Method and apparatus for analyzing graph using diffusion based kernel

Abstract

A graph analysis method using a diffusion-based kernel includes: a step in which an analysis device receives a graph; a step in which the analysis device inputs the graph into a graph convolution network model; and a step in which the analysis device analyzes the graph based on the output value of the graph convolution network model. A graph convolution network model can determine the range of neighborhood nodes of a target node to be considered during graph convolution operations using a diffusion-based kernel that has different range parameters for each node (node-wise), and then aggregate information between the target node and the determined neighborhood nodes.

Description

Technology Field

[0001] The technology described below relates to a method and apparatus for analyzing a graph using a diffusion-based kernel. Background Technology

[0002] Technologies for implementing artificial intelligence using artificial neural networks, such as deep learning, are being developed. Recently, technologies for analyzing graphs using models implemented with artificial intelligence are being developed. Graph analysis using artificial intelligence has been applied in fields such as medicine, information and communication technology (ICT) fields like recommendation systems, social network analysis, and anomaly detection.

[0003] In particular, approaches using graph artificial neural networks are being actively researched in neuropathological studies related to specific degenerative diseases. Prior art literature

[0004] U.S. Patent Publication US 2021-0397965 A1 The problem to be solved

[0005] In the past, there was the Graph Convolution Network as a graph analysis method using artificial neural networks.

[0006] Graph convolution networks perform graph convolution operations. During graph convolution, the operation must be repeated multiple times to utilize features from nodes located further away than directly connected nodes. Consequently, problems such as an increase in the number of training parameters, over-smoothing, and vanishing and exploding gradients have occurred.

[0007] To overcome this, there was a technique that performed graph convolution using conventional diffusion-based kernels. A representative example is “Graph convolutional networks using heat Kernel for semi-supervised learning” published by Xu, B. et al. However, conventional techniques using diffusion-based kernels utilized diffusion-based kernels with identical range parameters. Consequently, there was a problem in that accurate graph analysis could not be performed because the range of neighboring nodes that needed to be considered node-wise was processed uniformly.

[0008] The technology described below proposes a method for performing graph convolution operations that can retrieve information from nodes located at greater distances by utilizing a diffusion kernel. Additionally, by using a diffusion kernel with different range parameters for each node, it is possible to consider the characteristics of each node. means of solving the problem

[0009] A graph analysis method using a diffusion-based kernel comprises: a step in which an analysis device receives a graph; a step in which the analysis device inputs the graph into a graph convolution network model; and a step in which the analysis device analyzes the graph based on the output value of the graph convolution network model.

[0010] A graph convolution network model can determine the range of neighborhood nodes of a target node to be considered during graph convolution operations using a diffusion-based kernel that has different range parameters for each node (node-wise), and then aggregate the information of the target node and the determined neighborhood nodes. Effects of the invention

[0011] By utilizing the technique described below, graph convolution operations using diffusion-based kernels can be performed. Consequently, information about nodes located at greater distances can be retrieved without repeatedly executing convolution operations.

[0012] Using the technique described below, graph convolution with different range parameters can be performed node-wise. This enables more accurate graph analysis.

[0013] By using the technique described below, it is possible to determine how much neighboring nodes are considered for each node during convolution operations. This allows us to identify the relationship between a node and its neighboring nodes.

[0014] The technology described below can assist in the analysis of patients' medical images. Brief explanation of the drawing

[0015] Figure 1 shows the problems of a conventional graph analysis device. Figure 2 shows the overall process of an analysis device analyzing a graph using a diffusion-based kernel. Figure 3 is a flowchart of the process of analyzing a graph using a diffusion-based kernel. Figure 4 is an example visualizing the range parameters used when a graph convolution network model classifies input data as Alzheimer's patients. Specific details for implementing the invention

[0016] The technology described below may be subject to various modifications and may have various embodiments. Specific embodiments of the technology described below may be described in the drawings of the specification. However, this is for the purpose of explaining the technology described below and is not intended to limit the technology described below to specific embodiments. Accordingly, it should be understood that all modifications, equivalents, and substitutions that fall within the spirit and scope of the technology described below are included in the technology described below.

[0017] In the terms used below, singular expressions should be understood to include plural expressions unless the context clearly indicates otherwise, and terms such as "includes" should be understood to mean that the described features, number, steps, actions, components, parts, or combinations thereof exist, and not to exclude the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0018] Before providing a detailed description of the drawings, it is to clarify that the classification of components in this specification is merely based on the primary function each component is responsible for. That is, two or more components described below may be combined into a single component, or a single component may be divided into two or more components based on more subdivided functions. Furthermore, each component described below may additionally perform some or all of the functions of other components in addition to its own primary function, and it is obvious that some of the primary functions of each component may be exclusively performed by other components.

[0019] Furthermore, in performing the method or operation method, each process constituting the method may occur differently from the specified order unless a specific order is clearly indicated in the context. That is, each process may occur in the same order as specified, may be performed substantially simultaneously, or may be performed in the reverse order.

[0021] First, the problems of conventional graph analysis devices are explained.

[0022] Conventional graph analysis devices performed graph convolution operations using a diffusion-based kernel. The diffusion-based kernel utilizes range parameters that a node can consider during the graph convolution operation.

[0023] Conventional graph analysis devices used the same range parameter for all nodes during graph convolution operations using diffusion-based kernels.

[0024] FIG. 1 is an example of the process in which a conventional graph analysis device analyzes a graph and classifies the nodes of the graph.

[0025] FIGS. 1(a) and FIGS. 1(b) are examples of performing convolution using a diffusion-based kernel having the same range parameters (s1, s2), respectively (s1 <s2).

[0026] In FIGS. 1(b) and FIGS. 1(b), node n1 must be classified into class A. In FIGS. 1(a) and FIGS. 1(b), node n2 must be classified into class B.

[0027] In Fig. 1(a), when the range parameter is s1, node n1 can be considered as two nodes belonging to class A. In this case, n1 can be normally classified as class A.

[0028] On the other hand, in Fig. 1(a), node n2 may be considered as one node belonging to class A. In this case, n2 may be misclassified as class A.

[0029] In Fig. 1(b), when the neighbor scale is s2, node n1 may consider 2 nodes belonging to class A and 3 nodes belonging to class B. In this case, n1 may be misclassified as class A.

[0030] On the other hand, in Fig. 1(b), node n2 can be considered as one node belonging to class A and three nodes belonging to class B. In this case, n2 can be normally classified as class B.

[0031] As shown in Fig. 1, when performing graph convolution using a diffusion-based kernel with the same range parameter, incorrect judgment may occur. In other words, since conventional graph analysis devices performed graph convolution using the same range parameter for all nodes, there was a problem in that they could not account for cases where the range of neighboring nodes to be considered differed for each node.

[0033] The technology described below aims to solve the problems of conventional graph analysis devices by using a diffusion-based kernel that has different range parameters for each node.

[0034] In addition, the technique described below can analyze how much a single node considers neighboring nodes during graph convolution operations using range parameters.

[0036] The following describes the overall process of a graph analysis device using a diffusion-based kernel (hereinafter, analysis device) analyzing a graph using a diffusion-based kernel.

[0037] FIG. 2 shows the process of an analysis device (100) analyzing a graph using a diffusion-based kernel.

[0038] The analysis device (100) can receive a graph. The analysis device (100) can input the graph into a graph convolution network model. The analysis device (100) can analyze the graph based on the output value of the model.

[0039] The graph convolution network model may be a model trained to determine the neighborhood node range of the individual node using a diffusion-based kernel having adaptive range parameters for each node (node-wise) and to aggregate information of the neighborhood nodes within the determined range.

[0040] Furthermore, the analysis device (100) can visualize and display the range parameters of the diffusion-based kernel used for each individual node during graph convolution operations based on the results of analyzing the graph.

[0042] The following describes in detail the process by which the analysis device analyzes a graph using a diffusion-based kernel.

[0043] FIG. 3 is a flowchart of the process (200) in which an analysis device analyzes a graph using a diffusion-based kernel.

[0044] The analysis device can receive a graph (210).

[0045] A graph consists of nodes and edges. A graph can be represented as G, nodes as V, and edges as E. Therefore, it can be expressed as G = {V, E}.

[0046] A graph can be a directed graph or an undirected graph. Alternatively, a graph can be a complete graph, a subgraph, or a weighted graph.

[0047] A graph can be represented by an adjacency matrix, an edge matrix, and a feature matrix.

[0048] An adjacency matrix can be a matrix that contains information about how the nodes of a graph are connected to each other.

[0049] An adjacency matrix can be represented as a sparse matrix based on how each node is connected. For example, each node can be represented as 1 if connected and 0 if not connected.

[0050] An adjacency matrix can be a symmetric matrix if the graph is an undirected graph.

[0051] An edge matrix can be a matrix that holds information about the edges of a graph.

[0052] A feature matrix can be a matrix containing feature data for the nodes of a graph. For example, if each segment of the brain is represented as a graph, the feature matrix may include information about beta-amyloid (b-Amyloid) and cortical thickness.

[0053] The analysis device can input the graph into a graph convolution network model (220).

[0054] Graph convolution can be an operation that convolves a graph with a kernel (or filter).

[0055] Graph convolution can be performed based on spectral analysis. In other words, graph convolution can be carried out by converting the graph signal into the frequency domain, applying a filter, and then performing an inverse transformation.

[0056] Graph convolution can be a process of aggregating information between a target node and its neighbor nodes in a graph. Kernels can be used to determine how much weight to assign during the process of aggregating neighbor node information.

[0057] Graph convolution network models can perform graph convolution using diffusion-based kernels. Diffusion-based kernels can include heat kernels.

[0058] Diffusion-based kernels can transform a graph's adjacency matrix into a new weighted adjacency matrix containing structural information. By utilizing this transformed weighted adjacency matrix, information regarding neighboring nodes located far from the target node can be aggregated during convolution operations. This enables the aggregation of information regarding distant neighboring nodes without the need for iterative convolution layers.

[0059] Diffusion-based kernels can determine the extent to which the range of neighboring nodes is defined during convolution operations through range parameters.

[0060] For example, if the range parameter is large, the target node can perform the convolution operation by aggregating information from a wide range of neighboring nodes. Conversely, if the range parameter is small, the target node can perform the convolution operation by aggregating information from a small range of neighboring nodes.

[0061] A graph convolution network model can perform convolution operations using a diffusion-based kernel with adaptive parameters for each individual node. That is, a graph convolution network model can determine the range of neighbor nodes of a target node to be considered during graph convolution operations using a diffusion-based kernel with different range parameters for each individual node, and then aggregate information between the target node and neighbor nodes within the determined range.

[0062] For example, a graph convolution network model can perform convolution operations by using a diffusion-based kernel with adaptive range parameters at nodes n1 and n2 to determine the range of neighbor nodes to be considered during convolution operations for each individual node, and by aggregating the information of the determined neighbor nodes.

[0063] Graph convolution network models can be trained to have appropriate range parameter values.

[0064] For example, a graph convolution network model can be trained using a training method that calculates the range parameter that minimizes the loss value when using a diffusion-based kernel with the same parameter for all nodes in the graph, and then calculates the adaptive range parameter for each individual node that minimizes the loss value when using a diffusion-based kernel with an adaptive range parameter for each individual node.

[0066] Graph convolutional network models can be artificial neural network-based models.

[0067] A graph convolution network model can be a pre-trained model through the training process.

[0068] The learning process may be a process of learning to perform graph convolution operations using a diffusion-based kernel with the same parameters for all nodes in the graph, and then learning to perform graph convolution operations using a diffusion-based kernel with adaptive range parameters for individual nodes.

[0069] The specific process by which a graph convolution network model performs graph convolution operations is explained below.

[0070] The analysis device can analyze the graph based on the output value of the model (230).

[0071] Analyzing a graph may involve the process of classifying what type of graph it is.

[0072] For example, analyzing a graph can be the process of classifying the graph into one of multiple classes.

[0073] Alternatively, analyzing a graph may involve the process of classifying where the graph's nodes belong.

[0074] For example, analyzing a graph can be the process of classifying a specific node into one of multiple classes.

[0075] Furthermore, the analysis device can visualize and display the range parameters of the diffusion-based kernel used for each individual node during graph convolution operations based on the results of analyzing the graph (240).

[0076] This allows for the identification of connectivity between graph nodes. In other words, similarity using diffusion-based kernels can help determine the precise relationships between nodes.

[0077] For example, if it is confirmed that a node in a graph performs convolution operations using a diffusion-based kernel with small range parameters, it can be determined that the node has low connectivity with neighboring nodes.

[0079] The graph convolution operation is explained in detail below.

[0080] Graph convolution can be performed based on frequency analysis.

[0081] To convert a graph signal into the frequency domain, a Fourier Transform can be performed. To convert back from the frequency domain to the original domain, a Reverse Fourier Transform can be performed.

[0082] The Laplacian matrix can be used to perform a Fourier transform on a graph signal.

[0083] The Laplacian matrix is ​​the graph's degree matrix minus its adjacency matrix. Therefore, the Laplacian matrix contains positive degree values ​​and negative adjacency information.

[0084] Mathematical Equation 1 is the formula used to calculate the Laplacian matrix (L).

[0085]

[0086] In Equation 1, D represents the degree matrix. In Equation 1, A represents the adjacency matrix.

[0087] The Laplacian matrix can be used after being normalized.

[0088] Mathematical Equation 2 is the normalized Laplacian matrix ( It is a formula used to calculate.

[0089]

[0090] In mathematical formula 2, IN represents the identity matrix.

[0091] Normalized Laplacian matrix in Equation 2 Since it is a symmetric matrix with real values, it can have real, non-negative eigenvalues ​​and an orthonormal basis.

[0092] The Laplacian matrix can be utilized through eigenvalue decomposition. Eigenvalue decomposition refers to the process of decomposing a matrix into an eigenvalue matrix and an eigenvector matrix.

[0093] Equation 3 is the result of eigenvalue decomposition of the Laplacian matrix.

[0094]

[0095] The Fourier transform can be performed using the eigenvector matrix (U) of the Laplacian matrix. That is, the Fourier transform is performed by multiplying the graph signal by the transpose of the eigenvector matrix of the Laplacian matrix.

[0096] Mathematical Equation 4 is the equation used to perform the Fourier transform on a graph signal.

[0097]

[0098] The inverse Fourier transform can also be performed using the eigenvector matrix of the Laplacian matrix. That is, the inverse Fourier transform can be performed by multiplying the Fourier transform value by the eigenvector matrix of the Laplacian matrix.

[0099] Mathematical Equation 5 is the equation used to perform the inverse Fourier transform on the Fourier transform value.

[0100]

[0101] Mathematical Equation 6 is an equation used when analyzing graph convolution operations based on frequency analysis.

[0102]

[0103] In Equation 6, g represents the kernel (filter). In Equation 6, represents the Hadamard product.

[0104] If UTg = gθ is defined in Equation 6, Equation 6 can be expressed as Equation 7.

[0105]

[0106] g in mathematical formula 7 θ can mean kernel. g θ is diag({θ i} N i=1 )am.

[0107] Calculating mathematical equation 7 on a computer requires a large amount of computation. Therefore, a polynomial filter can be used.

[0108] A polynomial filter can be defined as in Equation 8.

[0109]

[0110] In mathematical equation 8, the parameter θ is a vector of polynomial coefficients.

[0111] Using the polynomial filter of Equation 8, Equation 7 can be expressed as Equation 9.

[0112]

[0113] In some cases, only a few terms may be used in Equation 9. For example, as in Equation 10, only the zero and first-order values ​​may be used.

[0114]

[0115] In Equation 10, a heat kernel, which is one of the diffusion-based kernels, can be used as the kernel.

[0116] Mathematical Equation 11 is the column kernel equation in the frequency domain between node p and node q.

[0117]

[0118] In mathematical equation 11, λ i Wow u i represents the eigenvalues ​​and eigenvectors of the graph Laplacian. In Equation 11, s represents the range parameter. The range parameter controls the time / scale of diffusion.

[0119] The larger the value of the range parameter, the larger the range of neighboring nodes considered by a single node during the convolution operation.

[0120] Using the column kernel of Equation 11, Equation 10 can be expressed as Equation 12.

[0121]

[0122] A column kernel extracts only the low-frequency region from a graph signal. In other words, a column kernel acts as a low-pass filter.

[0123] Graph convolution operations using heat kernels can also be verified through “Graph convolutional networks using heat Kernel for semi-supervised learning”.

[0125] The graph convolution network model is described below.

[0126] Graph convolution network models perform graph convolution operations using diffusion-based kernels.

[0127] A graph convolution network model includes multiple graph convolution layers. Graph convolution layers can adaptively aggregate information for each node.

[0128] An activation function can be applied to the output of a graph convolution layer. The activation function can be a non-linear activation function. For example, the activation function can be the ReLU (rectified linear unit) function.

[0129] Mathematical Equation 13 is the formula used to calculate the value output by the Kth graph convolution layer.

[0130]

[0131] In Equation 13, Hk represents the output value of the k-th convolution layer. In Equation 13, W k It refers to the parameter matrix being learned. In Equation 13, σ k means activation function.

[0132] The output value of the Kth graph convolution layer can be vectorized and applied to a readout function ψ. The readout function can be a multi-layer perceptron.

[0133] Graph convolution network models can output information about which class a graph belongs to as an output value.

[0134] In one embodiment, a graph convolution network model can calculate the probability of belonging to each class by applying a softmax to the value of each class.

[0136] The following describes the process of training a graph convolutional network model.

[0137] Training a graph convolutional network model can be understood as the process of finding the optimal parameter values ​​for the model. In other words, the training process involves finding appropriate range parameters for the diffusion-based kernel.

[0138] The learning process involves learning range parameters for the entire graph (Global) and then learning range parameters for each individual node.

[0139] Mathematical Equation 14 is the loss function (or objective function) used when learning a single neighbor measure for the entire graph.

[0140]

[0141] Y in mathematical formula 14 tc represents the correct answer value. In mathematical formula 14 represents the predicted value of the model. In Equation 14, λ represents a hyperparameter. In Equation 14, T represents the sample size. In Equation 14, s represents a range parameter. Equation 14 calculates the loss through the cross-entropy between the predicted value and the actual value for the t-th sample belonging to class c.

[0142] In the process of learning the parameters, Equation 14 is differentiated with respect to s and used.

[0143] Mathematical Equation 15 shows the process of differentiating with respect to the preceding term in Mathematical Equation 14.

[0144]

[0145] Mathematical Equation 16 is the formula used to differentiate the latter term in Mathematical Equation 14.

[0146]

[0147] Therefore, when Equation 14 is differentiated with respect to s, it can be expressed as Equation 17 for any kernel K(s) when T = 1.

[0148]

[0149] Each range parameter can be updated immediately by removing the marginalization for the node from the cross-entropy term of Equation 14.

[0150] Therefore, it can be written as in mathematical formula 18.

[0151]

[0152] In mathematical equation 18, si represents each range parameter. N s i and each have a cross-entropy term and a scale term as loss functions. For each s i For each node, the model can be updated independently so that the loss value for the weighted predictions of the redefined adjacency matrix between the node and neighboring nodes is minimized.

[0154] The researcher obtained training data to train a graph convolution network model.

[0155] Table 1 shows the contents of the training data obtained by the researcher.

[0156] Normal Cognitive (CN) Significant Memory Problems (SMC) Early Mild Cognitive Impairment (EMC) Late Mild Cognitive Impairment (LMC) Alzheimer's (AD) Number of subjects 89 53 132 55 72 Gender (M / F) 37 / 52 19 / 34 84 / 48 32 / 23 42 / 30 Age (Mean ± std) 72.6 ± 4.8 73.4 ± 4.8 70.3 ± 7.1 72.3 ± 6.2 75.8 ± 7.2

[0157] Diffusion-weighted imaging (DWI), amyloid-positron emission tomography (amyloid-PET), and fluorodeoxyglucose (FDG)-positron emission tomography (FDG-PET) data from a total of 401 subjects were used as training data. The subjects' brain regions were segmented into 148 cortical surface regions. The Destrieus atlas was used for this purpose.

[0158] Neurofiber tracing from brain diffusion-weighted imaging (DWI) was applied to construct a structural network by calculating white matter fibers connecting brain regions. The size of the structural network can be 148 x 148.

[0159] Within the same brain parcellation, features can be defined by region. The image features by region include the standard uptake value ratio (SUR) of beta-amyloid (β-amyloid) protein obtained from amyloid-PET, the standard uptake value ratio of metabolism level obtained from FDG-PET, and cortical thickness and nodal degree obtained from MRI images. In this case, the cerebellum was used as a reference for the normalization of the standard uptake value ratio.

[0160] 401 subjects were divided into five labels. Each label was classified as cognitive normal (CN), significant memory concern (SMC), early mild cognitive impairment (EMCI), late mild cognitive impairment (LMCI), and Alzheimer's disease (AD).

[0162] The researcher trained a graph convolution network model based on the acquired training data.

[0163] During the training process, the model parameters were initialized using Xavier Initialization. The training was performed using the Adam optimizer. The learning rate during the training process is 0.01.

[0165] The researcher evaluated the performance of the trained graph convolution network model.

[0166] Conventional models that analyze graphs were used as baselines for performance evaluation. Conventional models include Support Vector Machine (SVM), Graph Convolution Network (GCN), Graph Attention Network (GAT), GraphHeat (Graph convolution using heat kernel), and Graph Diffusion Convolution (GDC).

[0167] In addition, performance was evaluated based on the features used for each model.

[0168] Features include the degree of the nodes, cortical thickness, and metabolic levels through beta-amyloid (β-amyloid) protein and FDG.

[0169] Table 2 shows the performance evaluation results of the graph convolution network model.

[0170]

[0171] Table 2 shows that the graph convolution network model (Ours) generally performs better than the baseline model.

[0172] In particular, the highest accuracy of 96% is shown when using metabolic characteristics analyzed via FDG. Metabolic characteristics (FDG) are known to be widely used as a biomarker for diagnosing early Alzheimer's disease. The results in Table 2 are consistent with previously known facts.

[0173] In Table 2, the performance is good when all imaging features are used. However, it is slightly lower than when only FDG is used. This may be because cortical thickness is not sufficient as a biomarker to distinguish early Alzheimer's disease.

[0175] Figure 4 is an example visualizing the range parameters used when a graph convolution network model classifies input data as Alzheimer's patients.

[0176] Figure 4 (a) shows the case where the range parameter(s) is 2. Figure 4 (b) shows the case where the range parameter(s) is 1.586. Figure 4 (c) shows the case where the range parameter(s) is adaptively learned for each region of interest.

[0177] In Figure 4, regions with low range parameters are independent of other regions of interest. In other words, this demonstrates that regions of interest with low range parameters do not require the aggregation of information from neighboring nodes during graph convolution operations to be classified as Alzheimer's (AD).

[0178] Figure 4 shows that the cingulate gyrus and cingulate sulcus regions of the left and right hemispheres were performed using the lowest range parameters during convolution operations. This is because cognitive and executive functions became specific to Alzheimer's disease. This is a previously known fact, and the results in Figure 4 are consistent with this previously known fact.

[0179] Furthermore, other regions in Fig. 4 with low range parameters are points consistently found in conventional preclinical Alzheimer's disease. Fig. 4 demonstrates that regions with low range parameters play a crucial role in distinguishing the early stages of Alzheimer's disease.

[0181] The configuration of the analysis device is described below.

[0182] Figure 5 is an example of the configuration of an analysis device.

[0183] The analysis device (300) may correspond to the analysis device (100) described in FIG. 1.

[0184] The analysis device (300) can be physically implemented in various forms. For example, the analysis device (300) can take the form of a PC, laptop, smart device, server, or a chipset dedicated to data processing.

[0185] The analysis device (300) may include an input device (310), a storage device (320), a calculation device (330), an output device (340), an interface device (350), and a communication device (360).

[0186] The input device (310) may include an interface device (keyboard, mouse, touchscreen, etc.) for receiving certain commands or data. The input device (310) may include a configuration for receiving information through a separate storage device (USB, CD, hard disk, etc.). The input device (310) may receive input data through a separate measuring device or through a separate DB. The input device (310) may receive data via wired or wireless communication.

[0187] The input device (310) can receive information or a model necessary during the process of executing a graph analysis method using a diffusion-based kernel. The input device (310) can receive a graph. The input device (310) can receive a graph convolution network model.

[0188] The storage device (320) can store information received through the input device (310). The storage device (320) can store information generated during the process of the computation device (330) performing computations. That is, the storage device (320) may include memory. The storage device (320) can store the result calculated by the computation device (330).

[0189] The storage device (320) can store information or models necessary during the process of executing a graph analysis method using a diffusion-based kernel. The storage device (320) can store a graph. The storage device (320) can store a graph convolution network model.

[0190] The computing device (330) may be a device such as a processor, AP, or a chip with a program embedded therein that processes data and performs certain operations.

[0191] The computing device (330) can perform operations necessary to execute a graph analysis method using a diffusion-based kernel. The computing device (330) can be input into a graph convolution network model. The computing device (330) can analyze the graph based on the output value of the graph convolution network model. Based on the results of analyzing the graph, the computing device (330) can perform operations necessary to visualize the range variable of the diffusion-based kernel used for each individual node during graph convolution operations.

[0192] The output device (340) may be a device that outputs certain information. The output device (340) may output an interface required for a data process, input data, analysis results, etc. The output device (340) may be implemented in various physical forms, such as a display, a document output device, etc.

[0193] The output device (340) can output a result of visualizing the range parameter.

[0194] The interface device (350) may be a device that receives certain commands and data from the outside. The interface device (350) may receive a graph from a physically connected input device or an external storage device. The interface device (350) may receive a control signal to control the analysis device (300). The interface device (350) may output the results analyzed by the analysis device (300).

[0195] The communication device (360) may refer to a configuration that receives and transmits certain information via a wired or wireless network. The communication device (360) may receive control signals necessary to control the analysis device (300). The communication device (360) may transmit the results analyzed by the analysis device (300).

[0196] The graph analysis method using the aforementioned diffusion-based kernel can be implemented as a program (or application) that includes an executable algorithm that can be run on a computer.

[0198] The above program may be provided by storing it on a transitory or non-transitory computer-readable medium.

[0199] A non-transient readable medium refers to a medium that stores data semi-permanently and can be read by a device, rather than a medium that stores data for a short moment, such as a register, cache, or memory. Specifically, the various applications or programs described above may be stored and provided on a non-transient readable medium such as a CD, DVD, hard disk, Blu-ray disc, USB, memory card, ROM (read-only memory), PROM (programmable read-only memory), EPROM (Erasable PROM, EPROM), EEPROM (Electrically EPROM), or flash memory.

[0200] Transient readable media refers to various types of RAM such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), Enhanced SDRAM (ESDRAM), Synclink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM).

[0201] The embodiments and drawings attached to this specification merely clearly illustrate a part of the technical ideas included in the aforementioned technology, and it is self-evident that variations and specific embodiments that can be easily inferred by a person skilled in the art within the scope of the technical ideas included in the specification and drawings of the aforementioned technology are all included within the scope of the rights of the aforementioned technology.

Claims

Claim 1 A graph analysis method using a diffusion-based kernel, comprising: a step in which an analysis device receives a graph; a step in which the analysis device inputs the graph into a graph convolution network model; and a step in which the analysis device analyzes the graph based on the output value of the graph convolution network model; wherein the graph convolution network model is a model trained to determine the neighborhood node range of an individual node using a diffusion-based kernel having an adaptive range parameter for each individual node (node-wise) and to aggregate information of neighbor nodes within the determined range, and wherein the graph convolution network model is trained by a learning method that calculates a range parameter that minimizes the loss value when using a diffusion-based kernel having the same parameter for all nodes of the graph, and then calculates an adaptive range parameter for an individual node that minimizes the loss value when using a diffusion-based kernel having an adaptive range parameter for an individual node of the graph. Claim 2 A graph analysis method using a diffusion-based kernel, further comprising the step of visualizing and displaying the range parameters of the diffusion-based kernel used for each individual node during the graph convolution operation based on the result of the analysis device analyzing the graph in claim 1. Claim 3 A graph analysis method using a diffusion-based kernel, wherein the graph convolution operation is performed based on spectral analysis. Claim 4 A graph analysis method using a diffusion-based kernel, wherein the step of analyzing the graph in claim 1 comprises the step of classifying the graph into one of a plurality of classes. Claim 5 delete Claim 6 A graph analysis device using a diffusion-based kernel, comprising: an input device for receiving a graph; a computing device for inputting the graph into a graph convolution network model and analyzing the graph based on the output value of the graph convolution network model; and a storage device for storing the graph convolution network model; wherein the graph convolution network model is a model trained to determine the neighborhood node range of the individual node using a diffusion-based kernel having an adaptive range parameter for each individual node (node-wise) and to aggregate information of the neighborhood nodes within the determined range; and wherein the graph convolution network model is trained by a learning method that calculates a range parameter that minimizes the loss value when using a diffusion-based kernel having the same parameter for all nodes of the graph, and then calculates an adaptive range parameter for the individual node that minimizes the loss value when using a diffusion-based kernel having an adaptive range parameter for the individual node of the graph. Claim 7 A graph analysis device using a diffusion-based kernel according to claim 6, further comprising: a computing device that calculates information to visualize the range parameters of the diffusion-based kernel used for each individual node during the graph convolution operation based on the result of analyzing the graph, and an analysis device that outputs the result of visualizing the range parameters based on the result calculated by the computing device. Claim 8 In claim 6, the graph analysis device using a diffusion-based kernel, wherein the graph convolution operation is performed based on spectral analysis. Claim 9 A graph analysis device using a diffusion-based kernel, wherein, in claim 6, the computing device analyzes the graph by classifying the graph into one of a plurality of classes. Claim 10 delete Claim 11 A computer-readable recording medium storing a program for executing a graph analysis method using a diffusion-based kernel as described in any one of claims 1 to 4.

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