A method and system for spatial domain identification based on tissue proximity slicing

Abstract

The application discloses a kind of based on tissue adjacent section's spatial domain identification method and system, belong to information processing technical field, from the same organization adjacent section's space transcriptome data is modeled as undirected graph respectively;Using Gromov-Wasserstein distance to measure the similarity between different graphs, obtain the optimal mapping pair, and integrate the information of optimal mapping pair together;The integrated data is input into the graph attention autoencoder trained, and the encoded features are clustered using clustering algorithm, so as to identify spatial domain.The application can effectively process adjacent section data, overcome the problem of single section data limitation in the prior art;The application can integrate the information of adjacent section, provide more complete data input, so as to identify more accurate spatial domain.

Description

Technical Field

[0001] This invention belongs to the field of information processing technology, specifically relating to a method and system for spatial domain identification based on adjacent tissue slices, used for spatial domain identification of spatial transcriptome data. Background Technology

[0002] Spatial transcriptomics has revolutionized the detection of mRNA expression by preserving spatial information, thus facilitating the exploration of biological functions at the spatial level. Despite the development of various spatial resolution transcriptomics techniques, the analysis of spatial transcriptomics data remains a significant challenge, especially in the context of spatial domain analysis. A spatial domain refers to a specific region in space composed of multiple cells, typically associated with the anatomical structure and specific functions of a tissue. These spatial domains can be considered as basic functional units containing spatial information for downstream analysis. Several spatial domain identification methods have been developed to date.

[0003] In 2020, Pham D et al. proposed a tool called stLearn on BioRxiv, designed to analyze spatial transcriptome data and identify spatial domains. This tool provides an intra-tissue normalization technique that normalizes gene expression by morphological distance using features and spatial locations extracted from morphological images. This normalization method helps eliminate biases introduced by spatial heterogeneity, improving 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 utilizing 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 identification.

[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 dependencies of the data. Through graph convolution, SpaGCN aggregates the gene expression of each point from its neighboring points, thereby achieving expression consistency and spatial domain identification of histology.

[0006] In 2022, Dong and Zhang proposed a framework called STAGATE in Nature Communications. This framework learns low-dimensional latent embeddings by integrating spatial information and gene expression profiles, thereby accurately identifying spatial domains. To better characterize spatial similarity at domain boundaries, STAGATE employs an attention mechanism to adaptively learn the similarity of neighboring points.

[0007] With the continuous development of spatial transcriptomics technology, spatial transcriptomics sequencing data continues to accumulate, and much of this data is generated from multiple spatially or temporally adjacent two-dimensional tissue slices. However, the aforementioned spatial domain identification methods only analyze a single slice and do not consider integrating similar points from spatially adjacent two-dimensional tissue slices for data augmentation to address noise and missing events, thereby improving the accuracy of spatial domain identification and obtaining more comprehensive biological insights.

[0008] The most common form of spatial transcriptome data to date, much like the now abundant scRNA-seq data, is based on NGS, where spatial barcodes are used to map sequencing data to their respective spot locations. This type of sequencing data contains widespread noise and missing events, which have been well-studied in scRNA-seq methods. This means that the expression profile of a single spot itself cannot fully represent the true RNA abundance of that spot. This is also one of the reasons why clustering based solely on in-situ captured gene expression data fails to yield ideal results. Summary of the Invention

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

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

[0011] A spatial domain identification method based on tissue proximity slices includes the following steps:

[0012] Spatial transcriptome data from adjacent slices of the same tissue were modeled as undirected graphs.

[0013] The Gromov-Wasserstein distance metric is used to measure the similarity between different undirected graphs to obtain the optimal mapping pair.

[0014] After integrating the information of the optimal mapping pair, the data is input into the trained graph attention autoencoder. Clustering methods are then used to cluster the encoded features to obtain spatial domain recognition results.

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

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

[0017] Based on the spatial location information of spots in the spatial transcriptome dataset, calculate the corresponding Euclidean distance d for each pair of spots i and j;

[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 the undirected graph.

[0019] Preferably, before modeling the spatial transcriptome data of adjacent slices of the same tissue into undirected graphs, the spatial transcriptome data is preprocessed. The specific steps are as follows:

[0020] The two spatial transcriptome datasets were standardized, logarithmically transformed, and normalized. The resulting transcriptome matrix is ​​represented as follows:

[0021] Then, SVD is applied to the corresponding dot product to eliminate batch effects between adjacent slice spatial transcriptomics datasets through a cross-dataset matrix factorization strategy based on SVD.

[0022] Preferably, the Gromov-Wasserstein distance metric 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 used to find neighboring 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 problem of attribute graph alignment is addressed; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; by calculating the Gromov-Wasserstein distance, the most similar spot pairs between neighboring slices are found, and the transcriptomic features of each optimal mapping pair are summed and averaged to obtain complementary transcriptomic features, thereby achieving data augmentation and serving as attribute features of nodes on the attribute graph.

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

[0025]

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

[0027] Preferably, the graph attention autoencoder is composed of encoding units and decoding units with identical structures connected in series. Both the encoding and decoding units are composed of a fully connected layer with a graph attention mechanism and a regular fully connected layer connected in series. In the fully connected layer with the graph attention mechanism, a linear transformation is performed first, followed by graph attention aggregation. In the regular fully connected layer, only a linear transformation is performed.

[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 the opposite of those of the encoding unit, which are n*32 and n*128, respectively. 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 L represents the network reconstruction loss. reg This represents the regularization loss of the network.

[0032] Preferably, clustering the encoded features using a clustering method specifically involves:

[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] Secondly, embodiments of the present invention provide a spatial domain identification system based on adjacent tissue slices, comprising:

[0035] The module constructs undirected graphs to model spatial transcriptome data from adjacent slices of the same tissue.

[0036] The metric module uses the Gromov-Wasserstein distance metric to measure the similarity between different undirected graphs and obtains 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. It then uses a clustering method to cluster the encoded features to obtain spatial domain recognition results.

[0038] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described spatial domain identification method based on tissue proximity slices.

[0039] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program that, when executed by a processor, implements the steps of the above-described spatial domain identification method based on tissue proximity slices.

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

[0041] A spatial domain identification method based on adjacent tissue slices is proposed. This method models spatial transcriptome data from adjacent slices within the same tissue as undirected graphs and uses the Gromov-Wasserstein distance metric to measure the similarity between different graphs. This effectively integrates adjacent slice data, overcoming the limitations of single-slice data in existing technologies. By integrating the information of optimal mapping pairs, spatial transcriptome data is enhanced, providing more complete data input. This process significantly improves the accuracy and reliability of downstream analysis. A graph autoencoder is constructed based on graph neural network theory. By inputting the enhanced data into it, spatial information and gene expression profiles can be effectively integrated, learning more accurate low-dimensional latent embeddings and obtaining more accurate spatial domain identification results.

[0042] Furthermore, by treating each spot as a node in the graph and using preprocessed gene expression information as a node attribute, the spatial location information and gene expression profile of each spot can be preserved. This approach can more finely display the differences in gene expression across different regions within a tissue, helping to identify subtle changes and specific regions within the tissue. Modeling the spatial adjacency relationships between spots as edges in the graph allows for better preservation and utilization of spatial structure information. The edges between adjacent spots represent their spatial proximity within the tissue, a relationship crucial for understanding spatial patterns 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, i.e., 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 contribute to revealing spatial patterns of gene expression.

[0044] Furthermore, preprocessing can clean and repair missing values, noise, and outliers in the data, ensuring higher data quality and thus improving the reliability and stability of the model. Through standardization, logarithmic transformation, and normalization, the distribution of data features can be made more uniform, avoiding the excessive or insufficient influence of certain features on the method, thereby improving the convergence speed and prediction accuracy. A cross-dataset matrix factorization strategy based on SVD can fuse datasets from different sources, extracting common features and patterns, enhancing the overall comprehensive utilization value of the data, while dimensionality reduction reduces data complexity, lowers computational resource consumption, and improves algorithm speed.

[0045] Furthermore, by setting optimal mapping pairs, different datasets can be compared within the same coordinate system or reference frame, enhancing data consistency and playing a significant role in data integration, improving analytical accuracy, and revealing data relationships. Through reasonable mapping strategies, cross-dataset and cross-spatial domain data integration and analysis can be achieved, enhancing data consistency, improving method performance, and revealing potential relationships between complex data.

[0046] Furthermore, by adjusting the results of the attribute map alignment problem and summing and averaging the transcriptomics features, complementary transcriptomics features can be obtained, providing more comprehensive gene expression information and achieving data augmentation. This process not only improves the quality and accuracy of the data but also lays the foundation for constructing more accurate attribute maps, thereby enhancing the effectiveness of spatial domain identification.

[0047] Furthermore, a graph autoencoder with graph attention mechanism can effectively integrate node attributes and graph structure information, capture complex relationships between nodes, and improve the accuracy of feature extraction and reconstruction. The design of the encoding and decoding units ensures the consistency and efficiency of feature compression and recovery, and the introduction of the ELU activation function further enhances the model's nonlinear expressive power.

[0048] Furthermore, by clustering the encoded features, different spatial domains in tissue slices can be effectively identified and segmented, simplifying the data structure, discovering potential biological patterns, and improving the efficiency and accuracy of data analysis. The mclust and louvain clustering algorithms each have their advantages, capable of handling different data characteristics and analytical needs, providing strong support for spatial transcriptomics analysis.

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

[0050] In summary, the present invention can effectively process data from neighboring slices, overcoming the limitations of single-slice data in the prior art; it can integrate information from neighboring slices, providing more complete data input, thereby identifying a more accurate spatial domain.

[0051] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0052] Figure 1 This is a flowchart of the method of the present invention;

[0053] Figure 2 This is a visualization of the spatial domain identification results in mouse brain slices using the STAGATE method, compared to the present invention.

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

[0055] Figure 4 This is a block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

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

[0059] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0060] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. 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] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0062] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0063] This invention provides a spatial domain identification method based on adjacent tissue slices. By modeling spatial transcriptome data from adjacent slices of the same tissue as undirected graphs, the problem of finding the optimal mapping of sampling points between adjacent slices is transformed into an attribute graph alignment problem, enabling this invention to effectively process adjacent slice data. The Gromov-Wasserstein distance is used to measure the similarity between different graphs, obtaining the optimal mapping pair. The information of the optimal mapping pair is then integrated to enhance the spatial transcriptome data, overcoming the limitations of single-slice data in existing technologies. This allows the invention to integrate information from adjacent slices, providing a more complete data input. The enhanced data is then input into a graph attention autoencoder to further integrate spatial information and gene expression profiles to learn low-dimensional embeddings, thereby accurately identifying spatial domains.

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

[0065] S1. Preprocessing spatial transcriptomics data;

[0066] Spatial transcriptomics data are represented as D={(g (i) ,s (i) Let i = 1, 2, ..., N, where N is the number of spots, and g (i) ∈R G ,s (i) ∈R 2 Let G represent 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, this invention uses their overlapping features. For ease of representation, this 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 slices of the same tissue.

[0067] In an attempt to correct batch effects between samples, this invention employs a cross-dataset matrix factorization strategy based on SVD as a preprocessing step.

[0068] S101. This invention performs standardization, logarithmic transformation, and normalization on two spatial transcriptome datasets. The resulting transcriptome matrix is ​​represented as follows:

[0069] S102. Then, SVD is applied to the corresponding dot product, and a cross-dataset matrix factorization strategy based on SVD is adopted to eliminate the batch effect between adjacent slice spatial transcriptomics datasets.

[0070]

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

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

[0073]

[0074] Where M represents taking the first M singular values.

[0075] S2. Model the spatial transcriptome data from adjacent slices of the same tissue after preprocessing in step S1 into an undirected graph, where 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 nodes represent the spatial adjacency relationship between these spots.

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

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

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

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

[0080] The Euclidean distance d is:

[0081]

[0082] Where (x1,y1) are the spatial coordinates of spot i, and (x2,y2) are the spatial coordinates 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. Connect each spot with the first K spots in its sorted sequence to form the edges of the undirected graph.

[0084] The adjacency matrix of an undirected graph is represented as A∈{0,1}. N×N When the side (v) i ,v j When )∈E, V ij =1, otherwise A ij =0.

[0085] S3. The problem of finding the optimal mapping of spots between neighboring slices is transformed into an attribute graph alignment problem; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; by calculating the Gromov-Wasserstein distance, the most similar spot pairs between neighboring slices are found, and the information of these optimal mapping pairs is integrated to achieve data augmentation.

[0086] S301, Searching for 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 The property graph alignment problem of (V2,E2,X2);

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

[0088] Define source graph G s and target image G t Let X and Y be the metric spaces, respectively, and μ be the source graph G. s The uniform distribution of μ across all n nodes in the target graph, and the uniform distribution of v across all m nodes in the target graph, the GW distance between μ and v is reformulated as:

[0089]

[0090] Where Ds and Dt represent the cost matrices in the source space and target space, respectively, and π ik and π jl Let 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 quadruple summation represents traversing all possible combinations of point pairs.

[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 by finding the optimal transmission π based solely on two in-graph cost matrices, Ds and Dt.

[0093] Construct the in-graph cost matrices Ds and Dt. In the above formula, the optimal transmission π can be solved using only these two in-graph cost matrices, Ds and Dt. However, 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 transcriptomics feature after preprocessing in step S1, and z is the transcriptomics feature after first-order graph convolution. D (1) D (2) and D (3) The cost matrices are for three different perspectives.

[0098] Based on information from multiple perspectives, the cost matrix D is defined. s and D t as follows:

[0099]

[0100] β is used to measure the weight of information from each perspective; it is obtained automatically and does not need to be specified manually.

[0101] The alignment result is obtained from π, and the optimal match is obtained. The expression is as follows:

[0102]

[0103] in, Let π represent a matching set, which is selected from all possible matching sets M. ik It is usually a weight value, representing the weight from u. i to v k The matching strength or weight. Indicate u i and v k In the matching set A pair of matches in the equation.

[0104] The goal of this formula is to find an optimal set of matches. Make the weight π in the matching set ik Maximizing the sum of weights. In the graph alignment problem, this helps to find a match between the vertex sets of two graphs such that the sum of the weights of the match is maximized, thus obtaining the optimal mapping pair.

[0105] S303. Obtain the most similar spot pairs between neighboring slices from step S302, and sum and average the transcriptomic features of each optimal mapping pair to obtain complementary transcriptomic features, thereby achieving data augmentation, and using these as attribute features of nodes on the attribute graph.

[0106] S4. Based on graph neural network theory, construct a graph attention autoencoder (GAE);

[0107] The graph attention autoencoder network consists of encoding and decoding units with identical structures connected in series. Each encoding and decoding unit consists of a fully connected layer with graph attention mechanism and a regular fully connected layer connected in series. In the fully connected layer with graph attention mechanism, a linear transformation is performed first, followed by graph attention aggregation.

[0108] In a typical fully connected layer, only a linear transformation is performed. The ELU activation function is applied after the output of each layer.

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

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

[0111] S5, Training a graph attention autoencoder network;

[0112] The hyperparameters of the graph attention autoencoder network are set, using the Adam optimizer 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 augmented node feature data is input into the graph attention autoencoder model, and the network parameters are iteratively updated until the network's loss function converges.

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

[0114]

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

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

[0117]

[0118] Among them, L regλ represents the regularization loss of the network, λ is the regularization coefficient that 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 a weighted sum of the reconstruction loss and the regularization loss:

[0120] L = L recon +L reg

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

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

[0123] The enhanced data is input into the system, integrating spatial information and gene expression profiles, and spatial domains are 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] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "platform."

[0126] In another embodiment of the present invention, a spatial domain recognition system based on tissue proximity slices is provided. This system can be used to implement the above-mentioned spatial domain recognition method based on tissue proximity slices. Specifically, the spatial domain recognition system based on tissue proximity 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;

[0128] The metric module uses the Gromov-Wasserstein distance metric to measure the similarity between different undirected graphs and obtains 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. It then uses a clustering method to cluster the encoded features to obtain spatial domain recognition results.

[0130] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes 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 (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for operations based on a spatial domain identification method for adjacent tissue slices, including:

[0131] Spatial transcriptome data from adjacent slices of the same tissue were modeled as undirected graphs. The Gromov-Wasserstein distance was used to measure the similarity between different undirected graphs to obtain the optimal mapping pair. The information of the optimal mapping pair was integrated and input into a trained graph attention autoencoder. Clustering methods were used to cluster the encoded features to obtain spatial domain recognition results.

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

[0133] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0134] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0135] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the spatial domain identification method based on tissue proximity slices in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0136] Spatial transcriptome data from adjacent slices of the same tissue were modeled as undirected graphs. The Gromov-Wasserstein distance was used to measure the similarity between different undirected graphs to obtain the optimal mapping pair. The information of the optimal mapping pair was integrated and input into a trained graph attention autoencoder. Clustering methods were used to cluster the encoded features to obtain spatial domain recognition results.

[0137] Please see Figure 3 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the fluid composition calculation method in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the fluid composition calculation system in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here.

[0138] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 3 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

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

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

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

[0142] Any references to memory, databases, or other media used in the embodiments provided in this 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. By way of illustration and not limitation, RAM may take many forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0143] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0144] Please see Figure 4 The terminal device 600 is an electronic device, which takes the form of a general-purpose 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 storage unit 620 and processing unit 610), a display unit 640, etc.

[0145] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

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

[0147] 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 or some combination of these examples may include an implementation of a network environment.

[0148] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0149] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with 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.

[0150] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0151] 1. Simulation experimental conditions:

[0152] The hardware platform for the simulation experiment of this invention is: i7-12700H CPU with a main frequency of 2.30GHz and 32GB of memory.

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

[0154] The spatial transcriptome gene expression data for the simulation experiments of this invention are: the mouse brain dataset provided by the 10x Genomics platform and the DLPFC dataset provided by The spatialLIBD package.

[0155] The simulation experiment 1 of this invention uses two adjacent coronal slices of the mouse brain dataset from adult mice. The two slices contain 2235 spots and 19465 genes, and 2310 spots and 19465 genes, respectively.

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

[0157] 2. Simulation content and result analysis

[0158] The present invention includes two simulation experiments, which use the present invention and existing technologies to conduct simulation experiments on two different datasets.

[0159] Simulation Experiment 1 uses the present invention and a prior art technique (STAGATE) to conduct simulation experiments on two adjacent coronal slice datasets of the adult mouse brain, respectively, to obtain the spatial domain recognition results of the two methods. The visualization results of the spatial domain are as follows. Figure 2 As shown.

[0160] The existing technology 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", abbreviated as STAGATE.

[0161] Please see Figure 2 The effects of the present invention are further described using simulation diagrams, as follows:

[0162] Figure 2 (a) and Figure 2 (b) is a staining pattern of two adjacent coronal sections of the brain from an adult mouse. Due to their spatial proximity, the staining patterns of the two sections are very similar.

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

[0164] Figure 2 (e) is a visualization result of the spatial domain identified by the present invention. Each point in the figure represents a spot (sampling point), and the position of each point represents the position of the spot in the organization space. 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 these two adjacent tissue slices into one of the slices with fewer spots, enhancing its gene expression characteristics, and then using a graph attention autoencoder to identify the spatial domain, this invention can identify two key regions, cornu ammonis (CA region) and dentate gyrus (dentate gyrus), corresponding to the stained image in the hippocampus of adult mice, and obtain comprehensive and accurate spatial domain identification results.

[0166] Simulation Experiment 2 uses the present invention and four existing technologies (stLearn, BayesSpace, SpaGCN, STAGATE) to conduct a simulation experiment 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 existing technology stLearn refers to the spatial domain identification method proposed by Pham D et al. in “stLearn: integrating spatiallocation, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues, in BioRxiv, (2020): 2020-05”, abbreviated as stLearn.

[0168] The existing technology 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.", which is abbreviated as BayesSpace.

[0169] The existing technology 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 existing technology STAGATE used is the same as that used in simulation experiment 1.

[0171] For the spatial domain identification result of each slice, the adjusted Land coefficient (ARI) is calculated to quantify its score, and all the calculation results are plotted in Table 1, as follows:

[0172] Table 1. Spatial domain recognition results of five methods in the human dorsolateral prefrontal cortex: ARI quantization scores.

[0173]

[0174]

[0175] Table 1 shows that the spatial domain recognition results obtained by the present invention in 12 slices of the DLPFC dataset are generally better than the existing technologies, proving that the present invention can more accurately identify spatial domains.

[0176] In summary, this invention provides a spatial domain identification method and system based on adjacent tissue slices. By utilizing information from adjacent tissue slices, it overcomes the limitations of single-slice data. Through the combination of advanced techniques such as undirected graph modeling, Gromov-Wasserstein distance metric, graph neural networks, and graph autoencoders, this invention achieves effective integration and enhancement of adjacent slice data, reducing the impact of noise and missing events in sequencing data. It achieves more accurate spatial domain identification results on spatial transcriptome datasets with artificial annotations and obtains more comprehensive spatial domain identification results on spatial transcriptome datasets without artificial annotations. This invention has significant application potential and value in the fields of tissue slice analysis and spatial domain identification.

[0177] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to 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 embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0178] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

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

[0180] In the embodiments provided by this 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 merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

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

[0182] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0183] If the integrated module / unit is implemented as 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, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed 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 electrical carrier signals and telecommunication signals.

[0184] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0185] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0186] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0187] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A spatial domain identification method based on adjacent tissue slices, characterized in that, Includes the following steps: Spatial transcriptome data from adjacent slices of the same tissue were modeled as undirected graphs. In this modeling process, each spot was treated as a node, with preprocessed gene expression information used as node attributes. Edges between nodes represented the spatial adjacency between spots, connecting their K nearest neighbors in two-dimensional space. This process effectively modeled the spatial information of spots in the preprocessed spatial transcriptome as a spatial graph. ; The Gromov-Wasserstein distance metric is used to measure the similarity between different undirected graphs, and the optimal mapping pair is obtained, specifically: Two spatial transcriptome datasets will be used to find neighboring slice pairs. and The optimal mapping problem between spots is transformed into a corresponding space graph. and The problem of attribute graph alignment is addressed; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; by calculating the Gromov-Wasserstein distance, the most similar spot pairs between neighboring slices are found, and the transcriptomic features of each optimal mapping pair are summed and averaged to obtain complementary transcriptomic features, thereby achieving data augmentation and serving as attribute features of nodes on the attribute graph. Corresponding spatial diagram and The specific results of the attribute graph alignment problem are as follows: in, Represents a matching set. Indicates from arrive The matching strength or weight, express and In the matching set A pair of matches; After integrating the information of the optimal mapping pair, the data is input into the trained graph attention autoencoder. Clustering methods are then used to cluster the encoded features to obtain spatial domain recognition results.

2. The spatial domain identification method based on adjacent tissue slices according to claim 1, characterized in that, The steps for calculating the K nearest neighbors in a two-dimensional space are as follows: Based on the spatial location information of spots in the spatial transcriptome dataset, calculate the corresponding Euclidean distance for each pair of spots i and j. ; 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 the undirected graph.

3. The spatial domain identification method based on adjacent tissue slices according to claim 1, characterized in that, Before modeling the spatial transcriptome data of adjacent slices from the same tissue into undirected graphs, the spatial transcriptome data is preprocessed. The specific steps are as follows: The two spatial transcriptome datasets were standardized, logarithmically transformed, and normalized. The resulting transcriptome matrix is ​​represented as follows: ; Then, SVD is applied to the corresponding dot product to eliminate batch effects between adjacent slice spatial transcriptomics datasets through a cross-dataset matrix factorization strategy based on SVD.

4. The spatial domain identification method based on adjacent tissue slices according to claim 1, characterized in that, Graph attention autoencoders consist of encoding and decoding units with identical structures connected in series. Each encoding and decoding unit is composed of a fully connected layer with graph attention mechanism and a regular fully connected layer connected in series. In the fully connected layer with graph attention mechanism, a linear transformation is performed first, followed by graph attention aggregation. In the regular fully connected layer, only a linear transformation is performed. The ELU activation function is applied after the output of each layer, and the input and output dimensions of the encoding unit are n, respectively. 128, n 32; The input and output dimensions of the decoding unit are the opposite of those of the encoding unit, and are n respectively. 32 and n 128, where n equals the number of spots in the dataset.

5. The spatial domain identification method based on adjacent tissue slices according to claim 4, characterized in that, Loss function of graph attention autoencoder for: in, This represents the network reconstruction loss. This represents the regularization loss of the network.

6. The spatial domain identification method based on adjacent tissue slices according to claim 1, characterized in that, Clustering methods are used to cluster the encoded features in the following ways: 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.

7. A spatial domain identification system based on adjacent tissue slices, characterized in that, include: The construction module models the spatial transcriptome data of adjacent slices from the same tissue as undirected graphs. During this modeling process, each spot (or "spot") is treated as a node, with preprocessed gene expression information used as node attributes. Edges between nodes represent the spatial adjacency between spots, connecting their K nearest neighbors in a two-dimensional space. This process effectively models the spatial information of spots in the preprocessed spatial transcriptome as a spatial graph. ; The metrics module uses the Gromov-Wasserstein distance to measure the similarity between different undirected graphs and obtains the optimal mapping pair. Specifically: Two spatial transcriptome datasets will be used to find neighboring slice pairs. and The optimal mapping problem between spots is transformed into a corresponding space graph. and The problem of attribute graph alignment is addressed; the Gromov-Wasserstein distance is used to measure the similarity between different graphs; by calculating the Gromov-Wasserstein distance, the most similar spot pairs between neighboring slices are found, and the transcriptomic features of each optimal mapping pair are summed and averaged to obtain complementary transcriptomic features, thereby achieving data augmentation and serving as attribute features of nodes on the attribute graph. Corresponding spatial diagram and The specific results of the attribute graph alignment problem are as follows: in, Represents a matching set. Indicates from arrive The matching strength or weight, express and In the matching set A pair of matches; The recognition module integrates the information of the optimal mapping pair and inputs it into the trained graph attention autoencoder. It then uses a clustering method to cluster the encoded features to obtain spatial domain recognition results.

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