A method for spatial domain identification based on spatial multi-omics data

Abstract

The application provides a method for spatial domain identification based on spatial multi-omics data, belongs to the technical field of bioinformatics, and solves the problems that the prior art cannot fully utilize spatial multi-omics data and cannot identify discrete spatial domains, and comprises the following steps: step 1, obtaining a spatial multi-omics comprehensive data set and performing pretreatment; step 2, constructing a deep neural network model; step 3, training the deep neural network model based on the pretreated spatial multi-omics comprehensive data set; and step 4, inputting to-be-detected data into the trained deep neural network model to perform spatial domain identification.

Description

Technical Field

[0001] This invention relates to a method for spatial domain identification based on spatial multi-omics data, belonging to the field of bioinformatics technology. Background Technology

[0002] The advent of single-cell RNA sequencing (scRNA-seq) technology has enabled biologists to acquire expression profiles of the entire genome at the single-cell level, thereby effectively analyzing heterogeneous cell populations in complex samples. The rapid development of single-cell technology has provided a unique perspective for understanding cellular heterogeneity and dynamic changes in complex biological systems. In recent years, emerging multi-omics sequencing technologies such as CITE-seq, SNARE-seq, and TEA-seq have allowed researchers to simultaneously capture multiple omics data, including transcriptome and epigenome data, at the single-cell level, enabling the analysis of cellular heterogeneity from multiple perspectives. However, in the tissues of multicellular organisms, cells typically form specific structures or tissue regions in an interwoven manner based on their specific spatial location and functional similarities within a given tissue. These regions contribute to specific biological functions. For example, hepatocytes in the liver can form liver lobules, and cardiomyocytes in the heart are arranged into myocardial layers. Linking gene expression information with its spatial distribution is crucial for understanding the relevant functions of tissues. Current spatial transcriptome sequencing technologies are mainly divided into in situ sequencing-based technologies, such as 10×Visiu, Slide-seq, and Stereo-seq, and imaging-based technologies, such as MERFISH and seqFISH+. These spatial transcriptome sequencing technologies can acquire not only spot transcriptome data but also spatial location information, making it possible to decipher tissue function and cellular composition. However, these technologies can only capture RNA-seq information, resulting in inherent information scarcity. Therefore, spatial transcriptome technology is expanding into spatial multi-omics, enabling biologists to simultaneously capture expression patterns of different omics data on a single tissue slice. Recently, several spatial multi-omics sequencing methods combining multi-omics sequencing technologies have been developed. For example, DBiT-seq and spatial-CITE-se can simultaneously acquire gene expression profiles, protein data, and spatial location information of a spot. SpatialATAC–RNA-seq and CUT&Tag-RNA-seq can capture gene expression profiles, chromatin accessibility, and spatial location information. This additional omics information provides multiple perspectives for a deeper understanding and analysis of tissue heterogeneity and the function of different tissue structures.

[0003] Identifying spatial domains is a crucial step in analyzing spatial transcriptome data and is fundamental to understanding tissue heterogeneity. Over the years, methods for analyzing spatial transcriptome data have been continuously enriched and developed. However, the amount of information contained in a single omics dataset is limited, especially when tissue structures are complex. Spatial domain identification methods developed for transcriptome data often fail to achieve ideal results. The emergence of spatial multi-omics sequencing technology has broken the limitation of traditional spatial transcriptome sequencing techniques that only capture single omics datasets, leading to information scarcity. Therefore, spatial domain partitioning methods are shifting from applying single spatial transcriptome data to fusing spatial multi-omics data.

[0004] In the analysis of spatial multi-omics data, the information provided by different omics data is complementary, enabling the characterization of organizational structures from multiple perspectives. By integrating spatial multi-omics data, the inherent limitations of single-omics data can be overcome, thereby achieving more accurate spatial domain identification. Although the recently developed SpatialGlue and SSGATE methods can decipher spatial domains using spatial multi-omics data, their performance still needs improvement. Developing a more reliable method for identifying spatial domains using spatial multi-omics data remains an urgent problem to be solved. Furthermore, this invention notes that when these methods identify the same spatial domain discretely distributed within an organization or spatial domains that are structurally subtle but closely connected to other organizational layers, they overemphasize the importance of spatial information while neglecting the attribute information of the spot itself. This results in these organizational structures being divided into different spatial domains and making it difficult to separate adjacent organizational structures. Summary of the Invention

[0005] To address the problem that existing technologies struggle to fully utilize spatial multi-omics data and identify discrete spatial domains, this invention proposes a method for spatial domain identification based on spatial multi-omics data.

[0006] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0007] Step 1: Obtain the spatial multi-omics integrated dataset and perform preprocessing;

[0008] Step 2: Construct a deep neural network model;

[0009] Step 3: Train the deep neural network model based on the preprocessed spatial multi-omics integrated dataset;

[0010] Step 4: Input the test data into the trained deep neural network model for spatial domain recognition.

[0011] Preferably, the spatial multi-omics integrated dataset in step 1 includes a multi-omics dataset composed of RNA-seq data and ATAC-seq data, and a multi-omics dataset composed of RNA-seq data and ADT-seq data.

[0012] Preferably, the preprocessing of the spatial multi-omics integrated dataset in step 1 specifically includes:

[0013] Step 1.1: Filter out genes expressed in fewer than 10 spots in the RNA-seq data. Use the SCANPY package to perform logarithmic transformation and standardization on the filtered gene expression counts. Select the top 3000 highly variable genes in the standardized RNA-seq data for dimensionality reduction. The dimensionality reduction dimension is set to be consistent with the feature dimension of the proteomics. The SCANPY package is a Python-based single-cell analysis toolkit to complete the preprocessing of RNA-seq data.

[0014] Step 1.2: The original protein expression counts in the ADT-seq and ATAC-seq data were normalized to a central log ratio. The normalized ADT-seq and ATAC-seq data were then dimensionality-reduced to complete the preprocessing of the ADT-seq and ATAC-seq data.

[0015] Preferably, the deep neural network model constructed in step 2 includes:

[0016] Feature extraction module and feature fusion module;

[0017] The feature extraction module includes an autoencoder and a multi-scale adaptive graph convolution module;

[0018] Autoencoders are used to extract attribute features from different omics data;

[0019] The multi-scale adaptive graph convolution module includes three MACM sub-modules for extracting structural features from different omics data containing neighbor information of different orders;

[0020] The feature fusion module is used to fuse the attribute features extracted by the autoencoder with the structural features extracted by the multi-scale adaptive graph convolution module.

[0021] Preferably, step 3 specifically includes:

[0022] Step 3.1: Select the first n-1 principal components of the preprocessed ADT-seq data and ATAC-seq data, as well as the preprocessed RNA-seq data, as the input data for the autoencoder;

[0023] Step 3.2: Use the k nearest neighbor algorithm to convert the spatial location information of the input data spot into a neighborhood graph G = (V, E). For a specific point i in the neighborhood graph V, calculate the Euclidean distance between point i and all other points according to the spatial location information, and select the k nearest points as the neighbors of point i.

[0024] Step 3.3: Extract attribute features from the input data using an autoencoder;

[0025] Step 3.4: Extract structural features of the input data using a multi-scale adaptive graph convolution module;

[0026] Step 3.5: Use the feature fusion module to adaptively fuse the attribute features and structural features of the extracted corresponding omics data to obtain the multi-source fusion features of the corresponding omics data;

[0027] Step 3.6: Repeat step 3.5 to obtain the multi-source fusion features of different omics data, concatenate the multi-source fusion features of different omics, and combine the common constraints of multiple losses to obtain the fusion feature Z which contains the attribute information and structural information of multiple omics data;

[0028] Step 3.7: Use the K-means method to perform cluster analysis on the fusion feature Z, identify the spatial domains of different tissues, and complete the training of the deep neural network model.

[0029] Preferably, step 3.3 specifically includes:

[0030] Step 3.3.1: Extract gene expression attribute features of different sopts in the input data based on the encoder in the autoencoder;

[0031] Step 3.3.2: Reconstruct the gene expression attribute features of different sopts based on the decoder in the autoencoder to obtain the attribute features of the input data;

[0032] Step 3.3.3: Calculate the mean square error between the reconstructed data and the original data from the input data and use it as the reconstruction loss L. R If reconstruction results in a loss of L R If the value is greater than the first preset value, repeat step 3.3.2 until the reconstruction loss L is reached. R Less than the first preset value;

[0033] The gene expression attribute feature expression of RNA-seq data is:

[0034]

[0035] In formula (1), Encoder for RNA-seq data;

[0036] The gene expression attribute feature expression of ADT-seq data is:

[0037]

[0038] In formula (1), Encoder for ADT-seq data;

[0039] The expression for gene expression profile reconstruction from RNA-seq data is:

[0040]

[0041] In formula (3), Different layers of the decoder for RNA-seq data;

[0042] The expression for gene expression profile reconstruction from ADT-seq data is:

[0043]

[0044] In formula (4), Different layers of the decoder for ADT-seq data;

[0045] Reconstruction loss L R The expression is:

[0046]

[0047] In formula (5), n is the number of spots.

[0048] Preferably, step 3.4 specifically includes:

[0049] Step 3.4.1: Obtain a set of learned feature matrices for all spots based on the structural features of the input data;

[0050] Step 3.4.2: Calculate the feature codes containing k-order neighbor information based on a set of learned feature matrices of all spots. Merge the feature codes of k-order neighbor information through the MACM submodule to obtain a set of multi-scale feature codes H containing different neighbor information.

[0051] Step 3.4.3: Perform average pooling on the feature codes at each scale and concatenate them together. Use the MLP module to adaptively learn the importance of feature codes at different scales and calculate the importance score matrix.

[0052] Step 3.4.4: Use the importance scoring matrix to fuse the multi-scale feature encoding H containing neighbor information of different orders to obtain the final feature representation h containing multi-scale structural information;

[0053] The expression for the feature encoding of k-order neighbor information is:

[0054] h k =A k Tanh(XW (k) (6);

[0055] In formula (6), h k Let A be the feature encoding containing information about the k-th order neighbors, A be the adjacency matrix, Tanh be the activation function, X be the omics feature matrix, and W be the feature encoding. (k) The learnable parameters for the k-th order neighbor information;

[0056] The expression for the multi-scale feature encoding H of different neighbor information is:

[0057] H = [h1; h2; h3; ...; h k (7);

[0058] The expression for performing average pooling and concatenation on the feature encodings is:

[0059] h m =[f mean (h1,dim=0),f mean (h2,dim=0),…,f mean (h k [,dim=0)] ​​(8);

[0060] In formula (8), f mean To perform average pooling on the feature matrix, h m Encode features at different scales after splicing;

[0061] The expression for the importance score matrix is:

[0062] W = softmax(f m (h m )) (9);

[0063] In formula (9), f m To use the MLP module to access h m Perform importance-adaptive learning;

[0064] The formula for calculating the feature representation h of multi-scale structural information is:

[0065] h = h1W (0) +h2W (1) +h3W (3) +…+h k W (k) (10);

[0066] In formula (10), h is the feature representation that incorporates multi-scale structural information, and W (k) The importance of the feature matrix that contains information about the k-th order neighborhood.

[0067] Preferably, step 3.5 specifically includes:

[0068] Step 3.5.1: Perform multi-step fusion of the attribute features extracted by the autoencoder and the multi-scale structural features of the corresponding omics data extracted by the multi-scale adaptive graph convolution module to obtain the multi-source fusion feature H of the corresponding omics data. RNA ;

[0069] Step 3.5.2: Repeat step 3.5.2 to obtain the multi-source fusion feature H of the omics data. ADT ;

[0070] Step 3.5.3: Utilize the graph decoder to perform node embedding reconstruction on the multi-source fusion features of different omics, where the graph decoder and the autoencoder have a symmetrical structural distribution;

[0071] Step 3.5.4: Calculate the graph feature reconstruction loss L for different omics data. G If the graph feature reconstruction loss is greater than the second preset value, repeat steps 3.5.1-3.5.3 until the graph feature reconstruction loss is less than the second preset value, and output the reconstructed multi-source fusion features of different omics.

[0072] Multi-source fusion features H of omics data RNA The calculation formula is:

[0073]

[0074] In formulas (11)-(13), a is a hyperparameter, n is the number of layers in the graph encoder, A is the adjacency matrix constructed based on spatial location information, and H... RNA This represents a multi-source feature fusion representation of attribute features and multi-scale structural features in RNA omics data. These are the attribute features extracted from different layers of the autoencoder.

[0075] The expression for node embedding reconstruction is:

[0076]

[0077]

[0078] In formulas (14) and (15), Z RNA and Z ADT The reconstructed omics embedding features include neighbor information and relevant topological information. and It is an omics embedding decoder for different omics data;

[0079] Image feature reconstruction loss L G The calculation formula is:

[0080]

[0081] Preferably, step 3.6 specifically includes:

[0082] Step 3.6.1: Concatenate the multi-source fusion features of different omics after reconstruction to obtain the feature representation Z;

[0083] Step 3.6.2: Introduce graph-based constraints, reconstruct the graph structure based on feature representation Z, and calculate the binary cross-entropy loss as the structure reconstruction loss L. S And calculate the contrastive learning loss L con ;

[0084] Step 3.6.3: Based on structural reconstruction loss L S Contrast learning loss L con Reconstruction loss L R And graph feature reconstruction loss L G Construct the total loss L, and train the deep neural network model based on the total loss L;

[0085] The formula for calculating the feature representation Z is:

[0086] Z = [H] RNA H ADT (17);

[0087] Structural reconstruction loss L S The calculation formula is:

[0088] A' = sigmoid(ZZ) T (18);

[0089]

[0090] In formulas (18) and (19), A' is the reconstructed image obtained by decoding based on the fusion feature Z;

[0091] Contrast learning loss L con The calculation formula is:

[0092]

[0093] In formula (20), N i Let i be the neighborhood set of spot, and cos(Z) i Z j ) represents the cosine similarity between spot i and j, and τ is a hyperparameter;

[0094] The formula for calculating the total loss L is:

[0095] L = L R +L G +L con +L S (twenty one).

[0096] The beneficial effects of this invention are:

[0097] 1. This invention proposes a spatial domain identification method, spaMGCN, which combines an autoencoder and a multi-scale adaptive graph convolutional network. spaMGCN integrates transcriptomic and epigenetic data, combining attribute information from different omics data of a spot with structural information considering the attribute information of adjacent spots, achieving accurate identification of the same spatial domain in a discrete distribution and clear separation of adjacent spatial domains.

[0098] 2. This invention demonstrates that the spaMGCN model (deep neural network model) achieves excellent spatial domain recognition performance on various types of spatial multi-omics datasets. Compared with other state-of-the-art spatial domain recognition methods, the spaMGCN model exhibits superior performance across multiple evaluation metrics.

[0099] 3. The spaMGCN model constructed in this invention can also process multiple slice datasets in parallel, while eliminating batch effects in spatial transcriptome data. Attached Figure Description

[0100] Figure 1 A flowchart of a method for spatial domain identification based on spatial multi-omics data provided by the present invention;

[0101] Figure 2 A schematic diagram of the structure of the deep neural network model provided by this invention;

[0102] Figure 3 This is a comparison chart showing the spatial domain recognition performance of four datasets provided by this invention using different methods. Figure 3 middle, Figure 3 'a' represents the clustering performance evaluation metric of the spaMGCN method compared to other methods on the S1 dataset. Figure 3 b represents the clustering performance evaluation metric of the spaMGCN method compared to other methods on the S3 dataset. Figure 3 c is a diagram comparing the spatial domain recognition performance of the spaMGCN method with other methods on the Mouse Thymu dataset. Figure 3 d is a schematic diagram comparing the spatial domain recognition performance of the spaMGCN method with other methods on the Mouse Spleen dataset;

[0103] Figure 4This is a visualization of the spatial domain prediction results of this invention and other methods on the human lymph node S3 dataset;

[0104] Figure 5 This is a comparison chart showing the performance of different spatial multi-omics spatial domain recognition methods provided by the present invention for discrete spatial domain recognition. Figure 5 middle, Figure 5 a is a schematic diagram illustrating the F1 score of this invention and other methods for T-cell zone identification on the Mouse Spleed dataset. Figure 5 b is a schematic diagram illustrating the F1 score of follicle identification on the human lymph node S3 dataset using the present invention and other methods. Figure 5 c is a schematic diagram illustrating the actual distribution of T cell zones. Figure 5 d、 Figure 5 e and Figure 5 f is a schematic diagram illustrating the prediction results of the three methods;

[0105] Figure 6 This is a schematic diagram illustrating the capsule recognition performance of different methods provided by the present invention. Figure 6 middle, Figure 6 a and Figure 6 b is a schematic diagram comparing the spatial domains identified by the spaMGCN method and the SpatialGlue method. Figure 6 c is a schematic diagram showing the distribution of capsules identified by spaMGCN and the actual distribution.

[0106] Figure 7 This is a diagram showing the distribution of transcriptome data before and after feature reconstruction provided by the present invention. Figure 7 middle, Figure 7 a is a schematic diagram of the data distribution of slice 3, slice 1, and slice 2. Figure 7 c represents the data distribution of the three slices after reconstruction using spaMGCN. Figure 7 b and Figure 7 d is a schematic diagram of the distribution of spots in the same spatial domain after data reconstruction;

[0107] Figure 8 This is a performance comparison chart of different methods on the Human Placenta dataset provided by this invention. Figure 8 middle, Figure 8 a, Figure 8 b and Figure 8 c is a schematic diagram illustrating the cell clustering performance of different methods. Figure 8 d、 Figure 8 e Figure 8 f、 Figure 8 g and Figure 8h is a schematic diagram of the feature space of different methods visualized using umap;

[0108] Figure 9 A difference analysis diagram of the spatial domains partitioned by spaMGCN provided in this invention. Figure 9 middle, Figure 9 a is a bubble chart of differentially expressed genes. Figure 9 b is a bubble diagram of the epiprotein. Figure 9 c is a schematic diagram showing the distribution of differentially expressed genes strongly correlated with the actual spatial domain in tissues. Figure 9 d is a visualization of spatially differentially related proteins. Detailed Implementation

[0109] Specific implementation method one: Combining Figure 1 and Figure 2 This embodiment describes the spaMGCN method, which is a proposed method for spatial domain identification based on spatial multi-omics data. Figure 1 As shown, the steps of a method for spatial domain identification based on spatial multi-omics data described in this embodiment include:

[0110] S1: Obtain and preprocess the spatial multi-omics integrated dataset;

[0111] The spatial multi-omics integrated dataset includes a multi-omics dataset composed of RNA-seq data and ATAC-seq data, and a multi-omics dataset composed of RNA-seq data and ADT-seq data;

[0112] This implementation method obtained five multi-omics datasets from the authors of the SpatialGlue and SpaMosaic papers. These datasets were sequenced using three spatial multi-omics sequencing technologies: 10x Genomics Visium, Stereo-CITE-seq, and SPOTS, which can simultaneously measure protein markers, the whole transcriptome, and spatial location information. The Mouse Thymus dataset was sequenced using Stereo-CITE-seq technology, the Mouse Spleen dataset was sequenced using SPOTS technology, and the human lymphnode dataset contained data from three slices, all sequenced using 10x Genomics Visium technology. In addition, this implementation method obtained the human_placenta dataset, a single-cell resolution human placenta spatial multi-omics dataset, from the Broad Institute Single Cell Portal SCP2601. This dataset provides cellular gene expression data, chromatin accessibility data, and spatial location information.

[0113] Preprocessing specifically includes:

[0114] S101: Filter out genes expressed in fewer than 10 spots in the RNA-seq data, use the SCANPY package to perform logarithmic transformation and standardization on the filtered gene expression counts, select the top 3000 highly variable genes in the standardized RNA-seq data for dimensionality reduction, and set the dimensionality reduction dimension to be consistent with the feature dimension of epiproteomics. The SCANPY package is a Python-based single-cell analysis toolkit to complete the preprocessing of RNA-seq data.

[0115] S102: The original protein expression counts in the ADT-seq and ATAC-seq data were normalized by a central log ratio. The normalized ADT-seq and ATAC-seq data were then dimensionality-reduced to complete the preprocessing of the ADT-seq and ATAC-seq data.

[0116] S2: Construct a deep neural network model;

[0117] The spaMGCN model constructed in this implementation is a deep neural network model, such as... Figure 2 As shown, it includes a feature extraction module and a feature fusion module;

[0118] The feature extraction module includes an autoencoder and a multi-scale adaptive graph convolution module;

[0119] Autoencoders are used to extract attribute features from different omics data;

[0120] The multi-scale adaptive graph convolution module includes three MACM sub-modules for extracting structural features from different omics data containing neighbor information of different orders;

[0121] The feature fusion module is used to fuse the attribute features extracted by the autoencoder with the structural features extracted by the multi-scale adaptive graph convolution module.

[0122] S3: Training deep neural network models based on preprocessed spatial multi-omics integrated datasets;

[0123] S301: Constructing a neighborhood graph. In this implementation, the k-nearest neighbor algorithm is used to convert the spatial location information of the spot into a neighborhood graph G = (V, E). Here, V represents the set of points, E represents the set of edges connecting the points, and k is the number of neighbors. Specifically, for a specific point i belonging to V, the Euclidean distance between this point and all other points is calculated based on the spatial location information, and the k nearest points are selected as its neighbors.

[0124] S302: Attribute features of different omics data are extracted using an autoencoder. The gene expression attribute feature extraction process for different sopts is simply represented as follows:

[0125]

[0126] In formula (1), Encoder for RNA-seq data;

[0127] The extraction of attribute features from other omics data is similar; the following examples all use protein as an example:

[0128]

[0129] In formula (1), The encoder for ADT-seq data captures multiple omics attributes from different spots; the decoder is the inverse process of the encoder, used to reconstruct different omics data. The gene expression profile reconstruction process is represented as follows:

[0130]

[0131] In formula (3), Different layers of the decoder for RNA-seq data;

[0132] The reconstruction process for other omics data is as follows:

[0133]

[0134] In formula (4), Different layers of the decoder for ADT-seq data;

[0135] This implementation uses the mean squared error between the reconstructed data and the original data from different omics systems as the reconstruction loss L. R To ensure that the features extracted by the autoencoder remain consistent with the original features, it is represented as follows:

[0136]

[0137] In formula (5), n is the number of spots. Extracting the attribute information of the spots themselves helps to divide the same spatial domain that is spatially discrete into one.

[0138] S303: This implementation utilizes a multi-scale adaptive convolutional module to extract structural features and performs multi-step fusion of attribute and structural features. Inspired by multi-scale graph clustering networks, this implementation leverages its proposed MACM submodule to capture graph structural information and adaptively fuse multiple feature matrices containing neighborhood information of different orders, obtaining more complex and comprehensive structural features. The MACM submodule conveys multi-order neighbor information by constructing multiple high-order adjacency matrices. This method overcomes the limitations of direct adjacency and merges multi-order neighbor information, thus making the structural representation of the spot more comprehensive and richer. The specific implementation is as follows:

[0139] S30301:X∈R N×d Let N be a set of omics feature matrices for all spots on a tissue slice, where N is the number of spots and d is the feature dimension. The feature encoding representation including k-order neighbor information is as follows:

[0140] h k =A k Tanh(XW (k) (6);

[0141] In formula (6), h k Let A be the feature encoding containing information about the k-th order neighbors, A be the adjacency matrix, Tanh be the activation function, X be the omics feature matrix, and W be the feature encoding. (k) Let H be the learnable parameters for the k-th order neighbor information. In this way, this implementation can obtain a set of multi-scale feature codes H containing different neighbor information, which are represented as follows:

[0142] H = [h1; h2; h3; ...; h k (7);

[0143] S30302: The feature codes for each scale are average-pooled and concatenated together, as shown below:

[0144] h m =[f mean (h1,dim=0),f mean (h2,dim=0),…,f mean (h k [,dim=0)] ​​(8);

[0145] In formula (8), f mean To perform average pooling on the feature matrix, h m Encode features at different scales after splicing;

[0146] S30303: An MLP module is used to adaptively learn the importance of feature encodings at different scales. The importance score matrix is ​​represented as follows:

[0147] W = softmax(f m (h m )) (9);

[0148] In formula (9), f m To use the MLP module to access h m Perform importance-adaptive learning;

[0149] S30304: The importance scoring matrix is ​​used to fuse multi-scale feature codes containing information about neighbors of different orders, resulting in a final feature representation containing multi-scale structural information, as follows:

[0150] h = h1W (0) +h2W (1) +h3W (3) +…+h k W (k) (10);

[0151] In formula (10), h is the feature representation that incorporates multi-scale structural information, and W (k) The importance of the feature matrix that contains information about the k-th order neighborhood.

[0152] S30305: The structural feature extraction module consists of a three-layer MACM as a graph encoder to extract structural features. In the process of extracting structural features, this embodiment fuses the attribute features extracted from different layers of the autoencoder with the multi-scale structural features extracted by the MACM module in multiple steps, thereby ensuring the full fusion of attribute information and structural information. This avoids only considering the spatial structural information of the central node while ignoring the attribute information of the spot itself during the feature extraction process. It is represented as follows:

[0153]

[0154] In formulas (11)-(13), a is a hyperparameter, n is the number of layers in the graph encoder, A is the adjacency matrix constructed based on spatial location information, and H... RNA This represents a multi-source feature fusion representation of attribute features and multi-scale structural features in RNA omics data. The attribute features extracted from different layers of the autoencoder; the extraction of multi-scale structural information can take into account the fact that multicellular biological tissues are often clustered together in reality during the spatial domain partitioning process, so that spaMGCN does not lose its accuracy in recognizing continuous and clustered spatial domains. Through a multi-step fusion approach, spaMGCN comprehensively considers the attribute and structural information of different omics data, so that the extracted low-dimensional representation can be applied to the recognition of more types of spatial domains.

[0155] S304: Node embedding reconstruction is performed on multi-source fusion features from different omics using a graph decoder. The decoder and encoder have symmetrical structures, which simplifies the learning process. The node embedding reconstruction is represented as follows:

[0156]

[0157] In formulas (14) and (15), Z RNA and Z ADT The reconstructed omics embedding features include neighbor information and relevant topological information. and Omics embedding decoders for different omics data;

[0158] S305: Calculate the graph feature reconstruction loss for different omics data, as follows:

[0159]

[0160] Graph feature reconstruction loss is the calculation of reconstruction loss for omics embeddings that include neighbor information. Omics embedding reconstruction is crucial for a deeper understanding of the intrinsic properties and spatial information of spot.

[0161] S306: Multi-omics Data Fusion: To further fuse the low-dimensional representations of different omics, this implementation first concatenates the multi-source fusion features of different omics, as shown below:

[0162] Z = [H] RNA H ADT (17);

[0163] The fusion of multiple omics features enables the model to analyze the spatial domain from multiple perspectives. Furthermore, inspired by Deep Graph Structural Infomax, this implementation introduces graph-based constraints to facilitate the learning of point representations. This implementation reconstructs the graph structure based on the feature representation Z and calculates the binary cross-entropy loss as the structural reconstruction loss L. S , means as follows:

[0164] A' = sigmoid(ZZ) T(18);

[0165]

[0166] In formulas (18) and (19), A' is the reconstructed image obtained by decoding based on the fusion feature Z;

[0167] To make the feature representation Z of spots more informative and discriminative, this implementation calculates a contrastive learning loss similar to InfoNCE, which makes physically adjacent spots closer to each other in the feature space, and non-adjacent spots farther apart in the feature space, as shown below:

[0168]

[0169] In formula (20), N i Let i be the neighborhood set of spot, and cos(Z) i Z j Let be the cosine similarity between spots i and j, and τ be a hyperparameter; for a given spot, its neighboring spots are defined as positive pairs, and its non-neighboring spots are defined as negative pairs. The final overall loss is defined as:

[0170] L = L R +L G +L con +L S (twenty one).

[0171] S307: After acquiring spatial multi-omics fusion data, the K-means method is used to perform cluster analysis on the fusion feature Z to identify the spatial domains of different tissues and complete the training of the deep neural network model.

[0172] S4: Input the test data into the trained deep neural network model for spatial domain recognition.

[0173] Specific Implementation Method Two: To verify the technical effects of Specific Implementation Method One, this implementation method designs the following experiment:

[0174] This implementation first conducted experiments on three sets of human lymph node spatial multi-omics datasets measured using 10x Genomics Visium technology, comparing the spaMGCN method with six other algorithms. Figure 3 a, Figure 3b presents the clustering performance evaluation metrics of these methods on the S1 and S3 datasets, including AMI, NMI, and ARI. The results show that spaMGCN outperforms other methods in all three clustering metrics. Furthermore, during the experiments, this implementation method found that most methods for identifying spatial domains using spatial multi-omics data outperform conventional methods for identifying spatial domains using single-omics data. This result further verifies that identifying spatial domains using spatial multi-omics data is effective and necessary. This is because, compared to single-omics data, these multi-omics data provide richer information on organizational heterogeneity and can explain different organizational structures from different perspectives. Therefore, integrating multi-omics data for analysis can help this implementation method identify spatial domains more accurately.

[0175] To evaluate the generalization ability of the spaMGCN model, experiments were conducted on two other spatial multi-omics datasets measured using Stereo-CITE-seq and SPOTS techniques: Mouse Thymu and Mouse Spleen. Figure 3 Tables c and 3d illustrate the spatial domain identification performance of different methods on the Mouse Thymu and Mouse Spleen datasets, respectively. Table 1-3 shows the data type performance of different methods on all datasets. spaMGCN also achieved the best spatial domain identification performance on both datasets. Overall, spaMGCN achieves good performance when faced with spatial multi-omics data measured by different sequencing technologies, demonstrating its strong generalization ability. In the experimental setup, this implementation method applied a classic single-cell multi-omics clustering method, scDMC, to identify spatial domains. Its performance on all datasets was inferior to methods using spatial multi-omics data for spatial domain identification. This is attributed to its failure to utilize spatial location information, a key element for spatial domain identification, leading to the fragmentation of most spatially continuous domains and the emergence of a series of isolated points. However, compared to other methods using single-omics data for spatial domain identification, its performance varied across different datasets. This implementation method hypothesizes that for spatially continuous organizations, spatial location information is often more important; when spatial domains are relatively discrete, multiple omics features can often provide richer node attribute information, helping to identify discontinuous but structurally similar spatial domains.

[0176] To further demonstrate the spatial domain recognition performance of spaMGCN, this implementation visualizes the clustering results of spaMGCN and four other spatial domain recognition methods on human lymph node S3, such as... Figure 4As shown, overall, the prediction results of spaMGCN are largely consistent with the actual situation in the spatial domain. The important tissue structure of medulla is also clearly predicted and separated from the cortex and capsule, which is highly consistent with the fact that human lymph nodes can be roughly divided into the external cortical region and the internal medullary region.

[0177] Table 1

[0178] spaMGCN 0.4626 0.1477 0.2824 0.244 0.2926 SpatialGlue 0.45296 0.0974 0.2385 0.2273 0.2314 SSGATE 0.29258 0.07242 0.15584 0.13098 0.18134 GraphST 0.16294 0.0128 0.11562 0.07936 0.13338 GAAEST 0.0656 0.0084 0.06104 0.0197 0.08188 scMDC 0.2673 0.0373 0.094 0.0834 0.0777 SpaGIC 0.1372 0 0.0967 0.0921 0.1138

[0179] Table 2

[0180]

[0181]

[0182] Table 3

[0183] spaMGCN 0.5012 0.2064 0.4209 0.3779 0.4347 SpatialGlue 0.48472 0.20422 0.379 0.3654 0.3839 SSGATE 0.3914 0.13582 0.30096 0.255 0.32834 GraphST 0.27668 0.03896 0.23712 0.18262 0.25344 GAAEST 0.1060 0.0240 0.10952 0.03398 0.11706 scMDC 0.3716 0.0666 0.16 0.1413 0.1312 SpaGIC 0.224 0.0398 0.2064 0.2088 0.2302

[0184] To demonstrate that spaMGCN can more accurately identify the same spatial domain that is discretely distributed within an organization. Figure 5 The performance of different methods in identifying discrete spatial domains is demonstrated.

[0185] In multicellular organisms, the tissue structure is mostly layered and continuous. However, there are also cell clusters that belong to the same tissue structure and perform the same function, but are discretely distributed throughout the tissue. For example, in the kidneys, T cell zones play a crucial role and are important aggregation areas of immune cells in the spleen, responsible for monitoring and responding to pathogens and foreign substances in the system. They are often discretely distributed in kidney tissue. In lymph nodes, follicles play a vital role in the immune system. They are mainly composed of B cells and are the primary source of B cells. Follicles filter and capture antigens (such as bacteria and viruses) in lymph nodes, ensuring that these antigens can be recognized by the immune system and trigger an appropriate immune response. They are also discretely distributed in lymphatic tissue. These discrete tissue structures also play important roles, and clear identification of these tissue structures is crucial. To verify the effectiveness of spaMGCN in re-identifying discrete tissue structures, this implementation analyzes two datasets: Mouse Spleen and human lymph node S3. Different spatial domain recognition methods are used to analyze these two datasets. Then, the Hungarian algorithm is used to match the predicted results with the true labels, and the F1 scores for T-cell zone recognition on the Mouse Spleen dataset and follicle recognition on the human lymph node S3 dataset are calculated using different methods. Figure 5 a and Figure 5 As shown in b. To more intuitively demonstrate the performance of spaMGCN in recognizing discrete spatial domains, this implementation visualizes the recognition performance of spaMGCN, SpatialGlue, and SSGATE, three methods utilizing spatial multi-omics data, on the discrete spatial domain of T cellZone. Figure 5 c shows the actual distribution of T cell zones. Figure 5 Tables 5d, 5e, and 5f illustrate the prediction results of the three methods. Observing the red box, we can see that spaMGCN's prediction best matches the real situation. This is attributed to the fact that during model training, this implementation method utilizes an autoencoder to extract the spot's attribute information and uses MACM to extract the spot's multi-order neighbor information, thus making the boundaries clear and able to classify discrete regions into the same category. SSTAGE is a dual-path graph neural network model; however, due to its overemphasis on the importance of spatial information and neglect of the spot's own attribute information, its boundaries are unclear.

[0186] Furthermore, to further verify spaMGCN's ability to separate adjacent tissue structures, this implementation was tested on a lymph node dataset. Lymph nodes are an important component of the lymphatic system and play a vital role in the human immune system. They are generally composed of the mantle, cortex, medulla, and other small tissues. Because the capsule is adjacent to the cortex, pericapsular adipose tissue often classifies these two tissues into the same category during spatial domain segmentation, making it difficult to separate the tissue structures. To demonstrate spaMGCN's performance in recognizing such adjacent tissues in lymphatic tissue, this implementation was compared with the spatial domains identified by the current best-performing SpatialGlue method, such as... Figure 6 As shown; observation Figure 6 As can be seen from a and 6b, spaMGCN clearly identifies capsule tissue without mixing with the surrounding lymphatic fat and cortex; within the spatial domain identified by SpatialGlue, the capsule is incorporated into its adjacent, larger cortex and Pericapsular adipose tissue structures. To further highlight the recognition performance of spaMGCN for this important tissue structure, this embodiment... Figure 6 In C, the distribution of capsules identified by spaMGCN and the actual distribution are specifically visualized. It can be seen that the distribution identified by spaMGCN is consistent with the actual distribution, which can effectively solve the problem of adjacent tissues being classified into the same spatial domain.

[0187] In actual analysis, there are datasets containing multiple slice data. Parallel processing of multiple slice data can greatly simplify the analysis process. Therefore, this implementation merges the adjacency matrices of three slice datasets of human lymph nodes. Similarly, this implementation performs parallel analysis on datasets containing three slice data under five random seeds using five-fold cross-validation. The performance is shown in Table 4.

[0188] Table 4

[0189] humanlymphnodeS1* 0.2627 0.4201 0.4384 humanlymphnodeS2* 0.2465 0.3272 0.3486 humanlymphnodeS3* 0.3272 0.4238 0.4383 humanlymphnodeS1 0.2824 0.4025 0.4209 humanlymphnodeS2 0.2440 0.3570 0.3779 humanlymphnodeS3 0.2926 0.4162 0.4347

[0190] As shown in Table 4, the performance of spaMGCN in parallel analysis of multiple slices is comparable to that of individual analysis, demonstrating that spaMGCN can perform parallel analysis of multi-slice datasets while maintaining comparable spatial domain recognition performance. Furthermore, during the experiment, this implementation method used UMAP to visualize the data distribution of the multi-slice dataset before and after reconstruction, such as... Figure 7 As shown.

[0191] observe Figure 7 As can be seen, the data distribution of slice 3 deviates significantly from that of slices 1 and 2, which is due to the batch effect. Figure 7 c shows the data distribution of the three slices after reconstruction by spaMGCN. It can be seen that the data from the three slices are mixed together, and the batch effect has been successfully removed. Furthermore, compared... Figure 7 In images b and 7d, it is evident that spots in the same spatial domain cluster together after data reconstruction, demonstrating to some extent that spaMGCN can interpolate transcriptome data, making the reconstructed data more consistent with actual biological distribution. These findings further demonstrate that spaMGCN is also competitive in removing data noise.

[0192] To verify the applicability of spaMGCN to high-resolution spatial multi-omics data, this implementation method acquired high-resolution spatial multi-omics data of human placenta in a recent study. spaMGCN was compared with four other methods. Figure 8The diagram illustrates the cell clustering performance of different methods. The comparison shows that two spatial multi-omics methods exhibit the worst cell clustering performance on high-resolution spatial multi-omics datasets. SSGATE_F and scMDC, two single-cell multi-omics clustering methods, outperform SpatialGlue and SSGATE_S, making them more suitable for such high-resolution spatial multi-omics data. The spatial multi-omics clustering method spaMGCN proposed in this embodiment achieves the best performance. This is because spaMGCN utilizes MAM to obtain multi-scale structural information, allowing it to comprehensively consider multi-level neighbor information of the graph. Simultaneously, it uses an autoencoder to preserve the attribute information of different spots, making it applicable to both low-resolution and high-resolution spatial multi-omics datasets. To visually demonstrate the distribution of different cell types in the feature spaces of different methods, this embodiment uses UMAP to visualize the feature spaces of different methods, such as... Figure 8 As shown in dh. The umap plot shows that the separation of different cell types is relatively good in the feature space of spaMGCN, and the cell cluster separation in SSGATE_F is also relatively good, but there are instances of identical cell clusters being fragmented. In the feature spaces of SpatialGlue and scMDC, cells of the same type do not aggregate well. In SSGATE_S, due to the smooth transition of graph convolution, the features of different cell types lack distinguishability and are difficult to separate.

[0193] Marker genes can be used to annotate specific cell types. By studying their expression patterns, this implementation can elucidate cellular heterogeneity and potential gene regulatory mechanisms. Spatial patterns of specific gene markers also exist between different spatial domains. To further demonstrate the accuracy of spatial domain division using the spaMGCN method, this implementation employed a non-parametric Wilcoxon rank-sum test to select the top three differentially expressed features (genes, epiproteins, and open chromatin regions) for each predicted spatial domain, and validated their association with actual tissue structures using previous research papers. Furthermore, this implementation generated bubble diagrams of differentially expressed genes and epiproteins, such as... Figure 9 As shown in a and 9b, some of the predicted domain-specific features show significant differences across different spatial domains, and can identify specific spatial domains to some extent. These may be potential domain-specific genes and epithelial proteins. This embodiment also visualizes the distribution of some differentially expressed genes strongly correlated with actual spatial domains in tissues. For example: Figure 9In the annotation, CCL21, TRBC2, and TRAC clearly indicate the Cortex region. Previous studies have shown that CCL21 is mainly expressed in lymphoendothelial cells, which is consistent with the actual annotation region. The spatial distribution of CLEC4G and CCL14 is consistent with the medulle region. The CLEC4G gene encodes a glycan-binding receptor and a member of the C-type lectin family, which plays a role in the immune response. This is highly consistent with the function of the medulle in providing lymphocytes. The spatial distribution pattern of FABP4, GPX3, GSN, and ADIRF is consistent with the Pericapsular Adipose tissue. FABP4 is mainly expressed in cells encoding lipoproteins. ADIR plays a role in adipocyte development, promoting adipogenic differentiation and stimulating major adipogenic factors in the early stages of pre-adipocyte differentiation. This is very consistent with the fact that the Pericapsular Adipose tissue is mainly composed of adipocytes. The distribution of CXCL13 is consistent with the follice region. It is a T cell exhaustion marker and can be used for lymphocyte homing and localization in follicles of secondary lymphoid tissue. By analyzing the spatial domains delineated by spaMGCN, this implementation method can identify some marker genes that are strongly associated with the function of the spatial domains or have been confirmed. This further proves the effectiveness of spaMGCN, which can identify spatial domains consistent with biological facts. In addition, these domain-specific genes can help biologists analyze the cellular composition of different tissue structures, providing strong support for further understanding tissue heterogeneity.

[0194] In addition, this implementation also performed differential analysis on the epiprotein data in the human lymph node S3 dataset. Figure 9 b demonstrates spatially differentially expressed proteins identified using spatial domain analysis with the aid of spaMGCN. It can be seen that some epiproteins are strongly correlated with certain regions. This implementation further visualizes these strongly correlated spatially differentially expressed proteins, such as... Figure 9 As shown in d, HLA-DRA is mainly expressed in B lymphocytes, which is consistent with the fact that the Cortex region is predominantly B-cells, indirectly reflecting that the spatial domain division of spaMGCN is biologically based. Figure 9 In d, the spatial distribution of HLA-DRA and CD3E proteins is consistent with the Cortex region and is more effective at identifying the Cortex than the CCL21 gene. This also reflects the necessity of spatial domain division by integrating multiple omics data, and explains why spatial domain boundaries divided using multiple omics data are clearer and more consistent with biological facts.

[0195] During the differential analysis, this implementation method analyzed the spatial domains delineated by spaMGCN. The results showed that the distribution and related functions of spatially differentiated features in some domains were strongly correlated with the actual spatial domains, further demonstrating that the spatial domains delineated by spaMGCN possess biological significance and are consistent with biological facts. Furthermore, some genes and epiproteins exhibiting spatial patterns, although not previously shown to be associated with certain tissue structures, showed a high degree of consistency in their spatial distribution patterns with real biological tissues. These may be potential spatial domain markers, indicating that the spaMGCN model has potential value and application prospects in the identification of spatial domain-specific features, and is expected to provide guidance for biologists.

[0196] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for spatial domain identification based on spatial multi-omics data, characterized in that, The steps of the method for spatial domain identification based on spatial multi-omics data include: Step 1: Obtain the spatial multi-omics integrated dataset and perform preprocessing; Step 2: Construct a deep neural network model; The deep neural network model constructed in step 2 includes: Feature extraction module and feature fusion module; The feature extraction module includes an autoencoder and a multi-scale adaptive graph convolution module; The autoencoder is used to extract attribute features from different omics data; The multi-scale adaptive graph convolution module includes three MACM sub-modules, which are used to extract structural features of different omics data containing neighbor information of different orders; The feature fusion module is used to fuse the attribute features extracted by the autoencoder with the structural features extracted by the multi-scale adaptive graph convolution module. Step 3: Train the deep neural network model based on the preprocessed spatial multi-omics integrated dataset; Step 3 specifically includes: Step 3.1: Select the first part of the preprocessed ADT-seq data and ATAC-seq data. n -1 principal component and preprocessed RNA-seq data were used as input data for the autoencoder; Step 3.2: Utilize k The nearest neighbor algorithm converts the spatial location information of the input data spot into a neighborhood graph. G =( V, E For neighborhood graphs V A specific point i Calculate points based on spatial location information i Euclidean distances to all other points, and choose k The nearest point is taken as the point. i Neighbors; Step 3.3: Extract attribute features from the input data using the autoencoder; Step 3.4: Extract the structural features of the input data using the multi-scale adaptive graph convolution module; Step 3.5: Adaptively fuse the attribute features and structural features of the extracted corresponding omics data using the feature fusion module to obtain the multi-source fusion features of the corresponding omics data; Step 3.6: Repeat step 3.5 to obtain the multi-source fusion features of different omics data. Concatenate the multi-source fusion features of different omics and combine them with the common constraints of multiple losses to obtain fusion features that contain multiple omics data attribute information and structural information. ; Step 3.7: Use the K-means method to perform cluster analysis on the fused feature Z, identify the spatial domains of different tissues, and complete the training of the deep neural network model; Step 4: Input the test data into the trained deep neural network model for spatial domain recognition.

2. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, In step 1, the spatial multi-omics integrated dataset includes a multi-omics dataset composed of RNA-seq data and ATAC-seq data, and a multi-omics dataset composed of RNA-seq data and ADT-seq data.

3. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, Step 1, the preprocessing of the spatial multi-omics integrated dataset, specifically includes: Step 1.1: Filter out genes expressed in fewer than 10 spots in the RNA-seq data. Use the SCANPY package to perform logarithmic transformation and standardization on the filtered gene expression counts. Select the top 3000 highly variable genes in the standardized RNA-seq data for dimensionality reduction. The dimensionality reduction dimension is set to be consistent with the feature dimension of the proteomics. The SCANPY package is a Python-based single-cell analysis toolkit to complete the preprocessing of RNA-seq data. Step 1.2: The original protein expression counts in the ADT-seq and ATAC-seq data were normalized to a central log ratio. The normalized ADT-seq and ATAC-seq data were then dimensionality-reduced to complete the preprocessing of the ADT-seq and ATAC-seq data.

4. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, Step 3.3 specifically includes: Step 3.3.1: Extract gene expression attribute features of different sopts in the input data based on the encoder in the autoencoder; Step 3.3.2: Reconstruct the gene expression attribute features of different sopts based on the decoder in the autoencoder to obtain the attribute features of the input data; Step 3.3.3: Calculate the mean square error between the reconstructed data and the original data from the input data and use it as the reconstruction loss. If reconstruction results in losses If the value is greater than the first preset value, repeat step 3.3.2 until the reconstruction loss is reached. Less than the first preset value; The gene expression attribute feature expression of RNA-seq data is: （1）； In formula (1), An encoder for RNA-seq data, used to capture Multiple omics attributes of spot; The gene expression attribute feature expression of ADT-seq data is: （2）； In formula (1), An encoder for ADT-seq data, used to capture Multiple omics attributes of spot; The expression for gene expression profile reconstruction from RNA-seq data is: （3）； In formula (3), Different layers of the decoder for RNA-seq data; The expression for gene expression profile reconstruction from ADT-seq data is: （4）； In formula (4), Different layers of the decoder for ADT-seq data; Reconstruction losses The expression is: （5）； In formula (5), n This represents the number of spots.

5. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, Step 3.4 specifically includes: Step 3.4.1: Obtain a set of learned feature matrices for all spots based on the structural features of the input data; Step 3.4.2: Calculate the subset of features based on a set of learned feature matrices for all spots. k Feature encoding of neighbor information, through the MACM submodule k The feature codes of the first-order neighbors are merged to obtain a set of multi-scale feature codes that contain information from different neighbors. H ; Step 3.4.3: Perform average pooling on the feature codes at each scale and concatenate them together. Use the MLP module to adaptively learn the importance of feature codes at different scales and calculate the importance score matrix. Step 3.4.4: Encode multi-scale features containing information about neighbors of different orders using the importance score matrix. H The feature representation is then fused to obtain a final feature representation that includes multi-scale structural information. ; k The expression for the feature encoding of the order neighbor information is: （6）； In formula (6), For including the first k Feature encoding of neighbor information, A It is an adjacency matrix. Tanh For activation function, X For omics feature matrix, For the first k Learnable parameters of neighbor information; Multi-scale feature encoding of different neighbor information H The expression is: （7）； The expression for performing average pooling and concatenation on the feature encodings is: （8）； In formula (8), To perform average pooling on the feature matrix, Encode features at different scales after splicing; The expression for the importance score matrix is: （9）； In formula (9), To use the MLP module for Perform importance-adaptive learning; Feature representation of multi-scale structural information The calculation formula is: （10）； In formula (10), h To integrate feature representations that incorporate multi-scale structural information, For including the first k The importance of the feature matrix of the neighborhood information.

6. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, Step 3.5 specifically includes: Step 3.5.1: Perform multi-step fusion of the attribute features extracted by the autoencoder and the multi-scale structural features of the corresponding omics data extracted by the multi-scale adaptive graph convolution module to obtain the multi-source fusion features of the corresponding omics data. ; Step 3.5.2: Repeat step 3.5.1 to obtain the multi-source fusion features of the omics data. ; Step 3.5.3: Utilize the graph decoder to perform node embedding reconstruction on the multi-source fusion features of different omics, where the graph decoder and the autoencoder have a symmetrical structural distribution; Step 3.5.4: Calculate the graph feature reconstruction loss for different omics data If the graph feature reconstruction loss is greater than the second preset value, repeat steps 3.5.1-3.5.3 until the graph feature reconstruction loss is less than the second preset value, and output the reconstructed multi-source fusion features of different omics. Multi-source fusion features of omics data The calculation formula is: （11）； （12）； （13）； In formulas (11)-(13), a For hyperparameters, n The number of layers in the graph encoder. A This is an adjacency matrix constructed based on spatial location information. This represents a multi-source feature fusion representation of attribute features and multi-scale structural features in RNA omics data. These are the attribute features extracted from different layers of the autoencoder. The expression for node embedding reconstruction is: （14）； （15）； In formulas (14) and (15), and The reconstructed omics embedding features include neighbor information and relevant topological information. and It is an omics embedding decoder for different omics data; Image feature reconstruction loss The calculation formula is: （16）。 7. The method for spatial domain identification based on spatial multi-omics data according to claim 1, characterized in that, Step 3.6 specifically includes: Step 3.6.1: Concatenate the multi-source fusion features of different omics after reconstruction to obtain feature representations. ; Step 3.6.2: Introduce graph-based constraints, based on feature representation. The graph structure is reconstructed, and the binary cross-entropy loss is calculated as the structure reconstruction loss. And calculate the contrastive learning loss. ; Step 3.6.3: Based on structural reconstruction loss Comparative learning loss Reconstruction losses And graph feature reconstruction loss Constructing total loss L Based on total loss L Training a deep neural network model; Feature representation The calculation formula is: （17）； In formula (17), A multi-source feature fusion representation of attribute features and multi-scale structural features of RNA omics data; Structural reconstruction loss The calculation formula is: （18）； （19）； In formulas (18) and (19), To be based on fusion characteristics Z The reconstructed image obtained from decoding, Number of spots; Comparative learning loss The calculation formula is: （20）； In formula (20), For the neighborhood set of spot i , For spot i and j Cosine similarity between them For hyperparameters; Total loss L The calculation formula is: （21）。

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