized in that: The device comprises: An information acquisition module, used to acquire target characteristic information of each network node in the network structure diagram of the target power system in the current period; wherein the target characteristic information of each network node includes node attribute information and link connection information of the network node; A link prediction module, used to determine the link connection information of each of the network nodes in a future period based on the network link prediction model and the target feature information of each of the network nodes; The network link prediction model is obtained by training a dual-order graph attention autoencoder based on the historical feature information of each network node in a reference period and the link connection information between each network node in a comparison period; wherein the comparison period is the period after the reference period.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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