A spatial domain identification method and system based on spatial multi-omics technology of heterogeneous graph

Abstract

This invention proposes a spatial domain identification method and system based on heterogeneous graph spatial multi-omics technology, belonging to the field of bioinformatics. The method includes: acquiring spatial omics data and performing data preprocessing to obtain gene expression data; dividing the tissue image of the preprocessed spatial omics data into multiple sub-images according to the number of cells using the spatial location information of cells; constructing adjacency matrices from different perspectives based on extracted feature representations; constructing a graph encoder for each perspective to obtain graph-encoded features; constructing a heterogeneous graph based on an attention mechanism; constructing a training model; and inputting the spatial omics data to be identified into the trained model to obtain multi-omics spatial domain information. This method can effectively integrate and analyze spatial multi-omics data, explore spatial omics data from multiple perspectives, improve the accuracy and efficiency of spatial domain identification, and provide new tools and perspectives for a deeper understanding of the spatial functional relationships between cells.

Description

Technical Field

[0001] The present invention belongs to the technical field of bioinformatics, and in particular relates to a spatial domain identification method and system based on spatial multi-omics technology of heterogeneous graphs. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of bioinformatics and genomics technologies, multi-omics data analysis has become an important means to study gene expression, protein interactions, metabolic pathways, etc. in complex biological systems. Traditional multi-omics analysis methods usually rely on processing and analyzing different types of biological data separately. Although this method has promoted the progress of biomedical research to a certain extent, it shows certain limitations when processing spatial multi-omics data, especially in terms of spatial resolution and data integration.

[0004] Spatial multi-omics technology is an important breakthrough in the field of bioinformatics in recent years. It can provide spatial location information at the single-cell level, allowing researchers to explore gene expression, protein distribution and its function at the cellular or even subcellular level. However, biological tissue is a complex system, and the use of traditional spatial multi-omics analysis technology often lacks efficiency and accuracy, especially in identifying and integrating heterogeneous data from different spatial regions. There are huge challenges.

[0005] Heterogeneous graph technology, as an effective method for processing heterogeneous data, provides the possibility of integrating and analyzing information from different data sources. However, its application in spatial multi-omics data is still in its early stages, and there is an urgent need to develop a new method that can effectively use heterogeneous graph technology to solve the problem of spatial domain recognition. Summary of the invention

[0006] To overcome the shortcomings of the above-mentioned prior art, the present invention provides a spatial domain identification method of spatial multi-omics technology based on heterogeneous graphs, which can effectively integrate and analyze spatial multi-omics data, explore spatial omics data from multiple perspectives, improve the accuracy and efficiency of spatial domain identification, and provide new tools and perspectives for in-depth understanding of the spatial functional relationship between cells.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] In a first aspect, a spatial domain identification method of spatial multi-omics technology based on heterogeneous graphs is disclosed, comprising:

[0009] Acquire spatial omics data and perform data preprocessing to obtain gene expression data;

[0010] The spatial position information of cells is used to divide the tissue image of the preprocessed spatial omics data into multiple sub-images according to the number of cells, and feature representations are extracted from the multiple sub-images;

[0011] Construct adjacency matrices from different perspectives based on the extracted feature representation;

[0012] A set of graph encoders is constructed for each view. Each set of graph encoders contains two layers of GCN, which process the adjacency matrix and gene expression data constructed under different viewpoints respectively to obtain graph encoding features. GCN is a graph convolutional neural network.

[0013] Constructing heterogeneous graphs based on the attention mechanism: Using the attention mechanism to calculate the latent features of each view in the graph encoding features, the latent features under multiple views are added together to obtain the joint latent features of all views;

[0014] Calculate the joint probability density and empirical probability density based on the joint potential features of all perspectives, define the self-supervised objective function based on the joint probability density and empirical probability density, and build a training model;

[0015] The spatial omics data to be identified are input into the trained model to obtain multi-omics spatial domain information.

[0016] As a further technical solution, data preprocessing is performed on the acquired spatial omics data, including: deleting genes and mitochondrial genes whose expression levels are less than three cells in the spatial omics data;

[0017] Then the spatial omics data are regularized and logarithmic, and finally the highly expressed genes with the required amount of data are screened to obtain the gene expression data.

[0018] As a further technical solution, for multiple sub-images, each cell corresponds to a sub-image.

[0019] As a further technical solution, feature representations are extracted from multiple sub-images, specifically, by using a feature extractor to convert high-dimensional image data into low-dimensional feature representations.

[0020] As a further technical solution, each set of graph encoders includes two layers of GCN, wherein the features extracted by each layer of GCN integrate the information of neighboring nodes.

[0021] As a further technical solution, the specific expression of the graph coding feature is:

[0022]

[0023] Indicates The graph encoding feature of the layer is a matrix with the same size as the input feature matrix; is the adjacency matrix of the input adjacency matrix after preprocessing; yes The degree matrix of is a diagonal matrix whose diagonal elements are the degrees of each node; Indicates The graph encoding feature of the layer is the output of the previous layer; Indicates Layer to The weight matrix of the layer is a learnable parameter matrix; Represents the activation function.

[0024] In a second aspect, a spatial domain identification system based on spatial multi-omics technology of heterogeneous graph is disclosed, comprising:

[0025] The gene expression data acquisition module is configured to: acquire spatial omics data and perform data preprocessing to obtain gene expression data;

[0026] The feature representation extraction module is configured to: divide the tissue image of the preprocessed spatial omics data into a plurality of sub-images according to the number of cells by using the spatial position information of the cells, and extract feature representations from the plurality of sub-images;

[0027] The adjacency matrix construction module is configured to: construct adjacency matrices under different perspectives based on the extracted feature representations;

[0028] The graph encoding feature acquisition module is configured as follows: a set of graph encoders is constructed for each view. Each set of graph encoders contains two layers of GCN, which process the adjacency matrix and gene expression data constructed under different viewpoints respectively to obtain graph encoding features. GCN is a graph convolutional neural network.

[0029] The joint latent feature acquisition module is configured to: construct a heterogeneous graph based on the attention mechanism: use the attention mechanism to calculate the latent features of each view in the graph encoding features, and add the latent features under multiple views to obtain the joint latent features of all views;

[0030] The model training module is configured to: calculate the joint probability density and the empirical probability density based on the joint potential features of all perspectives, define the self-supervised objective function based on the joint probability density and the empirical probability density, and construct the training model;

[0031] The recognition module is configured to: input the spatial omics data to be recognized into the trained model to obtain multi-omics spatial domain information.

[0032] One or more of the above technical solutions have the following beneficial effects:

[0033] The technical solution of the present invention is a spatial domain identification method based on spatial multi-omics technology of heterogeneous graphs. This method can effectively integrate and analyze spatial multi-omics data, explore spatial omics data from multiple perspectives, improve the accuracy and efficiency of spatial domain identification, and provide new tools and perspectives for in-depth understanding of the spatial functional relationship between cells.

[0034] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0036] Figure 1 It is a schematic diagram of the process of the first embodiment of the present invention;

[0037] Figure 2 The recognition result diagram of the first embodiment of the present invention has an ARI of 0.46. DETAILED DESCRIPTION

[0038] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0039] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0040] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0041] Embodiment 1

[0042] This embodiment discloses a spatial domain identification method based on spatial multi-omics technology of heterogeneous graph, comprising the following steps:

[0043] S1: Gene expression data preprocessing: including data reading, data screening and regularization processing to obtain the gene expression matrix of each cell .

[0044] S2: Utilization of tissue image feature extraction Models such as these are used to extract the image information of each cell using spatial omics technology, including spatial position, gene expression, and histological images.

[0045] S3: Constructing the adjacency matrix ,include:

[0046] Constructing image-based multi-omics graph relationships (image perspective), , that is, forming an image icon.

[0047] Constructing gene-based multi-omics graph relationships (gene perspective), , that is, forming an expression graph.

[0048] Constructing multi-omics graph relationships based on spatial information (spatial perspective), , that is, forming a spatial graph.

[0049] S4: Building a multi-view graph encoder: generating A graph encoding convolutional encoder is used to obtain spatial omics embeddings from different perspectives. .

[0050] S5: Constructing heterogeneous graphs based on attention mechanism: Using attention mechanism, fusion , and obtain The weight of the perspective .

[0051] Fusion of multiple perspectives to construct spatially heterogeneous maps and multimodal joint embedding .

[0052] S6: Calculate joint probability density and the empirical probability density , with the help of the autoencoder clustering loss DEC (DeepEmbedded Clustering) training model, multi-omics spatial domain information is obtained.

[0053] For details, please refer to the attached Figure 1 As shown, including:

[0054] Regarding step S1: gene expression data preprocessing.

[0055] Obtain spatial omics data, delete genes and mitochondrial genes with expression levels less than three cells, reduce interference during analysis, and help focus on the main transcriptome activities in cells. Then, regularize the gene expression data and take the logarithm. Finally, screen 3,000 highly expressed genes to obtain gene expression data. , used as input for extracting graph encoding features in S4.

[0056] It should be noted that spatial omics data provide a more comprehensive perspective by combining gene expression data information with its spatial distribution in tissues.

[0057] In this step, genes with expression levels less than three cells may be noise or background signals and have no biological significance. Removing these genes can improve data quality and reduce interference during analysis; mitochondrial genes are often related to the health status and stress response of cells and may mask other important biological information in cells. Removing these genes helps focus on the main transcriptome activities in cells.

[0058] S2 Tissue image feature extraction.

[0059] Using spatial location information, the tissue image of spatial omics data obtained by searching the public database is divided into multiple sub-images according to the number of cells. Each cell corresponds to a sub-image, which can more accurately analyze the characteristics of each cell and facilitate the capture of the subtle structure and characteristics inside the cell. For data that are not measured by tissue image sequencing technology, such as Merfish, this step is skipped. In the same slice, given cells The two-dimensional space coordinates of . Indicates cells, a total of cells, Indicates The two-dimensional spatial coordinates of each cell.

[0060] In the above steps, by dividing the tissue image into multiple sub-images, the characteristics of each cell can be analyzed more accurately; the sub-images at the cell level provide higher resolution, making it easier to capture the subtle structures and characteristics inside the cells.

[0061] In the images of high-expressing tissues, centered The pixel area is used as the image data corresponding to each cell , select a suitable feature extractor, such as the Spatial-Transformer Network (STN) model, to extract feature representations from image data ,improving the accuracy and efficiency of the overall analysis, the extracted feature representation is subsequently used in S3 to build image-viewpoint-based distance calculations.

[0062] The above feature extractor can convert high-dimensional image data into low-dimensional feature representation, simplify the data, and facilitate subsequent analysis and processing; by extracting feature representation, the accuracy and efficiency of the overall analysis can be improved.

[0063] S3 builds adjacency matrix .

[0064] In this step, since the relationship between cells depends not only on spatial position, but also on multiple aspects of information such as gene expression and image features, these multi-dimensional information can be comprehensively considered by constructing adjacency matrices from different perspectives; multi-perspective adjacency matrices can provide a more comprehensive description of cell relationships and improve the accuracy and robustness of the analysis.

[0065] Construct distance calculation based on image and gene perspective: Calculate the cosine distance of the image between two cells based on the extracted features to construct image-based distance calculation. Cosine distance formula:

[0066]

[0067] in represents the dot product of vectors, and Represents vectors and The Jaccard distance formula is used to construct the distance calculation based on the gene perspective:

[0068]

[0069] in, Representing a collection and The size of the intersection of Representing a collection and The size of the union of .

[0070] Construct an adjacency distance calculation based on a spatial perspective: Calculate the distance between two cells based on the position information, that is, the Euclidean distance.

[0071]

[0072] The calculation based on Euclidean distance can accurately describe the spatial distribution and relationship of cells.

[0073] Constructing adjacency matrices from different perspectives: When constructing the adjacency matrix, it is expected that cells with similar distances have greater weights, and cells with farther distances have smaller weights. Therefore, the adjacency matrix is ​​as follows. The multi-perspective adjacency matrix can provide a more comprehensive description of cell relationships and improve the accuracy and robustness of the analysis.

[0074]

[0075] Introduced Hyperparameters, set the degree to which the adjacency matrix is ​​clustered toward the diagonal, and finally obtain all the adjacency matrices , is the number of viewing angles.

[0076] The relationship between cells depends not only on spatial position, but also on multiple aspects of information such as gene expression and image features. By constructing adjacency matrices from different perspectives, these multi-dimensional information can be comprehensively considered; multi-perspective adjacency matrices can provide a more comprehensive description of cell relationships and improve the accuracy and robustness of the analysis.

[0077] S4 builds a multi-view image encoder.

[0078] A set of graph encoders (GAE) is constructed for each view. Each set of graph encoders contains two layers of GCN. The adjacency matrix constructed under different viewpoints is and gene expression data , we can get the graph encoding features from different perspectives of each spatial omics data , each set of potential features is shown below, making the feature representation of the node richer and more diverse. The attention mechanism is then used to calculate the graph encoding features The weights and potential features of each perspective in .

[0079] Each perspective provides different information. By constructing a multi-perspective graph encoder, cell features can be extracted from multiple dimensions to fully reflect the diversity of cells. The features extracted by each layer of GCN integrate the information of neighboring nodes, making the feature representation of the nodes richer and more diverse.

[0080]

[0081] Indicates The graph encoding feature of the layer is a matrix with the same size as the input feature matrix; It is the adjacency matrix after preprocessing the input adjacency matrix, usually adding a self-loop operation so that each node is connected to itself; yes The degree matrix is ​​a diagonal matrix whose diagonal elements are the degrees of each node. Indicates The graph encoding feature of the layer is the output of the previous layer; Indicates Layer to The weight matrix of the layer is a learnable parameter matrix; Represents the activation function, commonly used ones include ReLU, Sigmoid, etc.

[0082] Finally, we get spatial omics embedding from different perspectives. .

[0083] S5 constructs heterogeneous graphs based on the attention mechanism, which is specifically manifested in constructing the adjacency matrix of the heterogeneous graph network.

[0084] A heterogeneous graph combines information from multiple perspectives (genes, images, space, etc.) to construct a graph structure that comprehensively reflects the relationship between cells.

[0085] Here, the attention mechanism is used to calculate the weight and potential features of each perspective, and the weight of each perspective is used to calculate the adjacency matrix of the heterogeneous graph network.

[0086]

[0087]

[0088] Then calculate the adjacency matrix of the heterogeneous graph network:

[0089]

[0090] Adding the potential features from multiple perspectives is the joint potential feature of all perspectives By combining potential features, we can comprehensively consider this information, improve the comprehensiveness of feature representation, enhance the expressiveness of features, and make them better reflect the complex relationship between cells. This is then used in S6 to calculate the similarity between data representation and cluster center vector.

[0091] Each perspective provides different types of information. By combining potential features, we can comprehensively consider this information and improve the comprehensiveness of feature representation. Adding information from different perspectives can enhance the expressive power of features and enable them to better reflect the complex relationships between cells.

[0092] S6: Calculate joint probability density and the empirical probability density .

[0093] Q is the empirical probability density, which represents the current similarity distribution between data points and cluster centers. It provides an estimate of the current data distribution and is used to guide the clustering process. is the joint probability density function, which represents the expected similarity distribution. It is the corrected target distribution and guides the model optimization so that the distribution of data points is more consistent with the expected clustering structure.

[0094] Using Student's T distribution as the kernel function, calculate the data representation and cluster center vector The similarity between

[0095]

[0096] in, It can be initialized by K-means algorithm.

[0097] Then calculate the target distribution

[0098]

[0099] The objective function of self-supervision is defined as Kullback-Leibler (KL) divergence loss, that is,

[0100]

[0101] The S7 model trains and identifies spatial domains, achieving spatial region division of different cell types.

[0102] Finally, the loss function The optimizer is passed in for iterative optimization, and the optimizer selects the Adam optimizer.

[0103] The spatial multi-omics data is put into the S4 multi-view encoder model to calculate the The specific calculation process is S6, and the cell label is obtained through the softmax activation function to finally identify the cell type. The Adam optimizer has the advantages of fast convergence and robustness, which can effectively optimize the model parameters and improve the training effect; through the softmax activation function, the model can accurately identify the cell type and is suitable for tasks such as cell clustering.

[0104] By minimizing the KL divergence loss, the model performs adaptive optimization in an unsupervised environment, enhancing the model's self-supervised learning ability. Using the Adam optimizer, which has the advantages of fast convergence and robustness, can effectively optimize model parameters and improve training results. Through the softmax activation function, the model can accurately identify cell types and is suitable for tasks such as cell classification and clustering.

[0105] The sub-technical solution of this embodiment comprehensively analyzes spatial omics data from multiple perspectives, including building multi-omics graph relationships using images, genes, and spatial information, and fusing multiple perspective information through graph convolution encoders and attention mechanisms, ultimately achieving efficient recognition and analysis of multi-omics spatial domain information. This method provides new tools and perspectives for in-depth understanding of the spatial functional relationship between cells, and is expected to play an important role in biomedical research.

[0106] Embodiment 2

[0107] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0108] Embodiment 3

[0109] The purpose of this embodiment is to provide a computer-readable storage medium.

[0110] A computer-readable storage medium stores a computer program, which executes the steps of the above method when executed by a processor.

[0111] Embodiment 4

[0112] The purpose of this embodiment is to provide a spatial domain identification system based on spatial multi-omics technology of heterogeneous graphs, including:

[0113] The gene expression data acquisition module is configured to: acquire spatial omics data and perform data preprocessing to obtain gene expression data;

[0114] The feature representation extraction module is configured to: divide the tissue image of the preprocessed spatial omics data into a plurality of sub-images according to the number of cells by using the spatial position information of the cells, and extract feature representations from the plurality of sub-images;

[0115] The adjacency matrix construction module is configured to: construct adjacency matrices under different perspectives based on the extracted feature representations;

[0116] The graph encoding feature acquisition module is configured as follows: a set of graph encoders is constructed for each view. Each set of graph encoders contains two layers of GCN, which process the adjacency matrix and gene expression data constructed under different viewpoints respectively to obtain graph encoding features. GCN is a graph convolutional neural network.

[0117] The joint latent feature acquisition module is configured to: construct a heterogeneous graph based on the attention mechanism: use the attention mechanism to calculate the latent features of each view in the graph encoding features, and add the latent features under multiple views to obtain the joint latent features of all views;

[0118] The model training module is configured to: calculate the joint probability density and the empirical probability density based on the joint potential features of all perspectives, define the self-supervised objective function based on the joint probability density and the empirical probability density, and construct the training model;

[0119] The recognition module is configured to: input the spatial omics data to be recognized into the trained model to obtain multi-omics spatial domain information.

[0120] Embodiment 5

[0121] The purpose of this embodiment is to provide a computer program product containing instructions, which, when running on a computer, enables the computer to execute the methods and functions involved in any of the above embodiments.

[0122] The steps involved in the apparatus of the above embodiment correspond to the method embodiment 1, and the specific implementation method can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0123] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0124] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A spatial domain identification method based on spatial multi-omics technology of heterogeneous graph, characterized by: include: Acquire spatial omics data and perform data preprocessing to obtain gene expression data; The spatial position information of cells is used to divide the tissue image of the preprocessed spatial omics data into multiple sub-images according to the number of cells, and feature representations are extracted from the multiple sub-images; Construct adjacency matrices from different perspectives based on the extracted feature representation; A set of graph encoders is constructed for each view. Each set of graph encoders contains two layers of GCN, which process the adjacency matrix and gene expression data constructed under different viewpoints respectively to obtain graph encoding features. GCN is a graph convolutional neural network. Constructing heterogeneous graphs based on the attention mechanism: Using the attention mechanism to calculate the latent features of each view in the graph encoding features, the latent features under multiple views are added together to obtain the joint latent features of all views; Calculate the joint probability density and empirical probability density based on the joint potential features of all perspectives, define the self-supervised objective function based on the joint probability density and empirical probability density, and build a training model; Input the spatial omics data to be identified into the trained model to obtain multi-omics spatial domain information; Constructing adjacency matrices from different perspectives ,include: Image perspective: constructing multi-omics graph relationships based on images, , i.e. forming an image icon; Gene perspective: constructing a multi-omics graph relationship based on genes, , that is, forming an expression graph; Spatial perspective: constructing multi-omics graph relationships based on spatial information, , that is, forming a spatial graph; specifically: Construct distance calculation based on image perspective and gene perspective: Calculate the cosine distance of the image between two cells according to the extracted features to construct the image-based distance calculation; Construct an adjacency distance calculation based on a spatial perspective: Calculate the distance between two cells based on the position information, i.e., the Euclidean distance; Building a Multi-View Graph Encoder: Generating A graph encoding convolutional encoder is used to obtain spatial omics embeddings from different perspectives. Specifically: A set of graph encoders is constructed for each view. Each set of graph encoders contains two layers of GCN. The adjacency matrix constructed under different viewpoints is and gene expression data , we can get the graph encoding features from different perspectives of each spatial omics data ; Using attention mechanism to calculate graph encoding features The weights and potential features of each perspective in Finally, we get spatial omics embedding from different perspectives. ; Constructing heterogeneous graphs based on attention mechanism: Using attention mechanism, fusion , and obtain The weight of each perspective Specific: Fusion of multiple perspectives to construct spatially heterogeneous maps and multimodal joint embedding ; Constructing heterogeneous graphs based on the attention mechanism, specifically constructing the adjacency matrix of the heterogeneous graph network; Here, the attention mechanism is used to calculate the weight and potential features of each perspective, and the weight of each perspective is used to calculate the adjacency matrix of the heterogeneous graph network; Then calculate the adjacency matrix of the heterogeneous graph network: Adding the potential features from multiple perspectives is the joint potential feature of all perspectives .

2. The spatial domain identification method based on spatial multi-omics technology of heterogeneous graph according to claim 1 is characterized in that: Data preprocessing was performed on the acquired spatial omics data, including: deleting genes and mitochondrial genes with expression levels less than three cells in the spatial omics data; Then the spatial omics data are regularized and logarithmic, and finally the highly expressed genes with the required amount of data are screened to obtain the gene expression data.

3. The spatial domain identification method based on spatial multi-omics technology of heterogeneous graph according to claim 1 is characterized in that: For multiple sub-images, each cell corresponds to one sub-image.

4. The spatial domain identification method based on spatial multi-omics technology of heterogeneous graph according to claim 1 is characterized in that: Extract feature representations from multiple sub-images, specifically: A feature extractor is used to convert high-dimensional image data into low-dimensional feature representation.

5. The spatial domain identification method based on spatial multi-omics technology of heterogeneous graph according to claim 1 is characterized in that: Each set of graph encoders contains two layers of GCN, where the features extracted by each layer of GCN integrate the information of neighboring nodes.

6. The spatial domain identification method based on spatial multi-omics technology of heterogeneous graph according to claim 1, characterized in that the graph The specific expression of the encoding feature is: Indicates The graph encoding feature of the layer is a matrix with the same size as the input feature matrix; is the adjacency matrix of the input adjacency matrix after preprocessing; yes The degree matrix of is a diagonal matrix whose diagonal elements are the degrees of each node; Indicates The graph encoding feature of the layer is the output of the previous layer; Indicates Layer to The weight matrix of the layer is a learnable parameter matrix; Represents the activation function.

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