Spatial domain identification method and system based on tissue adjacent slices

Abstract

The invention discloses a spatial domain identification method and system based on tissue adjacent slices, and belongs to the technical field of information processing. Spatial transcriptome data of adjacent slices from the same tissue are modeled into undirected graphs; measuring the similarity between different graphs by using a Gromov-Wasserstein distance to obtain an optimal mapping pair, and integrating the information of the optimal mapping pair together; and inputting the integrated data into a trained graph attention auto-encoder, and clustering encoded features by using a clustering algorithm so as to identify a spatial domain. According to the invention, data of adjacent slices can be effectively processed, and the problem of limitation of single slice data in the prior art is overcome; according to the invention, information of adjacent slices can be integrated, and more complete data input is provided, so that a more accurate spatial domain is identified.

Description

Background Art

[0002] Spatial transcriptomics technology has revolutionized the detection of mRNA expression by preserving spatial information, thereby facilitating the exploration of biological functions at the spatial level. Despite the development of various spatially resolved transcriptomic technologies, the analysis of spatial transcriptomic data remains a major challenge, especially in the context of spatial domain analysis. A spatial domain refers to a specific area in space composed of multiple cells, which is usually related to the anatomical structure and specific function of a tissue. These spatial domains can be regarded as basic functional units containing spatial information for downstream analysis. Currently, several spatial domain identification methods have been developed.

[0003] In 2020, Pham D et al. proposed a tool called stLearn on BioRxiv, which aims to analyze spatial transcriptome data and identify spatial domains. The tool provides an intra-tissue normalization technique that uses features and spatial positions extracted from morphological images to normalize gene expression by morphological distance. This normalization method helps eliminate the bias introduced by spatial heterogeneity and improves the accuracy of the identification results.

[0004] In 2021, Zhao et al. proposed an algorithm called BayesSpace in Nature Biotechnology. BayesSpace models a low-dimensional representation of the gene expression matrix while using spatial priors to encourage adjacent points to belong to the same category. This prior information is integrated into the model to strengthen the connection between adjacent points, thereby improving the accuracy of spatial domain recognition.

[0005] In 2021, Hu et al. proposed a method called SpaGCN in Nature Methods. It integrates gene expression, spatial location, and morphological data to generate an undirected weighted graph that captures the spatial dependency of the data. Through graph convolution, SpaGCN aggregates the gene expression of each point from neighboring points, thereby achieving expression consistency and histological spatial domain recognition.

[0006] In 2022, Dong and Zhang proposed a framework called STAGATE in Nature Communications. This framework integrates spatial information and gene expression profiles to learn low-dimensional latent embeddings to accurately identify spatial domains. In order to better characterize the spatial similarity at the boundaries of spatial domains, STAGATE uses an attention mechanism to adaptively learn the similarity of adjacent points.

[0007] With the continuous development of spatial transcriptome technology, spatial transcriptome sequencing data continues to accumulate, and many spatial transcriptome data are generated from multiple spatially or temporally adjacent two-dimensional tissue slices; however, the above-mentioned spatial domain recognition methods only analyze a single slice, and do not consider integrating similar points in spatially adjacent two-dimensional tissue slices for data enhancement to deal with noise and missing events, thereby improving the recognition accuracy of the spatial domain and obtaining more comprehensive biological insights.

[0008] The most common form of spatial transcriptome data to date is very similar to the now widely abundant scRNA-seq data, which is based on NGS, where spatial barcodes are used to map sequencing data to their respective spot positions. There are extensive noise and missing events in this type of sequencing data, which have been well studied in scRNA-seq methods. This results in the expression profile of a single spot itself not fully representing the true RNA abundance of the spot. This is also one of the reasons why clustering only gene expression data based on in situ capture cannot obtain ideal results. Summary of the invention

[0009] The technical problem to be solved by the present invention is to provide a spatial domain recognition method and system based on adjacent tissue slices to address the deficiencies in the above-mentioned prior art, so as to solve the technical problem of the limitation of single slice data, integrate similar points in spatially adjacent two-dimensional tissue slices for data enhancement, so as to reduce the impact of noise and missing events in sequencing data, make full use of the continuously accumulated spatial transcriptome sequencing data, and improve the accuracy of spatial domain recognition.

[0010] The present invention adopts the following technical solutions:

[0011] A spatial domain recognition method based on tissue adjacent slices comprises the following steps:

[0012] The spatial transcriptome data of adjacent sections of the same tissue were modeled as undirected graphs respectively;

[0013] Use the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtain the optimal mapping pair;

[0014] The information of the optimal mapping pair is integrated and input into the trained graph attention autoencoder, and the encoded features are clustered using a clustering method to obtain spatial domain recognition results.

[0015] Preferably, in the process of modeling an undirected graph, each spot is used as a node of the graph, the preprocessed gene expression information is used as the node attribute, the edges between the nodes represent the spatial adjacency relationship between the spots, the edges between the nodes connect the K nearest neighbors in the two-dimensional space, and the spatial information of the spots in the preprocessed spatial transcriptome is modeled as a spatial graph G.

[0016] Preferably, the steps for calculating the K nearest neighbors in the two-dimensional space are as follows:

[0017] According to the spatial location information of the spot in the spatial transcriptome dataset, for each pair of spot i and j, the corresponding Euclidean distance d is calculated;

[0018] Sort the Euclidean distance values ​​of each pair of spots in ascending order. The first K spots in the sorted sequence are the K nearest neighbors in the two-dimensional space. Connect each spot to the first K spots in its sorted sequence to form the edges of an undirected graph.

[0019] Preferably, before the spatial transcriptomic data of adjacent slices of the same tissue are modeled as undirected graphs, the spatial transcriptomic data are preprocessed, and the specific steps are as follows:

[0020] The two spatial transcriptome datasets were standardized, logarithmically transformed, and normalized. The transcriptomics matrix after the operation is expressed as

[0021] Then SVD was applied on the corresponding dot products to eliminate the batch effects between adjacent slice spatial transcriptomics datasets through an SVD-based cross-dataset matrix decomposition strategy.

[0022] Preferably, the Gromov-Wasserstein distance is used to measure the similarity between different undirected graphs, and the optimal mapping pair is obtained as follows:

[0023] Two spatial transcriptome datasets D will be searched for adjacent slice pairs s and D t The optimal mapping problem between spots is transformed into the corresponding spatial graph G s and G t The attribute graph alignment problem is solved; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; the most similar spot pairs between adjacent slices are found by calculating the Gromov-Wasserstein distance, and the transcriptomic features of each optimal mapping pair are summed and averaged to obtain complementary transcriptomic features, realize data enhancement, and serve as the attribute features of the nodes on the attribute graph.

[0024] Preferably, the corresponding space graph G s and G tThe results of the attribute graph alignment problem are as follows:

[0025]

[0026] in, represents a matching set, π ik Indicates that from u i to v k The matching strength or weight of Indicates u i and v k In the matching set A pair of matches in .

[0027] Preferably, the graph attention autoencoder is composed of an encoding unit and a decoding unit with the same structure connected in series in sequence, and the encoding unit and the decoding unit are each composed of a fully connected layer with a graph attention mechanism and a common fully connected layer connected in series in sequence; a linear transformation is first performed in the fully connected layer with the graph attention mechanism, and then graph attention aggregation is performed; and only a linear transformation is performed in the common fully connected layer;

[0028] The ELU activation function is applied after the output of each layer. The input and output dimensions of the encoding unit are n*128 and n*32 respectively; the input and output dimensions of the decoding unit are opposite to those of the encoding unit, which are n*32 and n*128 respectively, where n is equal to the number of spots in the dataset.

[0029] Preferably, the loss function L of the graph attention autoencoder is:

[0030] L=L tecon +L rrh

[0031] Among them, L trvon represents the reconstruction loss of the network, L reg represents the regularization loss of the network.

[0032] Preferably, clustering the encoded features using a clustering method is specifically as follows:

[0033] When the number of spatial domain labels is known, the mclust clustering algorithm is used; for data without prior information, the louvain algorithm implemented by the SCANPY package is used.

[0034] In a second aspect, an embodiment of the present invention provides a spatial domain recognition system based on tissue adjacent slices, comprising:

[0035] A building module was built to model the spatial transcriptome data of adjacent sections of the same tissue as undirected graphs respectively;

[0036] The measurement module uses the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtain the optimal mapping pair;

[0037] The recognition module integrates the information of the optimal mapping pair and inputs it into the trained graph attention autoencoder. The encoded features are clustered using a clustering method to obtain spatial domain recognition results.

[0038] In a third aspect, a computer device comprises 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-mentioned spatial domain identification method based on tissue adjacent slices when executing the computer program.

[0039] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned spatial domain identification method based on tissue adjacent slices.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects:

[0041] A spatial domain recognition method based on tissue adjacent slices, by modeling the spatial transcriptome data of adjacent slices from the same tissue as undirected graphs respectively, and using the Gromov-Wasserstein distance to measure the similarity between different graphs, the present invention can realize the effective integration of adjacent slice data, overcoming the problem of single slice data limitation in the prior art; the information of the optimal mapping pair is integrated together to realize the enhancement of spatial transcriptome data and provide more complete data input, which significantly improves the accuracy and reliability of downstream analysis; based on the graph neural network theory, a graph autoencoder is constructed, and by inputting the enhanced data into it, the spatial information and gene expression spectrum can be effectively integrated, and more accurate low-dimensional potential embedding can be learned to obtain more accurate spatial domain recognition results.

[0042] Furthermore, by treating each spot as a node in the graph and using the preprocessed gene expression information as node attributes, the spatial localization information and gene expression profile of each spot can be retained. This approach can more finely display the differences in gene expression in various regions within the tissue, helping to identify subtle changes and specific regions in the tissue. Modeling the spatial adjacency relationship between spots as edges in the graph can better preserve and utilize spatial structural information. The edges between adjacent spots represent their spatial proximity in the tissue, which is crucial for understanding the spatial pattern of gene expression.

[0043] Furthermore, the purpose of performing K nearest neighbor calculations in two-dimensional space is to identify and analyze local relationships between data points, that is, which points are close to each other in space. This helps to discover local patterns and clustering characteristics in the data, reveal local associations between data points, and help reveal spatial patterns of gene expression.

[0044] Furthermore, preprocessing can clean and repair missing values, noise and outliers in the data to ensure higher data quality, thereby improving the reliability and stability of the model. Through operations such as standardization, logarithmic transformation and normalization, the distribution of data features can be made more even, avoiding the influence of certain features on the method being too large or too small, and improving the convergence speed and prediction accuracy of the method. Through the SVD-based cross-dataset matrix decomposition strategy, data sets from different sources can be fused together to extract common features and patterns, enhance the comprehensive utilization value of the overall data, and reduce the complexity of the data through dimensionality reduction, reduce the consumption of computing resources, and improve the running speed of the algorithm.

[0045] Furthermore, by setting the optimal mapping pair, different data sets can be compared in the same coordinate system or reference frame, enhancing data consistency, which is of great significance in data integration, improving analysis accuracy, revealing data relationships, etc. Through a reasonable mapping strategy, data integration and analysis across data sets and spatial domains can be achieved, data consistency can be enhanced, method performance can be improved, and potential relationships between complex data can be revealed.

[0046] Furthermore, by setting the result of the attribute graph alignment problem and averaging the transcriptomic features, complementary transcriptomic features can be obtained, providing more comprehensive gene expression information and achieving data enhancement. This process not only improves the quality and accuracy of the data, but also provides a basis for building a more accurate attribute graph, thereby improving the effect of spatial domain recognition.

[0047] Furthermore, through the graph autoencoder with graph attention mechanism, node attributes and graph structure information can be effectively integrated to capture the complex relationship between nodes and improve the accuracy of feature extraction and reconstruction. The design of the encoding unit and decoding unit ensures the consistency and efficiency of feature compression and recovery, and the introduction of the ELU activation function further enhances the nonlinear expression ability of the model.

[0048] Furthermore, by clustering the encoded features, different spatial domains in tissue sections can be effectively identified and divided, data structures can be simplified, potential biological patterns can be discovered, and the efficiency and accuracy of data analysis can be improved. The mclust and louvain clustering algorithms each have their own advantages and can cope with different data characteristics and analysis requirements, providing strong support for the analysis of spatial transcriptomics.

[0049] It can be understood that the beneficial effects of the second aspect mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0050] In summary, the present invention can effectively process the data of adjacent slices, overcoming the problem of single slice data limitation in the prior art; it can integrate the information of adjacent slices, provide more complete data input, and thus identify a more accurate spatial domain.

[0051] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the method of the present invention;

[0053] Figure 2 This is a visualization result diagram of the spatial domain in mouse brain slices identified by the present invention and the existing method STAGATE;

[0054] Figure 3 A schematic diagram of a computer device provided by an embodiment of the present invention;

[0055] Figure 4 The present invention is a block diagram of an electronic device provided according to an embodiment. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0058] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0059] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0060] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0061] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0062] Various structural schematic diagrams of the embodiments disclosed in the present invention are shown in the accompanying drawings. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0063] The present invention provides a spatial domain recognition method based on tissue adjacent slices. The spatial transcriptome data of adjacent slices from the same tissue are modeled as undirected graphs respectively, and the optimal mapping problem of finding sampling points between adjacent slices is converted into an attribute graph alignment problem, so that the present invention can effectively process the data of adjacent slices; the Gromov-Wasserstein distance is used to measure the similarity between different graphs, and the optimal mapping pair is obtained, and the information of the optimal mapping pair is integrated together to realize spatial transcriptome data enhancement, which overcomes the problem of the limitation of single slice data in the prior art, so that the present invention can integrate the information of adjacent slices and provide more complete data input; the enhanced data is input into a graph attention autoencoder, and the spatial information and gene expression spectrum are further integrated to learn low-dimensional embedding, so as to accurately identify the spatial domain.

[0064] See also Figure 1 The present invention provides a spatial domain recognition method based on tissue adjacent slices, comprising the following steps:

[0065] S1. Preprocessing of spatial transcriptomics data;

[0066] The spatial transcriptomics data is represented as D = {(g (i) ,s (i) ),i=1,2,…,N}, where N is the number of spots, g (i) ∈R G ,s (i) ∈R 2 are the original transcriptomic features and spatial coordinates of spot i, respectively, where G is the number of transcriptomic features. For datasets containing different numbers of transcriptomic features, the present invention uses their overlapping features. For ease of representation, the present invention represents the combination of transcriptomic features and spatial coordinates of all spots in the dataset as matrices G∈R N×G , S∈R N×2 G1, G2 and S1, S2 were used to distinguish spatial transcriptome datasets from adjacent sections of the same tissue.

[0067] In order to try to correct the batch effect between samples, the present invention adopts a cross-dataset matrix decomposition strategy based on SVD as a preprocessing step.

[0068] S101. The present invention performs operations such as standardization, logarithmic transformation and normalization on two spatial transcriptome data sets. The transcriptomics matrix after the operation is expressed as:

[0069] S102, then applying SVD on the corresponding dot products, and using a cross-dataset matrix decomposition strategy based on SVD to eliminate batch effects between adjacent slice spatial transcriptomics datasets.

[0070]

[0071] Among them, U is an orthogonal matrix; ∑ is a diagonal matrix, where the elements on the diagonal are called singular values; V is an orthogonal matrix.

[0072] The batch-corrected embeddings for both datasets are:

[0073]

[0074] Among them, M means taking the first M singular values.

[0075] S2, modeling the spatial transcriptome data of adjacent slices from the same tissue after preprocessing in step S1 into an undirected graph, wherein each spot (sampling point) is a node of the graph, the preprocessed gene expression information is used as the node attribute, and the edges between the nodes represent the spatial adjacency relationship between these spots;

[0076] The present invention models the spatial information of the spot in the preprocessed spatial transcriptome as a spatial graph G = (V, E, X), where each node corresponds to a spot, with the batch-corrected embedding x (i) ∈R M as its node attributes, and these edges connect the K nearest neighbors in two-dimensional space.

[0077] The batch-corrected embedding refers to the result of the preprocessing in step S1.

[0078] The steps for calculating the K nearest neighbors in two-dimensional space are as follows:

[0079] S201, according to the spatial location information of the spot in the spatial transcriptome dataset, for each pair of spots i and j, calculate the corresponding Euclidean distance d;

[0080] The Euclidean distance d is:

[0081]

[0082] Among them, (x1, y1) is the spatial position coordinate of spot i, and (x2, y2) is the spatial position coordinate of spot j.

[0083] S202, sort the Euclidean distance values ​​of each pair of spots in ascending order, the first K spots in the sorted sequence are the K nearest neighbors in the two-dimensional space, and connect each spot to the first K spots in its sorted sequence to form an edge of an undirected graph.

[0084] Denote the adjacency matrix of an undirected graph as A∈{0,1} N×N , when the edge (v i ,v j )∈E, V ij =1, otherwise A ij =0.

[0085] S3, transform the problem of finding the optimal mapping of spots between adjacent slices into the problem of attribute graph alignment; use the Gromov-Wasserstein distance to measure the similarity between different graphs; find the most similar spot pairs between adjacent slices by calculating the Gromov-Wasserstein distance, and integrate the information of these optimal mapping pairs to achieve data enhancement;

[0086] S301, will find two spatial transcriptome datasets from adjacent tissue slice pairs and The optimal mapping problem between spots is transformed into their corresponding spatial graph G s =(V1,E1,X1) and G t = (V2, E2, X2) attribute graph alignment problem;

[0087] S302. Use Gromov-Wasserstein distance to solve the attribute graph alignment problem;

[0088] Define source graph G s and the target graph G t are the metric spaces X and Y respectively, and μ is the source graph G s is uniformly distributed over all n nodes in the target graph, v is uniformly distributed over all m nodes in the target graph, and the GW distance between μ and v is restated as:

[0089]

[0090] Among them, Ds and Dt represent the cost matrices in the source space and target space respectively, π ik and π jl They represent the variables in the optimal transmission π from point i in the source space to point k in the target space, and from point j in the source space to point l in the target space respectively. The fourfold summation represents traversing all possible point pair combinations.

[0091] The goal of this optimization problem is to find an optimal transportation plan π that minimizes the total transportation cost from the source distribution μ to the target distribution ν.

[0092] It can be seen that the GW distance optimization problem is solved based on only two intra-graph cost matrices Ds and Dt to find the optimal transmission π.

[0093] Construct the in-graph cost matrices Ds and Dt. In the above formula, the optimal transmission π can be solved based only on the two in-graph cost matrices Ds and Dt, and Ds and Dt need to be constructed manually, as follows:

[0094] D (1) =A

[0095] D (2) (i,j)=d(x i ,x j )=x i T x j

[0096]

[0097] Where A is the adjacency matrix, x is the transcriptomic feature after preprocessing in step S1, and z is the transcriptomic feature after the first-order graph convolution operation. (1) , D (2) and D (3) They are the cost matrices for the three perspectives respectively.

[0098] Integrate multi-view information and define the cost matrix D s and D t as follows:

[0099]

[0100] Among them, β is used to measure the weight of each perspective information; it is obtained through automatic calculation and does not need to be manually specified.

[0101] Get the alignment result from π, the best match It is expressed as:

[0102]

[0103] in, represents a matching set, which is selected from all possible matching sets M, π ik Usually a weight value, indicating the i to v k The matching strength or weight of . Indicates u i and v k In the matching set A pair of matches in .

[0104] The goal of this formula is to find an optimal matching set So that the weight π in the matching set ik In the graph alignment problem, this can help find a matching between the vertex sets of two graphs such that the sum of the matching weights is maximized in order to obtain the optimal mapping pair.

[0105] S303, obtaining the most similar spot pairs between adjacent slices from step S302, and summing and averaging the transcriptomic features of each optimal mapping pair to obtain complementary transcriptomic features, implement data enhancement, and use them as attribute features of nodes on the attribute graph.

[0106] S4. Based on the graph neural network theory, we build a graph attention autoencoder (GAE).

[0107] The graph attention autoencoder network is composed of an encoding unit and a decoding unit with the same structure connected in series. Both the encoding unit and the decoding unit are composed of a fully connected layer with a graph attention mechanism and a normal fully connected layer connected in series. In the fully connected layer with the graph attention mechanism, a linear transformation is first performed, and then graph attention aggregation is performed.

[0108] Only linear transformation is performed in ordinary fully connected layers. After the output of each layer, the ELU activation function is applied.

[0109] The input and output dimensions of the encoding unit are n*128 and n*32 respectively, where n is equal to the number of spots in the dataset.

[0110] The input and output dimensions of the decoding unit are opposite to those of the encoding unit, which are n*32 and n*128 respectively.

[0111] S5, training graph attention autoencoder network;

[0112] The graph attention autoencoder network hyperparameters are set, and the Adam optimizer is used to minimize the reconstruction loss. The initial learning rate is 0.0001, the weight decay is set to 0.0001, the attention coefficient is set to 0.8, and the number of iterations is set to 600. The attribute graph with node feature data enhancement is input into the graph attention autoencoder model, and the network parameters are iteratively updated until the network loss function converges.

[0113] The loss function of the graph attention autoencoder consists of two parts: reconstruction loss and regularization loss. The reconstruction loss is used to measure the ability of the autoencoder to reconstruct the input data, that is, the difference between the output reconstructed data and the original input data. Regularization loss is used to prevent the model from overfitting or improve the generalization ability of the model. Weight decay is used as the regularization loss to limit the complexity of the model by penalizing the size of the model parameters. The reconstruction loss of the network is as follows:

[0114]

[0115] Among them, L recon represents the reconstruction loss of the network, n represents the number of spots in the dataset, i.e. the number of nodes in the attribute graph, and x i is the original input data of the ith node, The reconstructed output data of the i-th node.

[0116] The regularized loss function of the network is as follows:

[0117]

[0118] Among them, L regrepresents the regularization loss of the network, λ is the regularization coefficient, which controls the proportion of the regularization term in the total loss, and W is the weight parameter of the model.

[0119] The final loss function is the weighted sum of reconstruction loss and regularization loss:

[0120] L=L recon +L reg

[0121] When the network's loss function converges, the graph attention autoencoder training is completed and the feature representation of the data can be effectively learned.

[0122] S6. Use clustering methods to cluster the encoded features to obtain spatial domain recognition results.

[0123] The augmented data is fed into it, spatial information and gene expression profiles are integrated, and the spatial domain is accurately identified by learning low-dimensional latent embeddings.

[0124] Different clustering methods are used to cluster the encoded features. When the number of spatial domain labels is known, the mclust clustering algorithm is used; for data without prior information, the louvain algorithm implemented by the SCANPY package is used.

[0125] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as a system, method or program product. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software, which may be collectively referred to herein as a "circuit", "module" or "platform".

[0126] In yet another embodiment of the present invention, a spatial domain recognition system based on tissue neighboring slices is provided. The system can be used to implement the above-mentioned spatial domain recognition method based on tissue neighboring slices. Specifically, the spatial domain recognition system based on tissue neighboring slices includes a construction module, a measurement module and a recognition module.

[0127] Among them, the construction module models the spatial transcriptome data of adjacent slices of the same tissue as undirected graphs respectively;

[0128] The measurement module uses the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtain the optimal mapping pair;

[0129] The recognition module integrates the information of the optimal mapping pair and inputs it into the trained graph attention autoencoder. The encoded features are clustered using a clustering method to obtain spatial domain recognition results.

[0130] In another embodiment of the present invention, a terminal device is provided, the terminal device includes a processor and a memory, the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the spatial domain recognition method based on the adjacent slices of the tissue, including:

[0131] The spatial transcriptome data of adjacent slices of the same tissue are modeled as undirected graphs respectively. The Gromov-Wasserstein distance is used to measure the similarity between different undirected graphs to obtain the optimal mapping pair. The information of the optimal mapping pair is integrated and input into the trained graph attention autoencoder. The encoded features are clustered using a clustering method to obtain spatial domain recognition results.

[0132] In another embodiment of the present invention, the present invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device, and can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples (non-exhaustive list) of the computer-readable storage medium here include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0133] Computer readable storage media also include data signals propagated in baseband or as part of a carrier wave, which carry readable program codes. Such propagated data signals can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than a readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above.

[0134] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0135] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the spatial domain identification method based on tissue adjacent slices in the above embodiment; the processor may load and execute the following steps:

[0136] The spatial transcriptome data of adjacent slices of the same tissue are modeled as undirected graphs respectively. The Gromov-Wasserstein distance is used to measure the similarity between different undirected graphs to obtain the optimal mapping pair. The information of the optimal mapping pair is integrated and input into the trained graph attention autoencoder. The encoded features are clustered using a clustering method to obtain spatial domain recognition results.

[0137] See also Figure 3 , the terminal device is a computer device, and the computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the method for calculating the composition of fluid in the reservoir transformation wellbore in the embodiment is realized. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the calculation system for the composition of fluid in the reservoir transformation wellbore in the embodiment are realized. To avoid repetition, it is not described one by one here.

[0138] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 3 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0139] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, central processing units, graphics processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, data processing logic based on quantum computing, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0140] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the computer device 60.

[0141] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0142] Any reference to memory, database or other medium used in the embodiments provided in the present application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0143] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0144] See also Figure 4 The terminal device 600 is an electronic device, and the electronic device is in the form of a general computing device. The components of the electronic device may include but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0145] The storage unit stores program codes, which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present invention described in the above method section of this specification. For example, the processing unit 610 can perform the following steps: Figure 1 Follow the steps shown in .

[0146] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache memory unit 6202 , and may further include a read-only memory unit (ROM) 6203 .

[0147] The storage unit 620 may also include a program / utility 6204 having a set (at least one) of program modules 6205, such program modules 6205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0148] Bus 630 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0149] The electronic device 600 may also communicate with one or more external devices 700 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed via an input / output (I / O) interface 650. Furthermore, the electronic device 600 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 via a bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0150] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0151] 1. Simulation experiment conditions:

[0152] The hardware platform of the simulation experiment of the present invention is: the processor is i7-12700H CPU, the main frequency is 2.30GHz, and the memory is 32GB.

[0153] The software platform for the simulation experiment of the present invention is: Windows 11 64-bit operating system and python 3.8.

[0154] The spatial transcriptome gene expression data of the simulation experiment of the present invention are: a mouse brain data set provided by the 10x Genomics platform and a DLPFC data set provided by the spatialLIBD package.

[0155] The simulation experiment 1 of the present invention uses two adjacent coronal slices of the brain from an adult mouse in the mouse brain data set, and the two slices contain 2235 spots, 19465 genes and 2310 spots, 19465 genes respectively.

[0156] The simulation experiment 2 of the present invention uses a complete human dorsolateral prefrontal cortex (DLPFC) data set, which contains 10X Genomics Visium ST data from three individuals, each individual has four slices (labeled slices a, b, c, d) for a total of 12 slices. Each slice has approximately 4000 spots, and each spot contains 33538 genes. For each individual, slice a and slice b, as well as slice c and slice d are 10 μm apart. However, the distance between slices b and c is farther, at 300 μm.

[0157] 2. Simulation content and results analysis

[0158] There are two simulation experiments of the present invention, and the present invention and the prior art are used to perform simulation experiments on two different data sets.

[0159] Simulation Experiment 1 The present invention and a prior art (STAGATE) were used to perform simulation experiments on two adjacent brain coronal slice data sets of adult mice, and the spatial domain results of the two methods were obtained. The visualization results of the spatial domain are shown in Figure 1. Figure 2 shown.

[0160] Prior art STAGATE refers to the spatial domain identification method proposed by Dong and Zhang et al. in “Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder,in Nature communications,13.1(2022):1739”, referred to as STAGATE.

[0161] See also Figure 2 The effects of the present invention are further described through simulation diagrams, as follows:

[0162] Figure 2 (a) and Figure 2 (b) is a staining image of two adjacent coronal sections of the brain of an adult mouse. Since they are adjacent in space, the staining images of the two sections are very similar.

[0163] Figure 2 (c) and Figure 2 (d) is the spatial domain visualization result diagram of the existing method STAGATE. Each point in the figure represents a spot (sampling point), the position of each point represents the position of the spot in the tissue space, and each color corresponds to a spatial domain.

[0164] Figure 2 (e) is a visualization result diagram of the spatial domain identified by the present invention. Each point in the diagram represents a spot (sampling point), the position of each point represents the position of the spot in the tissue space, and each color corresponds to a spatial domain.

[0165] Depend on Figure 2 (a) Figure 2 (b) Figure 2 (c) Figure 2 (d) Figure 2 (e) It can be seen that by integrating the information of the two adjacent tissue slices into one of the slices with fewer spots, enhancing its gene expression characteristics and then using the graph attention autoencoder to identify the spatial domain, the present invention can identify the two key areas of cornu ammonis (CA area) and dentate gyrus corresponding to the stained image in the hippocampus of adult mice, and obtain comprehensive and accurate spatial domain recognition results.

[0166] Simulation experiment 2 uses the present invention and four existing technologies (stLearn, BayesSpace, SpaGCN, STAGATE) to conduct simulation experiments on the human dorsolateral prefrontal cortex (DLPFC) dataset, and uses ARI to evaluate the classification results. The evaluation results are shown in Table 1.

[0167] The prior art stLearn refers to the spatial domain identification method proposed by Pham D et al. in “stLearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues, in BioRxiv, (2020): 2020-05”, referred to as stLearn for short.

[0168] The prior art BayesSpace refers to the spatial domain identification method proposed by Zhao et al. in “Spatial transcriptomics at subspot resolution with BayesSpace, in Nature biotechnology, 39.11(2021): 1375-1384.”, abbreviated as BayesSpace.

[0169] The prior art SpaGCN refers to the spatial domain identification method proposed by Hu et al. in “SpaGCN: Integrating gene expression, spatial location and histology to identify spatial domains and spatiallyvariable genes by graph convolutional network, in Nature methods, 18.11(2021): 1342-1351.”, abbreviated as SpaGCN.

[0170] In simulation experiment 2, the prior art STAGATE used is the same as that in simulation experiment 1.

[0171] For the spatial domain recognition results of each slice, the adjusted Rand index ARI is calculated to quantify its score, and all the calculation results are plotted in Table 1, as follows:

[0172] Table 1 ARI quantitative scores of spatial domain recognition results of five methods in human dorsolateral prefrontal cortex

[0173]

[0174]

[0175] In Table 1, the spatial domain recognition results obtained by the present invention in 12 slices on the DLPFC data set are generally better than the existing technology, proving that the present invention can more accurately identify the spatial domain.

[0176] In summary, the present invention, a spatial domain recognition method and system based on tissue adjacent slices, solves the technical problem of single slice data limitations by utilizing the information of tissue adjacent slices. Through the combination of advanced technologies such as undirected graph modeling, Gromov-Wasserstein distance metric, graph neural network and graph autoencoder, the present invention realizes the effective integration and enhancement of adjacent slice data, reduces the impact of noise and missing events in sequencing data, and achieves more accurate spatial domain recognition results on spatial transcriptome datasets with artificial annotations, and obtains more comprehensive spatial domain recognition results on spatial transcriptome datasets without artificial annotations. The present invention has significant application potential and value in the fields of tissue slice analysis and spatial domain recognition.

[0177] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0178] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0179] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0180] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0181] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0182] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0183] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0184] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0185] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0186] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0187] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A spatial domain recognition method based on tissue adjacent slices, It is characterized in that The following steps are involved: The spatial transcriptome data of adjacent sections of the same tissue were modeled as undirected graphs respectively; Use the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtain the optimal mapping pair; The information of the optimal mapping pair is integrated and input into the trained graph attention autoencoder, and the encoded features are clustered using a clustering method to obtain spatial domain recognition results.

2. The spatial domain recognition method based on tissue adjacent slices according to claim 1, It is characterized in that In the process of modeling an undirected graph, each spot is used as a node of the graph, and the preprocessed gene expression information is used as the node attribute. The edges between nodes represent the spatial adjacency relationship between spots. The edges between nodes connect the K nearest neighbors in the two-dimensional space, and the spatial information of the spots in the preprocessed spatial transcriptome is modeled as a spatial graph G.

3. The spatial domain recognition method based on tissue adjacent slices according to claim 2, It is characterized in that The steps for calculating the K nearest neighbors in two-dimensional space are as follows: According to the spatial location information of the spot in the spatial transcriptome dataset, for each pair of spot i and j, the corresponding Euclidean distance d is calculated; Sort the Euclidean distance values ​​of each pair of spots in ascending order. The first K spots in the sorted sequence are the K nearest neighbors in the two-dimensional space. Connect each spot to the first K spots in its sorted sequence to form the edges of an undirected graph.

4. The spatial domain identification method based on tissue adjacent slices according to claim 1, It is characterized in that Before modeling the spatial transcriptomic data of adjacent slices of the same tissue into undirected graphs, the spatial transcriptomic data were preprocessed. The specific steps are as follows: The two spatial transcriptome datasets were standardized, logarithmically transformed, and normalized. The transcriptomics matrix after the operation is expressed as Then SVD was applied on the corresponding dot products to eliminate the batch effects between adjacent slice spatial transcriptomics datasets through an SVD-based cross-dataset matrix decomposition strategy.

5. The spatial domain identification method based on tissue adjacent slices according to claim 1, It is characterized in that Using the Gromov-Wasserstein distance to measure the similarity between different undirected graphs, the optimal mapping pair is obtained as follows: Two spatial transcriptome datasets D will be searched for adjacent slice pairs s and D t The optimal mapping problem between spots is transformed into the corresponding spatial graph G s and G t The attribute graph alignment problem is solved; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; the most similar spot pairs between adjacent slices are found by calculating the Gromov-Wasserstein distance, and the transcriptomic features of each optimal mapping pair are summed and averaged to obtain complementary transcriptomic features, realize data enhancement, and serve as the attribute features of the nodes on the attribute graph.

6. The spatial domain identification method based on tissue adjacent slices according to claim 4, It is characterized in that Corresponding space graph G s and G t The results of the attribute graph alignment problem are as follows: in, represents a matching set, π ik Indicates that from u i to v k The matching strength or weight of Indicates u i and v k In the matching set A pair of matches in .

7. The spatial domain identification method based on tissue adjacent slices according to claim 1, It is characterized in that The graph attention autoencoder is composed of an encoding unit and a decoding unit with the same structure connected in series. Both the encoding unit and the decoding unit are composed of a fully connected layer with a graph attention mechanism and a normal fully connected layer connected in series. In the fully connected layer with the graph attention mechanism, linear transformation is first performed, and then graph attention aggregation is performed; in the normal fully connected layer, only linear transformation is performed. The ELU activation function is applied after the output of each layer. The input and output dimensions of the encoding unit are n*128 and n*32 respectively; the input and output dimensions of the decoding unit are opposite to those of the encoding unit, which are n*32 and n*128 respectively, where n is equal to the number of spots in the dataset.

8. The spatial domain identification method based on tissue adjacent slices according to claim 7, It is characterized in that The loss function L of the graph attention autoencoder is: L=L recon +L reg Among them, L recon represents the reconstruction loss of the network, L reg represents the regularization loss of the network.

9. The spatial domain identification method based on tissue adjacent slices according to claim 1, It is characterized in that The clustering method used to cluster the encoded features is as follows: When the number of spatial domain labels is known, the mclust clustering algorithm is used; for data without prior information, the louvain algorithm implemented by the SCANPY package is used.

10. A spatial domain recognition system based on tissue adjacent slices, It is characterized in that include: A building module was built to model the spatial transcriptome data of adjacent sections of the same tissue as undirected graphs respectively; The measurement module uses the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtain the optimal mapping pair; The recognition module integrates the information of the optimal mapping pair and inputs it into the trained graph attention autoencoder. The encoded features are clustered using a clustering method to obtain spatial domain recognition results.

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