Spatial domain identification method and apparatus for biological spatial transcriptome slices

Abstract

The application discloses a spatial domain identification method and device for biological spatial transcriptome slices, comprising the following steps: constructing a spatial neighbor cell network according to the spatial position information of cells in a noisy spatial transcriptome slice; constructing a gene expression cell network according to the gene expression data in the preprocessed noisy spatial transcriptome slice; performing joint feature decomposition on the spatial neighbor cell network and the gene expression cell network through non-negative matrix decomposition to obtain spatial features and gene expression features; constructing a cell affinity graph according to the spatial features and the gene expression features; and performing unsupervised clustering of cells in the noisy spatial transcriptome slice based on the leiden algorithm according to the cell affinity graph to realize spatial domain identification of the noisy spatial transcriptome slice. The application converts the analysis and spatial domain identification of the noisy spatial transcriptome slice into a network clustering problem, further reduces the influence of noise existing in the gene expression data from a global level, and realizes accurate spatial domain identification.

Description

Technical Field

[0001] This invention belongs to the field of biological data processing technology, specifically relating to a method and apparatus for spatial domain identification of biological spatial transcriptome slices. Background Technology

[0002] The function of biological tissues is closely related to their structure and cell types. In recent years, the development of spatial transcriptomics (ST) technology has brought tremendous opportunities to study the spatial distribution of cells within tissues, promoting research in related fields such as embryonic development, liver lobule structure, and tumor development. This is because spatial transcriptomics technology preserves the spatial coordinate information of cells during tissue sequencing.

[0003] Spatial domains refer to groups of cells that are spatially close in a tissue section and exhibit similar gene expression relationships. They represent important patterns or regularities embedded in spatial transcriptome data. Numerous studies have reported that spatial domains can serve as crucial inputs for downstream analytical tasks, such as tracking the occurrence and dynamic development of malignant diseases and monitoring biological tissue development. Accurate spatial domain identification provides a vital knowledge / prior basis for a deeper understanding of biological tissue structure and function.

[0004] However, due to technological limitations, spatial transcriptome data inevitably introduces noise during preparation. This noise originates from multiple sources and is commonly found in gene expression data. A low signal-to-noise ratio severely impacts spatial domain identification and many downstream tasks. Current computational methods lack explicit, forward-designed approaches to address the noise problem in spatial transcriptomes. This deficiency widens the gap between spatial domain identification and other downstream tasks based on spatial transcriptome data and their clinical and real-world applications. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a method and apparatus for spatial domain identification of biological spatial transcriptome slices.

[0006] The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] In a first aspect, the present invention provides a method for spatial domain identification of biological spatial transcriptome slices, the method comprising:

[0008] A spatial nearest neighbor cell network is constructed based on the spatial location information of cells in a noisy spatial transcriptome slice; wherein, the spatial nearest neighbor cell network is used to describe the geometric proximity relationship between cells in the spatial transcriptome slice;

[0009] Gene expression cell networks were constructed based on gene expression data from preprocessed noisy spatial transcriptome slices; these networks were used to characterize the gene expression similarity relationships among cells in the spatial transcriptome slices.

[0010] The spatial nearest neighbor cell network and the gene expression cell network are decomposed using nonnegative matrix factorization to obtain spatial features, gene expression features and noise features.

[0011] Construct a cell affinity map based on the spatial features and the gene expression features;

[0012] Based on the Leiden algorithm, unsupervised clustering of cells in the noisy spatial transcriptome slice is performed according to the cell affinity map to achieve spatial domain identification of the noisy spatial transcriptome slice.

[0013] Optionally, the unsupervised clustering of cells in the noisy spatial transcriptome slice based on the Leiden algorithm according to the cell affinity map to achieve spatial domain identification of the noisy spatial transcriptome slice includes:

[0014] Local preservation projection of gene expression characteristics is achieved through spatial nearest neighbor cell networks;

[0015] An objective function is constructed based on the spatial features, gene expression features, noise features, local preservation projection, cell affinity map, and contrastive learning optimization strategy.

[0016] In each iteration, the spatial features, gene expression features, and noise features are updated using the alternating direction multiplier method. The noise features are constrained by a soft threshold rule, and the cell affinity map is updated according to stochastic gradient descent until a preset number of iterations is reached or the numerical change of the objective function is less than a preset threshold, thus obtaining the updated spatial features, updated gene expression features, updated noise features, and updated cell affinity map.

[0017] Based on the updated cell affinity map, unsupervised clustering of cells in the noisy spatial transcriptome slice is performed using the Leiden algorithm to achieve spatial domain identification of the noisy spatial transcriptome slice.

[0018] Optionally, the process of performing feature decomposition on the spatial nearest neighbor cell network and the gene expression cell network through nonnegative matrix factorization can be represented as follows:

[0019] ;

[0020] in, This represents the gene-expressing cellular network. This represents the spatial nearest neighbor cell network. Represents the basis matrix. This indicates the gene expression characteristics. This represents the noise matrix corresponding to gene expression characteristics. This represents the spatial features. This represents the noise matrix corresponding to the spatial features. This indicates that we are looking for the 1-norm.

[0021] Optionally, the cell affinity diagram is represented as follows:

[0022] ;

[0023] in, This represents the cell affinity diagram. This represents the matrix transpose operation.

[0024] Optionally, the local preservation projection is represented as follows:

[0025] ;

[0026] in, This indicates finding the trace of a matrix. This indicates the gene expression characteristics. The Laplace matrix represents the spatial nearest neighbor network. This represents the matrix transpose operation.

[0027] Alternatively, the process of optimizing the affinity graph through contrastive learning can be represented as follows:

[0028] ;

[0029] in, Represents cell affinity diagrams. This indicates that we are looking for the 1-norm. Denotes the square of the Frobenius norm. This indicates the number of cells in a noisy spatial transcriptome slice. Represents cells Neighborhood determined by spatial location Represents an exponential function. The optimized cell affinity diagram shows the first cell... Line 1 Column elements, The optimized cell affinity diagram shows the first cell... Line 1 Column elements, To compare and learn about relevant temperature parameters.

[0030] Optionally, the objective function is expressed as follows:

[0031] ;

[0032] in, To preserve the weight parameters of the projection locally, The weight parameters for the optimized cell affinity map, Represents the basis matrix. This indicates the gene expression characteristics. This represents the noise matrix corresponding to gene expression characteristics. This represents the spatial features. This represents the noise matrix corresponding to the spatial features.

[0033] In a second aspect, the present invention provides a spatial domain identification device for biological spatial transcriptome slices, the device comprising:

[0034] The first network construction module is used to construct a spatial nearest neighbor cell network based on the spatial location information of cells in the noisy spatial transcriptome slice; wherein, the spatial nearest neighbor cell network is used to describe the geometric proximity relationship between cells in the spatial transcriptome slice;

[0035] The second network construction module is used to construct a gene expression cell network based on gene expression data from preprocessed noisy spatial transcriptome slices; wherein, the gene expression cell network is used to characterize the gene expression similarity relationship of cells in spatial transcriptome slices;

[0036] The feature decomposition module is used to perform feature decomposition on the spatial nearest neighbor cell network and the gene expression cell network through non-negative matrix factorization to obtain spatial features, gene expression features and noise features.

[0037] An affinity map construction module is used to construct a cell affinity map based on the spatial features and the gene expression features;

[0038] The spatial domain identification module is used to perform unsupervised clustering of cells in the noisy spatial transcriptome slice based on the Leiden algorithm and the cell affinity map, so as to realize the spatial domain identification of the noisy spatial transcriptome slice.

[0039] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0040] In the above technical solution, this invention constructs a cell gene expression network and a cell spatial nearest neighbor network based on gene expression data and coordinate information of noisy spatial transcriptome slices, respectively, transforming the analysis and spatial domain identification of noisy spatial transcriptome slices into a network clustering problem, providing a basic foundation for the analysis of noisy ST data; this invention utilizes non-negative matrix factorization to decompose the above-mentioned gene expression cell network and spatial nearest neighbor cell network, and achieves noise decomposition and characterization at the feature level; based on joint non-negative matrix factorization, this invention constructs a cell affinity map in a self-representational manner through gene expression features and spatial location features; further reducing the impact of noise in gene expression data at the global level, and achieving accurate spatial domain identification.

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0042] Figure 1 This is a flowchart of a method for spatial domain identification of biological spatial transcriptome slices provided in an embodiment of the present invention;

[0043] Figure 2 This is a block diagram of a spatial domain identification device for biological spatial transcriptome slices provided in an embodiment of the present invention. Detailed Implementation

[0044] 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.

[0045] Given spatial transcriptomics data ,in, Represents the spatial location information of cells. Represents the number of cells. Indicates the first The two-dimensional spatial coordinates of each cell. express Gene expression data of individual cells Statement No. Gene expression vectors of each cell. and All contain unavoidable noise. Given spatial transcriptomics data... The present invention will Included Each cell was divided into Cluster This invention studies the hard-partition clustering problem, requiring that the intersection of different clusters is an empty set, i.e. In addition, based on the requirement of connectivity within the same spatial domain, the spatial domain identification results of multilayer cellular networks... It is highly connected in all modes, that is... It exhibits a compact cluster structure in all modes.

[0046] Figure 1 This is a flowchart of a method for spatial domain identification of biological spatial transcriptome slices provided in an embodiment of the present invention, such as... Figure 1 As shown, the method may include the following steps:

[0047] S101. Construct a spatial nearest neighbor cell network based on the spatial location information of cells in the noisy spatial transcriptome slice; wherein, the spatial nearest neighbor cell network is used to describe the geometric proximity relationship between cells in the spatial transcriptome slice.

[0048] Understandable, Indicates based on spatial location information The constructed spatial nearest neighbor cell network, for the first Each cell is used to assess the proximity relationship between itself and other cells using Euclidean distance. This proximity relationship constitutes a spatial nearest neighbor network. The adjacency matrix.

[0049] S102. Construct a gene expression cell network based on the gene expression data in the preprocessed noisy spatial transcriptome slices; wherein, the gene expression cell network is used to characterize the gene expression similarity relationship of cells in the spatial transcriptome slices.

[0050] It is understandable that gene expression cell networks are constructed based on gene expression data from preprocessed noisy spatial transcriptome slices. .

[0051] S103. The spatial nearest neighbor cell network and the gene expression cell network are decomposed by nonnegative matrix factorization to obtain spatial features, gene expression features and noise features.

[0052] It is understandable that non-negative matrix factorization (NMF) is performed on spatial nearest neighbor cell networks and gene expression cell networks to reveal the noise features present in the constructed features (manifested as gene expression noise and spatial noise), and then sparsification constraints are imposed on them.

[0053] Optionally, the process of performing feature decomposition on spatial nearest neighbor cell networks and gene expression cell networks through nonnegative matrix factorization can be represented as follows:

[0054] ;

[0055] in, Represents a gene expression cellular network. Represents a spatial nearest neighbor cell network. Represents the basis matrix. Indicates gene expression characteristics, This represents the noise matrix corresponding to gene expression characteristics. Indicates spatial characteristics, This represents the noise matrix corresponding to the spatial features. This represents the calculation of the 1-norm. An implicit union between gene expression data and spatial location information is established through common-base decomposition. An explicit noise model and an implicit gene expression-spatial information union are provided; this union is a macroscopic deconstruction at the global level and does not form local information interaction. Further union methods can be adopted to make the similarity of spatial location information highly convergent with the similarity of gene expression data.

[0056] S104. Construct cell affinity maps based on spatial features and gene expression features.

[0057] It is understood that this invention constructs a cell affinity map based on learned features and is based on a noise-reduced spatial nearest neighbor cell network. The cell affinity map is optimized using self-supervised contrastive learning. The affinity map can be constructed using a self-representation learning method.

[0058] ;

[0059] in, Represents cell affinity diagrams. This represents the matrix transpose operation.

[0060] S105. Based on the Leiden algorithm, perform unsupervised clustering of cells in noisy spatial transcriptome slices according to cell affinity maps to achieve spatial domain identification of noisy spatial transcriptome slices.

[0061] Optionally, S105 may include:

[0062] Local preservation projection of gene expression characteristics is achieved through spatial nearest neighbor cell networks;

[0063] The objective function is constructed based on spatial features, gene expression features, noise features, local preservation projection, cell affinity maps, and contrastive learning optimization strategies.

[0064] In each iteration, the spatial features, gene expression features, and noise features are updated using the alternating direction multiplier method. The noise features are constrained by soft threshold rules, and the cell affinity map is updated according to stochastic gradient descent until the preset number of iterations is reached or the numerical change of the objective function is less than the preset threshold, thus obtaining the updated spatial features, updated gene expression features, updated noise features, and updated cell affinity map.

[0065] Based on the updated cell affinity map, unsupervised clustering of cells in noisy spatial transcriptome slices is performed using the Leiden algorithm to achieve spatial domain identification of noisy spatial transcriptome slices.

[0066] It is understood that the joint learning of this invention is embodied on two levels: first, implicit joint learning of gene expression features and spatial features; and second, explicit joint learning, which involves locally preserving the projection of gene expression features based on a denoised spatial nearest neighbor cell network. This invention uses a spatial nearest neighbor cell network to locally preserve the projection of gene expression features, as shown below:

[0067] ;

[0068] in, This indicates finding the trace of a matrix. Indicates gene expression characteristics, The Laplace matrix represents the spatial nearest neighbor network. This represents the matrix transpose operation.

[0069] Through the basis matrix and characteristic matrix To recover the spatial nearest neighbor cell network, the locally preserved projection evolves into the following form:

[0070] ;

[0071] in, This represents using NMF results to reconstruct a noise-free spatial nearest neighbor cell network. Represents its Laplace matrix, For noise reduction, a spatial nearest neighbor cell network.

[0072] Furthermore, the noise reduction spatial nearest neighbor cell network Binarization is performed, assuming each cell has 15 close neighbors, with their edges marked as 1; the rest are non-neighbors, with their edges marked as 0. Positive and negative samples are constructed based on the binarized graph, and an affinity graph is then processed using a contrastive learning strategy. The process of performing self-supervised optimization, which optimizes the affinity graph through comparative learning, is represented as follows:

[0073] ;

[0074] in, Represents cell affinity diagrams. This indicates that we are looking for the 1-norm. Denotes the square of the Frobenius norm. This indicates the number of cells in a noisy spatial transcriptome slice. Represents cells Neighborhood determined by spatial location Represents an exponential function. The optimized cell affinity diagram shows the first cell... Line 1 Column elements, The optimized cell affinity diagram shows the first cell... Line 1 Column elements, To facilitate comparative learning, the relevant temperature parameter is set to 1 in this invention. The affinity graph optimization employs a self-supervised contrastive learning strategy, which ensures noise estimation and removal at a global level. The construction of positive and negative samples uses the denoised and reconstructed spatial nearest neighbor graph as a reference. This conservative sampling strategy leads to the following joint optimization path: affinity graph learning → noise extraction and graph reconstruction → matrix factorization and feature learning. It should be noted that this joint optimization path is not a simple linear series but exhibits a multi-link coupling relationship. This coupling ensures that the invention is insensitive to changes in non-learned specified parameters. Subsequent technical details will be described in more detail.

[0075] Based on the above formula, the objective function is expressed as follows:

[0076] ;

[0077] in, To preserve the weight parameters of the projection locally, The weight parameters for the optimized cell affinity map, Represents the basis matrix. Indicates gene expression characteristics, This represents the noise matrix corresponding to gene expression characteristics. Indicates spatial characteristics, This represents the noise matrix corresponding to the spatial features.

[0078] This invention uses ADMM (Alternating Direction Method of Multipliers) to update and calculate variables. Spatial features, gene expression features, and local preservation projections can all be obtained by setting the partial derivatives of the corresponding variables to 0 to obtain the rules for variable iterative updates. However, the optimized cell affinity diagram cannot be directly solved by a similar method and needs to be solved by stochastic gradient descent. In addition, the optimization process of this invention makes two engineering approximations: (1) Because the spatial location coordinate noise is small, the spatial nearest neighbor cell network after denoising and restoration is relatively small. In the objective function, it can still be followed Calculations are performed. Therefore, in the locally preserved projection term, there is only one variable: gene expression characteristics; (2) For all sparse matrices, the process of finding the partial derivative is approximately handled according to the second norm, and a soft threshold rule to ensure sparsity is added when updating parameters. The soft threshold rule is defined as follows:

[0079] ;

[0080] Based on this, the spatial features, gene expression features, and local preservation projections after each iteration are described as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] The iterative update of the optimized cell affinity graph is more complex than that described above because the contrastive learning term makes it impossible to obtain a closed-form solution for the optimized cell affinity graph, and optimization can only be performed through stochastic gradient descent. Therefore, this invention divides its optimization process into two steps: (1) finding the partial derivative with respect to the cell affinity graph; (2) iterating the optimized cell affinity graph using stochastic gradient descent.

[0087] The partial derivatives of the cell affinity map can be divided into two parts: one is the affinity map learning related terms, and the other is the comparison learning related terms. These two parts of the partial derivatives with respect to the cell affinity map are denoted as... and ,but:

[0088] ;

[0089] ;

[0090] in, For each non-neighbor cell, a softmax weight is calculated, and in the gradient calculation (as described above) (Calculation formula) The larger In contrast The more distant they become.

[0091] According to the above formula, the partial derivative of the objective function with respect to the optimized cell affinity map is: Based on this, the update can be completed using an efficient gradient descent optimizer, Adam, and finally, an application is made. Approximate sparsification can be achieved.

[0092] This invention employs a multi-iteration approach to achieve the aforementioned optimization. Within each iteration, spatial features, gene expression features, local preservation projections, and optimized cell affinity maps are updated sequentially. After parameter updates, the objective function is evaluated and compared with its values ​​from previous iterations. Optimization terminates when the preset number of iterations is reached or the objective function converges to a relatively stable range over multiple iterations. The resulting updated spatial features, gene expression features, local preservation projections, and cell affinity maps, along with the local optimum solutions for each parameter, are obtained.

[0093] In this invention, the parameters used in the optimization process are set as follows: Preliminary experiments have shown that this invention is effective against... and The values ​​of exhibit good robustness. Furthermore, the objective function can also be optimized using deep learning frameworks through automatic differentiation and stochastic gradient descent, such as PyTorch and TensorFlow.

[0094] Figure 2 This is a block diagram of a spatial domain identification device for biological spatial transcriptome slices provided in an embodiment of the present invention, as shown below. Figure 2 As shown, the device 200 may include:

[0095] The first network construction module 201 is used to construct a spatial nearest neighbor cell network based on the spatial location information of cells in a noisy spatial transcriptome slice; wherein, the spatial nearest neighbor cell network is used to describe the geometric proximity relationship between cells in a spatial transcriptome slice.

[0096] The second network construction module 202 is used to construct a gene expression cell network based on gene expression data in the preprocessed noisy spatial transcriptome slices; wherein, the gene expression cell network is used to characterize the gene expression similarity relationship of cells in the spatial transcriptome slices;

[0097] The feature decomposition module 203 is used to perform feature decomposition on the spatial nearest neighbor cell network and the gene expression cell network through non-negative matrix decomposition to obtain spatial features, gene expression features and noise features.

[0098] Affinity map construction module 204 is used to construct cell affinity maps based on spatial features and gene expression features;

[0099] The spatial domain identification module 205 is used to perform unsupervised clustering of cells in noisy spatial transcriptome slices based on the Leiden algorithm and cell affinity maps, so as to realize spatial domain identification of noisy spatial transcriptome slices.

[0100] This invention constructs cellular gene expression networks and cellular spatial nearest neighbor networks based on gene expression data and coordinate information from noisy spatial transcriptome slices, transforming the analysis and spatial domain identification of noisy spatial transcriptome slices into a network clustering problem, providing a fundamental basis for the analysis of noisy ST data. This invention utilizes non-negative matrix factorization to decompose the aforementioned gene expression cellular networks and spatial nearest neighbor cellular networks, achieving noise decomposition and characterization at the feature level. Based on joint non-negative matrix factorization, this invention constructs a cell affinity map using gene expression features and spatial location features in a self-representational manner, further reducing noise in the gene expression data at a global level. The invention addresses the impact of noise in gene expression data and achieves accurate spatial domain identification. Based on the combined NMF (Non-Functional Multiplication), this invention constructs a cell affinity map using gene expression features and spatial location features in a self-representational manner. To further reduce the impact of noise in gene expression data at the global level, this invention utilizes self-supervised contrastive learning to optimize the cell affinity map. It iterative optimization is performed on variables with closed-form solutions using the alternating multiplier method, while analytical gradient descent is used to optimize variables without closed-form solutions. Furthermore, the objective function proposed in this invention can also be optimized using automatic differentiation based on a deep learning framework—a stochastic gradient descent approach.

[0101] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0102] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0103] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0104] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A spatial domain identification method for biological spatial transcriptome slices, characterized in that, The method comprises: constructing a spatial neighbor cell network according to spatial position information of cells in a noisy spatial transcriptome slice; wherein the spatial neighbor cell network is used to describe geometric proximity relationships between cells in the spatial transcriptome slice; constructing a gene expression cell network according to gene expression data in the preprocessed noisy spatial transcriptome slice; wherein the gene expression cell network is used to represent gene expression similarity relationships of cells in the spatial transcriptome slice; performing characteristic decomposition on the spatial neighbor cell network and the gene expression cell network through non-negative matrix decomposition to obtain spatial features, gene expression features, and noise features; constructing a cell affinity graph according to the spatial features and the gene expression features; performing unsupervised clustering of cells in the noisy spatial transcriptome slice based on a leiden algorithm according to the cell affinity graph to realize spatial domain recognition of the noisy spatial transcriptome slice; wherein the performing unsupervised clustering of cells in the noisy spatial transcriptome slice based on the leiden algorithm according to the cell affinity graph to realize spatial domain recognition of the noisy spatial transcriptome slice comprises: performing local preserving projection of the gene expression features through the spatial neighbor cell network; constructing an objective function according to the spatial features, the gene expression features, the noise features, the local preserving projection, the cell affinity graph, and a contrastive learning optimization strategy; updating the spatial features, the gene expression features, and the noise features through an alternating direction multiplier method in each iteration, performing soft threshold rule constraint on the noise features, and updating the cell affinity graph according to a stochastic gradient descent until a preset iteration number is reached or a numerical change of the objective function is less than a preset threshold, to obtain updated spatial features, updated gene expression features, updated noise features, and an updated cell affinity graph; performing unsupervised clustering of cells in the noisy spatial transcriptome slice based on the leiden algorithm according to the updated cell affinity graph to realize spatial domain recognition of the noisy spatial transcriptome slice.

2. The method for spatial domain identification of spatial transcriptomics slices according to claim 1, characterized in that, The process of performing characteristic decomposition on the spatial neighbor cell network and the gene expression cell network through non-negative matrix decomposition is as follows: ； wherein, represents the gene expression cell network, represents the spatial neighborhood cell network, represents the basis matrix, represents the gene expression feature, represents the noise matrix corresponding to the gene expression feature, represents the spatial feature, represents the noise matrix corresponding to the spatial feature, represents the 1-norm.

3. The method for spatial domain identification of spatial transcriptomics slices according to claim 2, characterized in that, The cell affinity graph is represented as follows: ； wherein denotes the cell affinity map, denotes the transpose operation of a matrix.

4. The method for spatial domain identification of spatial transcriptomics slices according to claim 1, characterized in that, The local preserving projection is represented as follows: ； wherein, denotes the trace of a matrix, denotes the gene expression signature, denotes the Laplacian matrix of the denoising spatial neighborhood network, denotes the transpose operation of a matrix.

5. The spatial domain identification method for spatial transcriptomic slices of biological space according to claim 4, characterized in that, The process of optimizing the affinity graph through contrastive learning is as follows: ； wherein, denotes a cell affinity map, denotes a 1-norm, denotes a number of cells in a noisy spatial transcriptomic slice, denotes a cell neighborhood determined by spatial location, denotes an exponential function, denotes an element in the cell affinity map at row and column , denotes an element in the cell affinity map at row and column , is a temperature parameter related to contrastive learning.

6. The method for spatial domain identification of spatial transcriptomics slices according to claim 5, characterized in that, The objective function is represented as follows: ； wherein, is a weight parameter for locally preserving projections, is a weight parameter for the optimized cell affinity map, denotes a basis matrix, denotes the gene expression signature, denotes a noise matrix corresponding to the gene expression signature, denotes the spatial feature, denotes a noise matrix corresponding to the spatial feature.

7. A spatial domain identification device for biological spatial transcriptome slices, characterized in that, The device comprises: a first network construction module configured to construct a spatial neighbor cell network according to spatial position information of cells in a noisy spatial transcriptome slice; wherein the spatial neighbor cell network is used to describe geometric proximity relationships between cells in the spatial transcriptome slice; a second network construction module configured to construct a gene expression cell network according to gene expression data in the preprocessed noisy spatial transcriptome slice; wherein the gene expression cell network is used to represent gene expression similarity relationships of cells in the spatial transcriptome slice; a characteristic decomposition module configured to perform characteristic decomposition on the spatial neighbor cell network and the gene expression cell network through non-negative matrix decomposition to obtain spatial features, gene expression features, and noise features; an affinity graph construction module configured to construct a cell affinity graph according to the spatial features and the gene expression features; a spatial domain identification module configured to perform unsupervised clustering of cells in the noisy spatial transcriptome section based on the cell affinity graph according to a leiden algorithm to achieve spatial domain identification of the noisy spatial transcriptome section; wherein the spatial domain identification module is further configured to perform local preserving projection on the gene expression features through a spatial neighborhood cell network; construct a target function according to the spatial features, the gene expression features, the noise features, the local preserving projection, the cell affinity graph, and a contrastive learning optimization strategy; update the spatial features, the gene expression features, and the noise features by using an alternating direction multiplier method in each iteration, perform soft threshold rule constraint on the noise features, and update the cell affinity graph according to a stochastic gradient descent until a preset iteration number is reached or a numerical change of the target function is less than a preset threshold, to obtain updated spatial features, updated gene expression features, updated noise features, and an updated cell affinity graph; perform unsupervised clustering of cells in the noisy spatial transcriptome section based on the updated cell affinity graph according to the leiden algorithm to achieve spatial domain identification of the noisy spatial transcriptome section. an affinity graph construction module configured to construct a cell affinity graph according to the spatial features and the gene expression features; a spatial domain identification module configured to perform unsupervised clustering of cells in the noisy spatial transcriptome section based on the cell affinity graph according to a leiden algorithm to achieve spatial domain identification of the noisy spatial transcriptome section; wherein the spatial domain identification module is further configured to perform local preserving projection on the gene expression features through a spatial neighborhood cell network; construct a target function according to the spatial features, the gene expression features, the noise features, the local preserving projection, the cell affinity graph, and a contrastive learning optimization strategy; update the spatial features, the gene expression features, and the noise features by using an alternating direction multiplier method in each iteration, perform soft threshold rule constraint on the noise features, and update the cell affinity graph according to a stochastic gradient descent until a preset iteration number is reached or a numerical change of the target function is less than a preset threshold, to obtain updated spatial features, updated gene expression features, updated noise features, and an updated cell affinity graph; perform unsupervised clustering of cells in the noisy spatial transcriptome section based on the updated cell affinity graph according to the leiden algorithm to achieve spatial domain identification of the noisy spatial transcriptome section.

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