A spatial domain recognition method and device based on multi-modal topology consistency

Abstract

The application discloses a kind of based on multi-modal topological consistency spatial domain identification method and device, and the application belongs to the field of transcriptome spatial domain identification, the method includes: based on the spatial transcriptome data of biological tissue, constructs and each modality information contained in it one-to-one correspondence multi-layer network;Extract consensus structure features shared by multi-layer network and specific structure features unique to each layer network;According to consensus structure features, specific structure features, multi-layer network, construct the cell consistency network of biological tissue;The cell consistency network is clustered, and the identification result of different spatial domains in biological tissue is obtained.This application can overcome the heterogeneity problem between different modal data, and the effect of spatial domain identification is better.

Description

Technical Field

[0001] This invention belongs to the field of transcriptome spatial domain identification technology, specifically relating to a spatial domain identification method and apparatus based on multimodal topological consistency. Background Technology

[0002] Biological tissues are typically composed of different types of cells that perform corresponding biological functions. In the last decade, the emergence of single-cell genomics has revolutionized transcriptome sequencing at the single-cell scale. This technology provides whole-genome information for cells at the individual cell level, enabling researchers to identify different cell types and their marker genes, thus offering a significant opportunity to explore the composition and dynamic evolution of biological tissues. However, cells of the same type often exist in different states in different regions of biological tissues and work in conjunction with other cell types to perform complex functions. For example, embryonic development, liver lobule structure, kidney function, and tumor formation all depend on the spatial arrangement of cells within the tissue. Therefore, studying cell function in conjunction with spatial context information is crucial.

[0003] However, existing single-cell sequencing technologies lose spatial location information during tissue dissociation, limiting the study of cell spatial distribution patterns within tissues. In recent years, spatial transcriptomics technology has emerged, which can preserve spatial coordinate information during tissue sequencing, providing unprecedented opportunities to explore cellular composition and function in a spatial context.

[0004] In spatial transcriptomics data, spatial domains are an important pattern, referring to groups of cells that are spatially adjacent and have similar gene expression. Identification of spatial domains is a prerequisite for downstream analyses, such as the dynamic tracking of disease progression and biological tissue development. Therefore, identifying different spatial domains in biological tissues lays the foundation for understanding tissue structure and biological function. Currently, the segmentation of tissue sections mainly relies on manual annotation by pathologists, which requires extremely high human resources. Therefore, developing automated spatial domain identification methods is of great significance.

[0005] Current popular spatial domain identification methods are mainly based on feature fusion. These methods often employ deep learning models to extract low-dimensional cellular features from spatial, morphological, and gene expression modalities, then fuse these features, and finally cluster the fused features to identify the spatial domain. However, this approach focuses heavily on extracting deep cellular features, neglecting the significant heterogeneity between different modalities. This limits the effectiveness of the fusion process and makes it difficult to achieve stable and accurate spatial domain division in complex tissue and disease-related data.

[0006] Therefore, current spatial domain recognition methods have poor recognition performance. Summary of the Invention

[0007] This invention provides a spatial domain identification method and apparatus based on multimodal topological consistency, which can solve the above-mentioned technical problems.

[0008] In a first aspect, embodiments of the present invention provide a spatial domain identification method based on multimodal topological consistency, the method comprising:

[0009] Based on spatial transcriptomics data of biological tissues, a multi-layer network is constructed that corresponds one-to-one with the information modalities of spatial transcriptomics data.

[0010] Extract the consensus structural features shared by the multi-layer network and the specific structural features unique to each layer;

[0011] Based on the consensus structural features, the specific structural features, and the multilayer network, a cell consistency network of the biological tissue is constructed.

[0012] Clustering was performed on the cell consistency network to obtain the identification results of different spatial domains in the biological tissue.

[0013] Secondly, embodiments of the present invention provide a spatial domain identification device based on multimodal topological consistency, comprising:

[0014] A multi-layer network construction module is used to construct a multi-layer network that corresponds one-to-one with the information modalities of spatial transcriptomics data based on spatial transcriptomics data of biological tissues.

[0015] The feature extraction module is used to extract the consensus structural features shared by the multi-layer network and the specific structural features unique to each layer of the network.

[0016] A consistency network construction module is used to construct a cell consistency network of the biological tissue based on the consensus structural features, the specific structural features, and the multilayer network.

[0017] A clustering module is used to perform clustering processing on the cell consistency network to obtain the identification results of different spatial domains in the biological tissue.

[0018] The beneficial effects of this invention compared to existing technologies are as follows: By constructing a multi-layer network with a one-to-one correspondence between information modalities, this invention can uniformly represent heterogeneous multimodal information in spatial transcriptomics data as a homogeneous multi-layer network structure. Furthermore, by extracting a cell consistency network, the spatial domain identification problem can be transformed into a multi-layer network clustering problem, effectively alleviating the high heterogeneity and difficulty in fusion between spatial information, pathological images, and gene expression information. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the implementation of a spatial domain identification method based on multimodal topological consistency, provided in an embodiment of the present invention;

[0020] Figure 2 A schematic diagram illustrating the spatial domain partitioning result provided in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of a spatial domain identification device based on multimodal topological consistency, provided in an embodiment of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0023] The spatial domain identification method based on multimodal topological consistency provided in this embodiment of the invention can be applied to electronic devices such as mobile terminals, personal laptops, and supercomputers. This embodiment of the invention does not impose any restrictions on the specific type of electronic device.

[0024] Example 1

[0025] Figure 1 The flowchart shown is an implementation flowchart of a spatial domain identification method based on multimodal topological consistency provided by an embodiment of the present invention. It is an example and not a limitation. The method may include steps S101 to S104, and each step is described below.

[0026] S101, based on spatial transcriptomics data of biological tissues, constructs a multi-layer network that corresponds one-to-one with the information modalities of spatial transcriptomics data.

[0027] In some embodiments, in order to overcome the heterogeneity problem among multiple modal information in spatial transcriptomics data, a network corresponding one-to-one with the information modality can be constructed to convert cell information of different modalities into a unified network structure representation, resulting in a multilayer network.

[0028] In one possible implementation, spatial transcriptomics data of biological tissues This can include spatial location information Gene expression information Cell morphology information .

[0029] For example, spatial location information can include the two-dimensional spatial coordinates of all cells in a biological tissue, which can be represented as: ,in The first in biological tissues Two-dimensional spatial coordinates of each cell These are parameters used to represent data dimensional information. This refers to the total number of cells in a biological tissue.

[0030] For example, gene expression information may include The expression level of a gene in various cells of a biological tissue can be represented as follows: ,in For the first Gene expression vector of each cell This represents the total number of genes.

[0031] For example, cell morphology information may include morphological features of individual cells extracted from pathological images of biological tissues, which can be represented as follows: ,in Indicates the first Cell Dimensional morphological characteristics, This represents the total number of cell dimensions.

[0032] Optionally, pathological images of biological tissues can be input into a pre-trained deep model to extract cellular morphology information of the biological tissues. .

[0033] In one example, an initial spatial matrix can be constructed based on the nearest neighbor algorithm and spatial location information. Since the nearest neighbor algorithm only describes first-order topological relationships, point mutual information methods can be further introduced to capture the higher-order topological structure of biological tissues, and updates can be made based on point mutual information methods. Obtaining cellular spatial networks .

[0034] For example, a cellular spatial network can satisfy the following formula:

[0035] (1.1),

[0036] in, For cellular spatial networks The Middle OK List the elements, , , These are the initial spatial matrices constructed based on spatial location information using the nearest neighbor algorithm. The Middle , , The degree of node density in each cell for The Middle OK List the elements, , , All are less than or equal to positive integers, The total number of cells in a biological tissue. To build The number of negative samples set at the time. Indicates taking the logarithm. This is the summation symbol.

[0037] Cellular spatial networks constructed by introducing point mutual information methods can more comprehensively reflect the spatial proximity relationships between cells.

[0038] In one example, similarly, the cosine similarity between cells in a biological tissue can be calculated based on the morphological characteristics of the cells; then, a cell morphology network can be constructed based on the nearest neighbor algorithm and the cosine similarity. .

[0039] In one example, representation learning methods can be used to construct a cell expression network based on gene expression information.

[0040] For example, a cell expression network initially constructed based on representation learning methods can be represented as:

[0041] (1.2),

[0042] in, For cellular expression networks, For gene expression information, Indicates minimization. Describing the L2 norm, Represents a diagonal matrix. This indicates a constraint.

[0043] Through constraints This ensures that each cell can only be characterized by other cells.

[0044] However, the initially constructed cell expression network has two problems. First, the network structure is relatively dense, which means that each cell is connected to other cells in the network structure. Second, the intrinsic geometric relationship between cells in gene expression information is lost.

[0045] To address the issue of dense network structures, sparsity constraints can be added to the initial solution model of the cell expression network (i.e., formula (1.2) above), ensuring that a cell can only be represented by a few other cells, resulting in the solution model of the cell expression network with added sparsity constraints (see formula (1.3) below). To preserve the local geometric structure contained in the gene expression information, a local distance-preserving term can be added to the solution model of the cell expression network with added sparsity constraints, allowing the cell expression network to maintain the inherent geometric relationships in the original gene expression information, resulting in the solution model with added local distance-preserving term (see formula (1.4) below). Finally, combining the sparsity constraints and the local distance-preserving term yields the final solution model of the cell expression network (see formula (1.5) below).

[0046] For example, the solution model of the cell expression network after adding sparse constraints can satisfy the following formula:

[0047] (1.3),

[0048] in, These are weighting parameters used to control the sparsity. It is an L1 norm.

[0049] For example, the solution model of a cell expression network after adding a local distance preservation term can satisfy the following formula;

[0050] (1.4),

[0051] in, Describes the rank of a matrix. Represents the Laplace matrix, Indicates transpose. , They are respectively The , line, indicating the first , The topology of individual cells on the cellular expression network. For cells With cells Connection strength on cellular expression networks It also represents the L2 norm.

[0052] For example, the solution model for a cell expression network can satisfy the following formula:

[0053] (1.5),

[0054] in, Indicates the degree of local distance preservation, higher This indicates a high degree of preservation of the intrinsic geometric relationships within the cellular expression network.

[0055] S102, extract the consensus structure features shared by the multi-layer network and the specific structural features unique to each layer of the network.

[0056] In one example, a nonnegative matrix factorization method can be used to decompose the multi-layer network constructed in step S101 to extract its topological features, decomposing each layer into the same basis matrix and different feature matrices. Then, the shared basis matrix of the multi-layer network is used as the consensus structural feature, and the different feature matrices of each layer are used as their respective specific structural features.

[0057] For example, the conventional single-layer network decomposition process can be represented as:

[0058] (1.6),

[0059] in, For the first Layered network, Less than or equal to positive integers, for The basis matrix, for eigenmatrix This represents the total number of network layers.

[0060] This decomposition method can extract low-dimensional topological features from a single network, which can then be directly extended to... Each network layer (in this invention) After constructing a multilayer network with a resolution of 3), the decomposition process of the multilayer network can be represented as follows:

[0061] (1.7).

[0062] However, the decomposition process shown in Formula (1.7) is based on the assumption that different network layers are independent of each other. Therefore, it is impossible to obtain the consensus structure characteristics shared by each network layer through Formula (1.7), nor can it characterize the potential correlation between layers.

[0063] Therefore, this invention introduces a shared basis matrix to represent the consensus structural features between each layer of the network by using a joint nonnegative decomposition strategy, and uses the feature matrix of each layer of the network to represent the specific structural features of each layer of the network. Then, combined with the above formula (1.7), the solution model for consensus structural features and specific structural features is obtained.

[0064] For example, the solution model for consensus structural features and specific structural features can satisfy the following formula:

[0065] (1.8),

[0066] in, As a consensus-based structural feature, , , Cellular spatial network Cellular expression network Cell morphology network Specific structural features, Describing the L2 norm, This indicates minimization.

[0067] By combining nonnegative matrix factorization methods, this invention can extract consensus-based and specific structural features of cellular multimodal information within a unified framework, providing a foundation for the subsequent construction of cellular consensus networks.

[0068] S103, based on consensus structural features, specific structural features, and multi-layer networks, constructs a cell consistency network for biological tissues.

[0069] In one example, traditional methods typically cluster directly on consensus topological features (i.e., consensus structural features) to identify spatial domains. This approach fails to fully utilize the structural relationships between cells, limiting the accuracy of spatial domain identification. Since the best outcome of spatial domain partitioning is that cells within the same spatial domain have similar structural relationships, meaning each cell can be represented by a linear combination of a few other cells within the same spatial domain, this invention employs a self-representation learning method to construct a cell consensus network.

[0070] For example, the process of constructing a cell consistency network using a self-representation learning method can be represented as follows:

[0071] (1.9),

[0072] in, This represents a cell-consistent network.

[0073] Formula (1.9) ensures that each cell in a biological tissue can be reconstructed by other cells, thereby reflecting the potential spatial domain structure.

[0074] Furthermore, to capture global structural relationships while ensuring that each cell can only be linearly represented by a finite number of other cells, a nuclear norm can be introduced into equation (1.9) to guarantee the low-rank property of the consistent network, while also introducing a noise term. To enhance the robustness of the cell consistency network to noise, equation (1.9) is modified as follows: ,in, This represents the nuclear norm. Finally, by combining the solution models for consensus-based structural features and specific structural features, a solution model for the cell consistency network is obtained.

[0075] For example, the solution model for a cell consistency network satisfies the following formula:

[0076] (1.10),

[0077] in, Represents the nuclear norm. For cell consistency networks, It is an L1 norm. For noise terms, , These are weight parameters used to control the low-rank degree of the cell consistency network and to control noise sensitivity, respectively.

[0078] S104. Based on consensus structural features, specific structural features, and multi-layer networks, the cell consistency network is clustered to obtain the identification results of different spatial domains in biological tissues.

[0079] In one example, see Figure 2 Graph clustering algorithms, such as spectral clustering, can be used to group biological tissues. Each cell was divided into c Within each cluster, a cluster after clustering is a spatial domain. Cells within the same spatial domain are spatially close and have similar biological functions.

[0080] For example, see Figure 2 Different shapes represent different types of cells, and multiple different types of cells perform similar biological functions in the same spatial domain.

[0081] For example, the spatial domains are highly connected in all modalities, and the intersection of different spatial domains is an empty set.

[0082] This invention constructs a multi-layer network with a one-to-one correspondence between information modalities, enabling the heterogeneous multimodal information in spatial transcriptomics data to be uniformly represented as a homogeneous multi-layer network structure. Based on this, by extracting a cell consistency network, the spatial domain identification problem can be transformed into a multi-layer network clustering problem, effectively alleviating the high heterogeneity and difficulty in merging between spatial information, pathological images, and gene expression information.

[0083] Furthermore, this invention, through a joint nonnegative matrix factorization strategy, can extract consensus topological features in a highly interpretable manner, reducing the complexity of multimodal data. A solution model for the cell consensus network is constructed using a self-representation learning method, ensuring that each cell in the network can be represented by other cells within a unified spatial domain. Adding low-rank constraints to the solution model guarantees a limited number of cells in each spatial domain, improving the accuracy and stability of spatial domain partitioning. By progressively optimizing the cell consensus network using the alternating multiplier method, the convergence efficiency and accuracy of the model can be improved without increasing the overall time complexity.

[0084] In some embodiments, the cell expression network can be obtained by iteratively solving the solution model based on the Alternating Direction Method of Multipliers (ADMM).

[0085] In one possible implementation, auxiliary variables can be introduced into the solution model of the cell expression network. Then, the objective function of the solution model after introducing auxiliary variables is rewritten based on the augmented Lagrangian method. Finally, based on the ADMM algorithm, other variables are fixed and the current variable is optimized separately. The cell expression network is updated and iterated multiple times until convergence is obtained.

[0086] For example, the solution model of a cell expression network after introducing auxiliary variables can satisfy the following formula:

[0087] (1.11),

[0088] in, This represents the objective function of the solution model after introducing auxiliary variables into the cell expression network.

[0089] For example, the objective function of the rewritten cell expression network solution model can be expressed as:

[0090] (1.12),

[0091] in, For constraint terms The penalty parameter, This represents the inner product of two matrices.

[0092] For example, the derivation process of updating each variable in the cell expression network solution model can be represented as follows:

[0093] (1.13),

[0094] in, Lagrange multipliers for solving models of cell expression networks.

[0095] By setting the above formula (1.13) , , Since the partial derivatives are 0, we can obtain the update formulas for each variable:

[0096] (1.14),

[0097] in, , They represent the first , The cell expression network after the first round of updates It indicates that each element is produced sequentially. , They represent the first , Auxiliary variables after round update , , They represent the first , The updated Lagrange multipliers , Indicates minimization. Represents the soft threshold function. It is a positive integer. express A diagonal matrix.

[0098] in:

[0099] (1.15),

[0100] in, , This represents two variables calculated using the soft threshold function.

[0101] In some embodiments, similarly, the solution model of the cell consistency network can be iteratively solved based on the ADMM algorithm to obtain the cell consistency network.

[0102] In one possible implementation, auxiliary variables can be introduced into the solution model of the cell consistency network. Then, based on the augmented Lagrangian method, the objective function of the solution model after introducing auxiliary variables into the cell consistency network is rewritten. Finally, based on the ADMM algorithm, other variables are fixed and the current variable is optimized separately. The cell consistency network is updated and iterated multiple times until it converges to obtain the cell consistency network.

[0103] For example, the solution model of the cell consistency network after introducing auxiliary variables can satisfy the following formula:

[0104] (1.16);

[0105] in, for The transpose of .

[0106] For example, the objective function of the rewritten cell consistency network can be expressed as:

[0107] (1.17),

[0108] in, This is also a penalty item. , , The three Lagrange multipliers are used to solve the model of the cell consistency network. This represents the objective function of the solution model for the cell consistency network.

[0109] For example, the derivation process of updating each variable in the solution model of the cell consistency network can be expressed as follows:

[0110] , (1.18).

[0111] By setting the above formula (1.18) , , , , , , , Since the partial derivatives are 0, we can obtain the update formulas for each variable:

[0112]

[0113] (1.19),

[0114] in, , They represent the first , The specific structural features of the cell expression network after each round of updates. , They represent the first , The specific structural features of the cell morphology network after each update. , They represent the first , The specific structural features of the cell expression network after each round of updates. , They represent the first , The characteristics of the consensus structure after the round of updates , They represent the first , Parameters after round update , , They represent the first , The updated cell consistency network , They represent the first , The noise term after the round update, , They represent the first , Auxiliary variables after round update . Represents the identity matrix. To and The temporary matrix resulting from combining the current residual with the Lagrange multipliers.

[0115] The noise term can be optimized by updating it column by column:

[0116] (1.20),

[0117] in, for The List, for The List, This is a Lagrange penalty term.

[0118] Example 2

[0119] Figure 3 The diagram shown illustrates the structure of a spatial domain identification device based on multimodal topological consistency, as provided in an embodiment of the present invention. As an example and not a limitation, the device 300 may include a multi-layer network construction module 310, a feature extraction module 320, a consistency network construction module 330, and a clustering module 340.

[0120] For example, the multi-layer network construction module 310 is used to construct a multi-layer network that corresponds one-to-one with the information modalities of the biological tissue based on the spatial transcriptomics data of the biological tissue; the feature extraction module 320 is used to extract the consensus structural features shared by the multi-layer network and the specific structural features unique to each layer of the network; the consistency network construction module 330 is used to construct a cell consistency network of the biological tissue based on the consensus structural features; and the clustering module 340 is used to perform clustering processing on the cell consistency network based on the consensus structural features, specific structural features, and multi-layer network to obtain the identification results of different spatial domains in the biological tissue.

[0121] This invention constructs a multi-layer network with a one-to-one correspondence between information modalities, enabling the heterogeneous multimodal information in spatial transcriptomics data to be uniformly represented as a homogeneous multi-layer network structure. Based on this, by extracting a cell consistency network, the spatial domain identification problem can be transformed into a multi-layer network clustering problem, effectively alleviating the high heterogeneity and difficulty in merging between spatial information, pathological images, and gene expression information.

[0122] 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.

Claims

1. A spatial domain identification method based on multimodal topological consistency, characterized in that, include: Based on spatial transcriptomics data of biological tissues, a multilayer network is constructed that corresponds one-to-one with the information modalities of the spatial transcriptomics data. The spatial transcriptomics data includes spatial location information, gene expression information, and cell morphology information. The multilayer network includes a cell spatial network, a cell expression network, and a cell morphology network. The cell morphology information includes the morphological features of each cell extracted from pathological images of the biological tissue. Extract the consensus structural features shared by the multi-layer network and the specific structural features unique to each layer; Based on the consensus structural features, the specific structural features, and the multilayer network, a cell consistency network of the biological tissue is constructed. Clustering is performed on the cell consistency network to obtain the identification results of different spatial domains in the biological tissue; The construction of the cell morphology network includes: calculating the cosine similarity between cells in the biological tissue based on the morphological features; and determining the cell morphology network based on the cosine similarity using the nearest neighbor algorithm. The step of extracting the shared consensus structural features and the unique structural features of each layer of the multi-layer network includes: decomposing the multi-layer network based on a joint nonnegative matrix factorization method, so that each layer of the network is decomposed into the same base matrix and different feature matrices; using the base matrix as the consensus structural features and the feature matrix of each layer of the network as its own unique structural features. The solution models for the consensus structural features and the specific structural features satisfy the following formula: ， in, This refers to the consensus structure feature. , , The cellular spatial network The cell expression network The cell morphology network Specific structural features, Represents the L2 norm. Indicates minimization. Indicates constraints; Wherein: the cell consistency network is constructed based on a self-representation learning method; The solution model for the cell consistency network satisfies the following formula: ， in, Represents the nuclear norm. This refers to the cell consistency network. It is an L1 norm. For noise terms, , These are weight parameters used to control the low-rank degree of the cell consistency network and to control the noise sensitivity, respectively. The cell consistency network is obtained by optimization using the alternating multiplier method. The derivation process of updating each variable in the solution model of the cell consistency network is expressed as follows: ， in, As a penalty item, , , The three Lagrange multipliers are used to solve the model of the cell consistency network. for The transpose of the matrix, Auxiliary variables introduced when solving the model for the cell consistency network.

2. The spatial domain identification method based on multimodal topological consistency according to claim 1, characterized in that, The cellular spatial network is obtained by constructing it based on the nearest neighbor algorithm and updating it using the point mutual information method. The cellular spatial network satisfies the following formula: ， in, For the cellular spatial network The Middle OK List the elements, , , These are the initial spatial matrices constructed based on the spatial location information using the nearest neighbor algorithm. The Middle , , The degree of node density in each cell for The Middle OK List the elements, , , All are less than or equal to positive integers, The total number of cells in the biological tissue. To build The number of negative samples set at the time. Indicates taking the logarithm. This is the summation symbol.

3. The spatial domain identification method based on multimodal topological consistency according to claim 1, characterized in that, in, The cell expression network was constructed based on representational methods; The solution model for the cell expression network satisfies the following formula: ， in, For the cell expression network, The gene expression information, Indicates minimization. Describing the L2 norm, It is an L1 norm. Represents a diagonal matrix. Indicates constraints. These are weighting parameters used to control the sparsity. Indicates the degree of local distance preservation. Describes the rank of a matrix. , This indicates transpose.

4. The spatial domain identification method based on multimodal topological consistency according to claim 1, characterized in that, The cell expression network was obtained by optimization using the alternating multiplier method.

5. A spatial domain identification device based on multimodal topological consistency, characterized in that, include: A multi-layer network construction module is used to construct a multi-layer network that corresponds one-to-one with the information modalities of the spatial transcriptomics data based on the spatial transcriptomics data of biological tissues. The spatial transcriptomics data includes spatial location information, gene expression information, and cell morphology information. The multi-layer network includes a cell spatial network, a cell expression network, and a cell morphology network. The cell morphology information includes the morphological features of each cell extracted from the pathological images of the biological tissues. The feature extraction module is used to extract the consensus structural features shared by the multi-layer network and the specific structural features unique to each layer of the network. A consistency network construction module is used to construct a cell consistency network of the biological tissue based on the consensus structural features, the specific structural features, and the multilayer network. A clustering module is used to perform clustering processing on the cell consistency network to obtain the identification results of different spatial domains in the biological tissue; Specifically, the multilayer network construction module is used to: calculate the cosine similarity between cells in the biological tissue based on the morphological features; and determine the cell morphology network based on the cosine similarity using the nearest neighbor algorithm. Specifically, the feature extraction module is used to: decompose the multi-layer network based on the joint nonnegative matrix factorization method, so that each layer of the network is decomposed into the same base matrix and different feature matrices; use the base matrix as the consensus structural feature, and use the feature matrix of each layer of the network as its own specific structural feature; The solution models for the consensus structural features and the specific structural features satisfy the following formula: ， in, This refers to the consensus structure feature. , , The cellular spatial network The cell expression network The cell morphology network Specific structural features, Represents the L2 norm. Indicates minimization. Indicates constraints; Wherein: the cell consistency network is constructed based on a self-representation learning method; The solution model for the cell consistency network satisfies the following formula: ， in, Represents the nuclear norm. This refers to the cell consistency network. It is an L1 norm. For noise terms, , These are weight parameters used to control the low-rank degree of the cell consistency network and to control the noise sensitivity, respectively. The cell consistency network is obtained by optimization using the alternating multiplier method. The derivation process of updating each variable in the solution model of the cell consistency network is expressed as follows: ， in, As a penalty item, , , The three Lagrange multipliers are used to solve the model of the cell consistency network. for The transpose of the matrix, Auxiliary variables introduced when solving the model for the cell consistency network.

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