Spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-credibility guidance

Abstract

The invention discloses a spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-credibility guidance, and belongs to the technical field of bioinformatics, and the method comprises the following steps: step 1, designing a multi-view construction module, and constructing an enhanced view to fully learn complementarity information of a gene expression structure; step 2, reconstructing gene expression data based on collaborative embedding; 3, performing clustering prediction on spatial embedding, feature embedding, enhanced embedding and collaborative embedding through a weight-shared pseudo-label classifier; and step 4, performing joint optimization to train the total loss function, and clustering the optimized collaborative embedding to generate a clustering label. The spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-credibility guidance is good in performance in spatial domain recognition, trajectory inference and cancer gene heterogeneity, and helps researchers to deeply understand the development process of cytobiology and diseases.

Description

Technical Field

[0001] The present invention relates to the technical field of bioinformatics, and in particular to a spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance. Background Art

[0002] As a cutting-edge molecular biology technology, the core of spatial transcriptomics is to accurately capture gene expression and simultaneously analyze the spatial distribution of these expression patterns within tissue sections. The clever integration of spatial dimension information helps to understand the regulation of gene expression by environmental factors, thereby better revealing the spatial heterogeneity of gene expression in disease states. In the analysis of spatial transcriptomes, accurately identifying spatial domains is a core challenge. Identifying spatial domains means identifying areas where the physical space is consistent in gene expression patterns and histology.

[0003] In order to overcome this problem, researchers have developed a series of innovative strategies in recent years, aiming to deeply integrate spatial information with gene expression profiles. Existing spatial domain recognition methods can be roughly divided into two categories: models based on probabilistic modeling and models based on deep learning. In the field of probabilistic modeling, Giotto introduced the hidden Markov random field model to achieve precise positioning of the spatial domain by capturing the complex spatial dependencies between spots. SpatialPCA innovatively improves the PCA method, taking location data as input, and using the kernel matrix to simulate and strengthen the correlation structure between spots to improve the clustering effect.

[0004] In the field of deep learning, GraphST combines graph neural networks with self-supervised contrastive learning to learn gene structure features by minimizing the embedding distance between spatially adjacent spots. Spatial-MGCN uses a multi-view convolutional encoder to jointly model spatial structure and gene expression similarity, and dynamically learns the complex dependencies between them through an attention mechanism. Although these methods have made significant progress, most of them focus on capturing the consistency information between gene expression and position coordinates, while the complementary information contained in the data has not been fully explored. Although Spatial-MGCN reveals the complementarity between data to a certain extent by evaluating the similarity of gene expression and spatial position separately, it is still insufficient to capture the complex nonlinear features of gene expression, which limits the further improvement of its performance. Therefore, further exploring how to more comprehensively integrate spatial position and gene expression data and deeply explore their complementarity is of great significance for promoting spatial transcriptome analysis to a new level. Summary of the invention

[0005] The purpose of the present invention is to provide a spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, which performs well in spatial domain identification, trajectory inference and cancer gene heterogeneity, and is conducive to helping researchers gain a deeper understanding of cell biology and the development process of diseases.

[0006] To achieve the above object, the present invention provides a spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, comprising the following steps:

[0007] Step 1: Design a multi-view construction module. First, construct a feature neighbor matrix and a spatial neighbor matrix, combine the gene expression matrix to form a feature view and a spatial view, and then construct a weighted neighbor matrix and generate a complementary enhanced gene expression matrix to construct an enhanced view to fully learn the complementary information of the gene expression structure.

[0008] Step 2: Build a multi-view collaborative convolutional network framework, independently learn the embedding representation of each view, then introduce the attention mechanism to integrate the embeddings of each view to generate a more comprehensive and accurate collaborative embedding, and finally use the zero-inflated negative binomial distribution ZINB decoder to reconstruct the gene expression data based on the collaborative embedding;

[0009] Step 3: Design a high-confidence clustering guidance module to perform clustering predictions on spatial embedding, feature embedding, enhanced embedding, and collaborative embedding through a weight-sharing pseudo-label classifier, and use the high-confidence clustering results as guidance to ensure the accuracy and stability of the clustering process;

[0010] Step 4: Jointly optimize the total training loss function, cluster the optimized collaborative embeddings, and generate cluster labels for downstream task analysis such as spatial domain recognition, visualization, and trajectory inference.

[0011] Preferably, step 1 specifically includes the following steps:

[0012] Step 1.1: The spatial view is composed of the spatial neighbor matrix and the original gene expression matrix X, is the preprocessed gene expression matrix, N is the number of spots, and M is the number of genes after filtering. i With spot j If the Euclidean distance between them is less than the set threshold r, then set Otherwise set in, is the value of the i-th row and j-th column of the spatial neighbor matrix, is the value of the jth row and ith column of the spatial neighbor matrix;

[0013] Step 1.2: Feature view is composed of feature neighbor matrix and the original gene expression matrix X, based on the k-nearest neighbor algorithm to select and spot i The k spots with the smallest cosine distance are taken as its neighbors. If spot j It's spot i 's neighbors, then otherwise in, is the value of the i-th row and j-th column of the feature neighbor matrix;

[0014] Step 1.3: Enhanced view by weighted neighbor matrix and enhanced gene expression matrix First, according to the neighbors of each spot screened out by the spatial view in step 1.1, the cosine distance between adjacent spots is calculated, and this distance is transformed into a similarity matrix through exponential transformation Weighted neighbor matrix A w Calculated according to the following formula:

[0015] S ij =exp(2-cosine_dist(spot i ,spot j ));

[0016]

[0017] Among them, S ij for spot i With spot j Feature similarity coefficient, is the value of the i-th row and j-th column of the weighted neighbor matrix;

[0018] Finally, the enhanced gene expression of each spot is obtained by comparing and learning the shared information of neighbors, thereby constructing the enhanced gene expression matrix, which is calculated according to the following formula:

[0019] X a =X+βXA w ;

[0020] where β is an adjustable parameter that can be manually set to control the impact of spatial neighborhood similarity on the spatial domain.

[0021] Preferably, step 2 specifically includes the following steps:

[0022] Step 2.1: The feature view, spatial view, and enhanced view obtained in step 1 are used as the feature convolution network FGCN, the spatial convolution network SGCN, and the enhanced convolution network AGCN to learn the embedded features of each view. The feature convolution network embeds H f , spatial convolutional network embedding H s , enhanced convolutional network embedding Ha , calculated according to the following formula:

[0023]

[0024] in, is the output of the l+1th convolutional layer of view ι, is the output of the l-th convolutional layer of view ι, W ι (l) is the trainable parameter matrix of the l-th layer convolution of view ι, view ι takes the value of {s, f, a}, and the initial value of the convolution network is set σ is the activation function in the convolutional network, yes The corner matrix of is the angle matrix The result of taking the reciprocal of the power is is an adjacency matrix with self-loops added, where I N is an N×N identity matrix;

[0025] Step 2.2: Based on the three views obtained in step 1, a co-convolutional network CoGCN is constructed to extract and construct the co-embedded representation between the three views. The propagation rule of the co-convolutional network is defined as follows:

[0026]

[0027] in, is the latent embedding extracted from the l+1th layer of the co-convolutional network for view ρ, is the trainable parameter matrix of the lth layer of the co-convolutional network, is the potential embedding extracted from the l-th layer of the co-convolutional network for view ρ, where the value of view ρ is {s, f, a} and the initial layer is set to yes The corner matrix of is an adjacency matrix with self-loops added, where I N is an N×N identity matrix, is the angle matrix The result of taking the reciprocal of the power;

[0028] Step 2.3: Based on the co-convolutional network in step 2.2, the feature co-embedding of the lth layer is obtained. Spatial co-embedding Enhanced co-embedding The co-embedding of the lth layer is calculated according to the following formula

[0029]

[0030] Step 2.4: Introduce the attention mechanism for adaptively learning the contribution of each embedding and integrate the feature embedding H f , spatial embedding H s , Enhanced Embedding H a and co-embedded H c , the collaborative embedding H is obtained to achieve fine-grained recognition in the spatial domain, and the embedding contribution of each view is calculated according to the following formula:

[0031] ξ ν =softmax(W ν ·σ(WH ν + b));

[0032] Among them, σ is the activation function, W is the trainable weight matrix, b is the bias vector, H ν represents the embedding of each view, where ν is {s, f, a, c}, ξ ν is the contribution coefficient of view ν to the collaborative embedding H. The final collaborative embedding H is obtained by combining the embeddings of each view, which is calculated as follows:

[0033]

[0034] in, is a single linear layer for learning highly variable features of embeddings;

[0035] Step 2.5: Use the ZINB distribution model to simulate the distribution of potential features and capture the characteristics of co-embedding, that is, use the distribution parameters of the co-embedding matrix to reconstruct the original gene expression matrix X data:

[0036]

[0037] ZINB(X|π,μ,θ)=π·δ0(x)+(1-π)·NB(X|μ,θ);

[0038] where μ and θ represent mean and dispersion, π controls the probability of the zero-value production process, NB(X|μ,θ) is the negative binomial distribution part, which represents the distribution in the non-zero generation process; Γ(X+θ) is the gamma function value of X+θ, Γ(θ) is the gamma function value of θ, X! is the factorial of X, and δ0(x) is an indicator function used to represent the zero-value generation process;

[0039] Step 2.6: After obtaining the co-embedding, connect 3 fully connected layers to learn the parameters corresponding to the ZINB model and use the negative log-likelihood reconstruction loss L zinb , defined as follows:

[0040] L zinb=∑-log(ZINB(X|π,μ,θ));

[0041] Preferably, step 3 specifically includes the following steps:

[0042] Step 3.1: Embed the space into H s , feature embedding H f , Enhanced Embedding H a and the collaborative embedding H is input into the weight-sharing pseudo-label classifier for cluster prediction to generate the corresponding cluster distribution matrix, Y s =gc(H s ), Y f =gc(H f ), Y a =gc(H a ), Y = gc(H), gc is a weight-sharing pseudo-label classifier, C is the number of clusters, and for ease of expression, we define Represents Y s The cluster distribution vector of the jth column, Y f ,Y a ,Y and Y s To express unity,

[0043]

[0044] in, Represents Y s The probability value of being assigned to the jth cluster, is the spot in the spatially embedded cluster distribution matrix i The probability value of being assigned to the jth cluster;

[0045] Step 3.2: Calculate feature embedding H f , spatial embedding H s and enhanced embedding H a The contrast loss between the cluster distribution vectors of each cluster in , by minimizing this loss, effectively reduces the ambiguity of the clustering results, calculated according to the following formula:

[0046]

[0047] in, Denotes the computational space embedding H s The contrast loss of the j-th cluster is, Denotes the computational feature embedding H f The contrast loss of the j-th cluster is, Denotes the computationally enhanced embedding H a The contrast loss of the j-th cluster is, for and The exponential result of the similarity function between for and The exponential result of the similarity function between for and The exponential result of the similarity function between them, τ is the cluster-level weight parameter that controls the softness, and the total contrast loss of clustering is expressed as follows:

[0048]

[0049] in, represents information entropy, is the maximum entropy, is the distribution probability of the t-th sample in the j-th cluster of the spatially embedded cluster distribution matrix, T(Y f ) is Y f The information entropy of a ) is Y a The information entropy of f ) and T(Y a ) and T(Y s ) is calculated in the same way;

[0050] Step 3.3: Based on the four cluster distribution matrices, the maximum cluster selection strategy is adopted. For each spot, the maximum value of the probability of belonging to each cluster is selected from the four matrices to determine the target cluster of the spot, and then the target distribution matrix Q is constructed. i The cluster soft label is calculated according to the following formula:

[0051]

[0052] Step 3.4: Soft label q based on step 3.3 ij To improve the high confidence of the collaborative embedding H, the target distribution matrix Q is normalized so that the sum of all cluster probabilities of each spot is 1, calculated as follows:

[0053]

[0054] Among them, p ij is the normalized probability value, ensuring that the sum of all cluster probabilities of each sample is 1. is the maximum probability value selected from the four cluster distribution matrices, which is used to determine the target cluster for each sample;

[0055] Step 3.5, the normalized target distribution matrix P is used as an auxiliary guide for clustering results, and the optimization target is calculated according to the following formula:

[0056]

[0057] Among them, KL(Y||P) represents the KL divergence between the cluster distribution matrix Y and the target distribution matrix P, y ij is the probability that the i-th sample in the cluster distribution matrix Y is in the j-th cluster.

[0058] Preferably, step 4 specifically includes the following steps:

[0059] Step 4.1. Calculate the cosine similarity matrix and spatial neighbor matrix A of the co-embedding H s The cross entropy loss ensures that the co-embedding of each spot during model training is as similar as possible to its neighboring spots in space. The spatial consistency constraint loss is calculated as follows:

[0060]

[0061] Where cosine_dist(H i ,H j ) means spot i With spot j Cosine similarity calculated based on collaborative embedding, δ i It's spot i The spatial neighbor set, H i for spot i The spatial embedding vector of j for spot j The spatial embedding vector of

[0062] Step 4.2: Jointly optimize the high-confidence clustering guidance loss, ZINB reconstruction loss, and spatial consistency constraint loss. The total loss target of stMHCG is defined as follows:

[0063] L=ε1L reg +ε2L clu +ε3L hcg +ε4L zinb ;

[0064] Among them, L reg is the spatial consistency constraint, L clu is the clustering loss, L hcg is the guidance loss for high confidence clustering, L zinb is the ZINB reconstruction loss, and ε1, ε2, ε3, and ε4 are weighting factors that weigh the impact of the loss function.

[0065] Therefore, the present invention adopts the above-mentioned spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, which performs well in spatial domain identification, trajectory inference and cancer gene heterogeneity, and is conducive to helping researchers gain a deeper understanding of cell biology and the development process of diseases.

[0066] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic diagram of the process of the present invention;

[0068] Figure 2 It is a manual annotation result of a human dorsolateral prefrontal cortex dataset and a box plot of ARI and NMI indicators of the present invention and other methods on the dataset;

[0069] Figure 3 It is a result diagram of spatial domain recognition on a human dorsolateral prefrontal cortex data set by the present invention and other methods;

[0070] Figure 4 It is a result diagram of spatial domain recognition on a mouse visual cortex dataset by the present invention and other methods;

[0071] Figure 5 This is a result diagram of visualization and trajectory inference of the present invention and other methods on a human dorsolateral prefrontal cortex dataset;

[0072] Figure 6 The result diagram of the spatial domain recognition of the present invention on the human breast cancer data set;

[0073] Figure 7 This is a result diagram of the gene heterogeneity analysis on the human breast cancer data set of the present invention. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0075] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0076] Embodiment 1

[0077] like Figure 1 As shown, the present invention provides a spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, comprising the following steps:

[0078] Step 1: Figure 1 As shown in A in the figure, a multi-view construction module is designed. First, a feature neighbor matrix and a spatial neighbor matrix are constructed. The feature view and the spatial view are constructed in combination with the gene expression matrix. Then, by constructing a weighted neighbor matrix and generating a complementary enhanced gene expression matrix, an enhanced view is constructed to fully learn the complementary information of the gene expression structure.

[0079] The specific steps include:

[0080] Step 1.1: The spatial view is composed of the spatial neighbor matrix and the original gene expression matrix X, is the preprocessed gene expression matrix, N is the number of spots, and M is the number of genes after filtering. i With spot j If the Euclidean distance between them is less than the set threshold r, then set Otherwise set in, is the value of the i-th row and j-th column of the spatial neighbor matrix, is the value of the jth row and ith column of the spatial neighbor matrix;

[0081] Step 1.2: Feature view is composed of feature neighbor matrix and the original gene expression matrix X, based on the k-nearest neighbor algorithm to select and spot i The k spots with the smallest cosine distance are taken as its neighbors. If spot j It's spot i 's neighbors, then otherwise in, is the value of the i-th row and j-th column of the feature neighbor matrix;

[0082] Step 1.3: Enhanced view by weighted neighbor matrix and enhanced gene expression matrix First, according to the neighbors of each spot screened out by the spatial view in step 1.1, the cosine distance between adjacent spots is calculated, and this distance is transformed into a similarity matrix through exponential transformation Weighted neighbor matrix A w Calculated according to the following formula:

[0083] S ij =exp(2-cosine_dist(spot i ,spot j ));

[0084]

[0085] Among them, S ij for spot i With spot j Feature similarity coefficient, is the value of the i-th row and j-th column of the weighted neighbor matrix;

[0086] Finally, the enhanced gene expression of each spot is obtained by comparing and learning the shared information of neighbors, thereby constructing the enhanced gene expression matrix, which is calculated according to the following formula:

[0087] X a =X+βXA w ;

[0088] where β is an adjustable parameter that can be manually set to control the impact of spatial neighborhood similarity on the spatial domain.

[0089] Step 2: Figure 1 As shown in B in Figure 1, a multi-view collaborative convolutional network framework is constructed to independently learn the embedding representation of each view. Then, an attention mechanism is introduced to integrate the embeddings of each view to generate a more comprehensive and accurate collaborative embedding. Finally, the zero-inflated negative binomial distribution ZINB decoder is used to reconstruct the gene expression data based on the collaborative embedding.

[0090] The specific steps include:

[0091] Step 2.1: The feature view, spatial view, and enhanced view obtained in step 1 are used as the feature convolution network FGCN, the spatial convolution network SGCN, and the enhanced convolution network AGCN to learn the embedded features of each view. The feature convolution network embeds H f , spatial convolutional network embedding H s , enhanced convolutional network embedding H a , calculated according to the following formula:

[0092]

[0093] in, is the output of the l+1th convolutional layer of view ι, is the output of the l-th convolutional layer of view ι, W ι (l) is the trainable parameter matrix of the l-th layer convolution of view ι, view ι takes the value of {s, f, a}, and the initial value of the convolution network is set σ is the activation function in the convolutional network, yes The corner matrix of is the angle matrix The result of taking the reciprocal of the power is is an adjacency matrix with self-loops added, where I N is an N×N identity matrix;

[0094] Step 2.2: Based on the three views obtained in step 1, a co-convolutional network CoGCN is constructed to extract and construct the co-embedded representation between the three views. The propagation rule of the co-convolutional network is defined as follows:

[0095]

[0096] in, is the latent embedding extracted from the l+1th layer of the co-convolutional network for view ρ, is the trainable parameter matrix of the lth layer of the co-convolutional network, is the potential embedding extracted from the l-th layer of the co-convolutional network for view ρ, where the value of view ρ is {s, f, a} and the initial layer is set to yes The corner matrix of is an adjacency matrix with self-loops added, where I N is an N×N identity matrix, is the angle matrix The result of taking the reciprocal of the power;

[0097] Step 2.3: Based on the co-convolutional network in step 2.2, the feature co-embedding of the lth layer is obtained. Spatial co-embedding Enhanced co-embedding The co-embedding of the lth layer is calculated according to the following formula

[0098]

[0099] Step 2.4: Introduce the attention mechanism for adaptively learning the contribution of each embedding and integrate the feature embedding H f , spatial embedding H s , Enhanced Embedding H a and co-embedded H c , the collaborative embedding H is obtained to achieve fine-grained recognition in the spatial domain, and the embedding contribution of each view is calculated according to the following formula:

[0100] ξ ν =softmax(W ν ·σ(WH ν + b));

[0101] Among them, σ is the activation function, W is the trainable weight matrix, b is the bias vector, H ν represents the embedding of each view, where ν is {s, f, a, c}, ξ ν is the contribution coefficient of view ν to the collaborative embedding H. The final collaborative embedding H is obtained by combining the embeddings of each view, which is calculated as follows:

[0102]

[0103] in, is a single linear layer for learning highly variable features of embeddings;

[0104] Step 2.5: Use the ZINB distribution model to simulate the distribution of potential features and capture the characteristics of co-embedding, that is, use the distribution parameters of the co-embedding matrix to reconstruct the original gene expression matrix X data:

[0105]

[0106] ZINB(X|π,μ,θ)=π·δ0(x)+(1-π)·NB(X|μ,θ);

[0107] where μ and θ represent mean and dispersion, π controls the probability of the zero-value production process, NB(X|μ,θ) is the negative binomial distribution part, which represents the distribution in the non-zero generation process; Γ(X+θ) is the gamma function value of X+θ, Γ(θ) is the gamma function value of θ, X! is the factorial of X, and δ0(x) is an indicator function used to represent the zero-value generation process;

[0108] Step 2.6: After obtaining the co-embedding, connect 3 fully connected layers to learn the parameters corresponding to the ZINB model and use the negative log-likelihood reconstruction loss L zinb , defined as follows:

[0109] L zinb =Σ-log(ZINB(X|π,μ,θ));

[0110] Step 3: If Figure 1 As shown in C in Figure 1, a high-confidence clustering guidance module is designed to perform clustering predictions on spatial embedding, feature embedding, enhanced embedding, and collaborative embedding through a weight-sharing pseudo-label classifier. The high-confidence clustering results are used as guidance to ensure the accuracy and stability of the clustering process.

[0111] The specific steps include:

[0112] Step 3.1: Embed the space into H s , feature embedding H f , Enhanced Embedding H a and the collaborative embedding H is input into the weight-sharing pseudo-label classifier for cluster prediction to generate the corresponding cluster distribution matrix, Y s =gc(H s ), Y f =gc(H f ), Y a =gc(H a ), Y = gc(H), gc is a weight-sharing pseudo-label classifier, C is the number of clusters, and for ease of expression, we define Represents Y s The cluster distribution vector of the jth column, Y f ,Y a,Y and Y s To express unity,

[0113]

[0114] in, Represents Y s The probability value of being assigned to the jth cluster, is the spot in the spatially embedded cluster distribution matrix i The probability value of being assigned to the jth cluster;

[0115] Step 3.2: Calculate feature embedding H f , spatial embedding H s and enhanced embedding H a The contrast loss between the cluster distribution vectors of each cluster in , by minimizing this loss, effectively reduces the ambiguity of the clustering results, calculated according to the following formula:

[0116]

[0117]

[0118] in, Denotes the computational space embedding H s The contrast loss of the j-th cluster is, Denotes the computational feature embedding H f The contrast loss of the j-th cluster is, Denotes the computationally enhanced embedding H a The contrast loss of the j-th cluster is, for and The exponential result of the similarity function between for and The exponential result of the similarity function between for and The exponential result of the similarity function between them, τ is the cluster-level weight parameter that controls the softness, and the total contrast loss of clustering is expressed as follows:

[0119]

[0120] in, represents information entropy, is the maximum entropy, is the distribution probability of the t-th sample in the j-th cluster of the spatially embedded cluster distribution matrix, T(Y f ) is Y f The information entropy of a ) is Y a The information entropy off ) and T(Y a ) and T(Y s ) is calculated in the same way, which is a strategy to avoid assigning all spots to the same cluster;

[0121] Step 3.3: Based on the four cluster distribution matrices, the maximum cluster selection strategy is adopted. For each spot, the maximum value of the probability of belonging to each cluster is selected from the four matrices to determine the target cluster of the spot, and then the target distribution matrix Q is constructed. i The cluster soft label is calculated according to the following formula:

[0122]

[0123] Step 3.4: Soft label q based on step 3.3 ij To improve the high confidence of the collaborative embedding H, the target distribution matrix Q is normalized so that the sum of all cluster probabilities of each spot is 1, calculated as follows:

[0124]

[0125] Among them, p ij is the normalized probability value, ensuring that the sum of all cluster probabilities of each sample is 1. is the maximum probability value selected from the four cluster distribution matrices, which is used to determine the target cluster for each sample;

[0126] Step 3.5, the normalized target distribution matrix P is used as an auxiliary guide for clustering results, and the optimization target is calculated according to the following formula:

[0127]

[0128] Among them, KL(Y||P) represents the KL divergence between the cluster distribution matrix Y and the target distribution matrix P, y ij is the probability that the i-th sample in the cluster distribution matrix Y is in the j-th cluster.

[0129] Step 4: Jointly optimize the total training loss function, cluster the optimized collaborative embeddings, and generate cluster labels for downstream task analysis such as spatial domain recognition, visualization, and trajectory inference;

[0130] The specific steps include:

[0131] Step 4.1. Calculate the cosine similarity matrix and spatial neighbor matrix A of the co-embedding H s The cross entropy loss ensures that the co-embedding of each spot during model training is as similar as possible to its neighboring spots in space. The spatial consistency constraint loss is calculated as follows:

[0132]

[0133] Where cosine_dist(H i ,H j ) means spot i With spot j Cosine similarity calculated based on collaborative embedding, δ i It's spot i The spatial neighbor set, H i for spot i The spatial embedding vector of j for spot j The spatial embedding vector of

[0134] Step 4.2: Jointly optimize the high-confidence clustering guidance loss, ZINB reconstruction loss, and spatial consistency constraint loss. The total loss target of stMHCG is defined as follows:

[0135] L=ε1L reg +ε2L clu +ε3L hcg +ε4L zinb ;

[0136] Among them, L reg is the spatial consistency constraint, L clu is the clustering loss, L hcg is the guidance loss for high confidence clustering, L zinb is the ZINB reconstruction loss, and ε1, ε2, ε3, and ε4 are weighting factors that weigh the impact of the loss function.

[0137] In order to verify the effectiveness of the present invention, the performance of the present invention was tested from three aspects: spatial domain recognition, trajectory inference and cancer heterogeneity analysis.

[0138] 1. Dataset and evaluation indicators

[0139] (1) Dataset

[0140] Gene expression matrices, spatial location information, and histological images of three datasets from the 10X Visium and STARmap platforms were obtained, and the dataset overview is shown in Table 1. The first dataset is the cortex (Layer1-Layer6) and white matter (WM) of 12 human dorsolateral prefrontal cortex slices manually annotated by marker genes and cell structures by Maynard et al., and the second dataset is the mouse visual cortex with 7 strip regions. The third dataset comes from the 10X Visium platform, focusing on human breast cancer tissue, and contains 20 spatial regions.

[0141] (2) Evaluation indicators

[0142] The most direct way to quantify the impact of clustering is to evaluate the differences in clustering results from different clustering vectors. stMHCG uses the Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI) as indicators to evaluate the effectiveness of clustering. The higher the ARI and NMI values, the higher the consistency of the clustering results with the ground truth, thus reflecting the higher accuracy of clustering.

[0143] Table 1 Dataset overview

[0144]

[0145] 2. Comparative analysis of experimental results

[0146] (1) Spatial domain recognition experiment

[0147] a. Human dorsolateral prefrontal cortex dataset

[0148] like Figure 2 As shown in Figure 1, stMHCG first implemented experiments on 12 slices of the human dorsolateral prefrontal cortex dataset. Figure 2 A in the figure is the manually annotated spatial domain result of the DLPFC151510 dataset, which is used as the benchmark for the experiment. Figure 2 B and Figure 2 As shown in Figure C, the performance of stMHCG is compared with five cutting-edge methods (SpaGCN, SEDR, STAGATE, GraphST, and Spatial-MGCN). The experimental results show that the average ARI and NMI values ​​of stMHCG on 12 slices have reached the highest level. This shows that the design of the stMHCG enhanced view supplements the original gene expression and spatial coordinate data, provides complementary information on the potential structure of gene expression, and improves clustering accuracy.

[0149] like Figure 3 As shown in the figure, in the visualization results of spatial domain recognition, stMHCG also demonstrated the ability to be closest to the actual annotation results. In contrast, SpaGCN and STAGATE are unable to distinguish the boundaries of different spot types, resulting in unnecessary discrete points in the same area. SEDR failed to accurately identify Layer 2, and incorrectly identified the strip area of ​​Layer 1. Although GraphST and Spatial-MGCN accurately identified the seven main areas, the recognition width of Layer 6 exceeded the actual range. With the guidance of high-confidence multi-view clustering, stMHCG can accurately capture the true width of Layer 6 and achieve more accurate boundary division.

[0150] b. Mouse visual cortex dataset

[0151] like Figure 4 As shown in the figure, a spatial domain recognition experiment was further conducted in the seven ribbon layers of the mouse visual cortex. Figure 4 A in the figure is the manual annotation result of the data. The six methods are compared and analyzed using the two evaluation indicators ARI and NMI. Figure 4 As shown in B in Figure 1, the ARI value of stMHCG is 0.463, ranking first, and the NMI value is 0.721, slightly lower than the STAGATE method, ranking second. Due to its enhanced data and highly reliable algorithm design, stMHCG successfully and relatively accurately delineated 7 different bar areas, such as Figure 4 C1 in , thus verifying its advantages in analyzing complex spatial structures. Figure 4 C2 in Figure 4 C3 and Figure 4 As shown in C4 in Figure 3, GraphST, STAGATE, and SEDR exhibited varying degrees of misclassification during clustering, including incorrect fusion of the L1 layer with the L2-3 layer and unclear boundaries between different regions, which together indicate their limitations in processing specific spatial patterns. In conclusion, stMHCG exhibited excellent performance and robustness in spatial domain recognition tasks associated with the STARmap mouse visual cortex, highlighting its potential as a valuable tool for neuroscience research.

[0152] (2) Trajectory inference experiment

[0153] like Figure 5 As shown, to prove that the learned features of stMHCG can be well generalized to other downstream tasks, the unified manifold approximation and projection (UMAP) is further used on the human dorsolateral prefrontal cortex dataset to visualize the distance between clusters and PAGA to infer spatial trajectories. In the UMAP images of SEDR and SpaGCN, the spots of layers 2 and 4, and layers 3 and 5 are mixed. STAGATE, GraphST, Spatial-MGCN, and stMHCG all separate all clusters well, but it can be seen that the tracking inference of STAGATE and GraphST is wrong. Only Spatial-MGCN and stMHCG correctly infer the trajectories from the first layer to the sixth layer to the VM layer. In the visualization results, stMHCG shows a higher degree of aggregation and differentiation than other methods, promoting tighter clustering of similar cell types.

[0154] (3) Cancer heterogeneity analysis experiments

[0155] like Figure 6As shown, when stMHCG performed a spatial domain recognition task on a human breast cancer dataset, it was found that stMHCG identified two different spot types (cluster 3 and cluster 13) in cluster IDC_8. SEDR and STAGATE also responded to this observation, but stMHCG showed superior cluster boundaries. Similarly, in cluster DCIS / LCIS_4, stMHCG accurately separated the two spot types (cluster 2 and cluster 12). In order to further study the molecular basis of these cell clusters, the top four differentially expressed genes between clusters 3 and 13 and clusters 2 and 12 were selected, respectively. The different expression patterns of these genes between clusters are depicted by violin plots, highlighting the substantial differences between cluster 3 and cluster 13, as shown in Figure 2. Figure 7 As shown in A.

[0156] To further analyze the gene expression differences between cluster IDC_6 and cluster DCIS / LCIS_2, a volcano plot was drawn to identify 109 statistically significant differentially expressed genes, such as Figure 7 As shown in B. Among them, matrix metalloproteinase-7 (MMP-7) and secretory leukocyte protease inhibitor (SLPI) play a key role in the invasiveness and metastatic process of breast cancer and the survival prognosis of patients. The close association between MMP-7 single nucleotide polymorphism and the survival rate of breast cancer patients has been widely and systematically verified. On the other hand, the study found that in the highly metastatic triple-negative breast cancer TNBC4T1 cell model, the gene expression level of SLPI was significantly increased compared with non-metastatic cells. This finding has opened up new horizons for the treatment strategy of breast cancer, suggesting that targeted inhibition of SLPI secretion may become a potential novel therapeutic approach that can effectively reduce the incidence of breast cancer.

[0157] Therefore, the present invention adopts the above-mentioned spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, which performs well in spatial domain identification, trajectory inference and cancer gene heterogeneity, and is conducive to helping researchers gain a deeper understanding of cell biology and the development process of diseases.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance, characterized by: The following steps are involved: Step 1: Design a multi-view construction module. First, construct a feature neighbor matrix and a spatial neighbor matrix, combine the gene expression matrix to form a feature view and a spatial view, and then construct a weighted neighbor matrix and generate a complementary enhanced gene expression matrix to construct an enhanced view to fully learn the complementary information of the gene expression structure. Step 2: Build a multi-view collaborative convolutional network framework, independently learn the embedding representation of each view, then introduce the attention mechanism to integrate the embeddings of each view to generate a more comprehensive and accurate collaborative embedding, and finally use the zero-inflated negative binomial distribution ZINB decoder to reconstruct the gene expression data based on the collaborative embedding; Step 3: Design a high-confidence clustering guidance module to perform clustering predictions on spatial embedding, feature embedding, enhanced embedding, and collaborative embedding through a weight-sharing pseudo-label classifier, and use the high-confidence clustering results as guidance to ensure the accuracy and stability of the clustering process; Step 4: Jointly optimize the total training loss function, cluster the optimized collaborative embeddings, and generate cluster labels for downstream task analysis such as spatial domain recognition, visualization, and trajectory inference.

2. The spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance according to claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: The spatial view is composed of the spatial neighbor matrix and the original gene expression matrix X, is the preprocessed gene expression matrix, N is the number of spots, and M is the number of genes after filtering. i With spot j If the Euclidean distance between them is less than the set threshold r, then set Otherwise set in, is the value of the i-th row and j-th column of the spatial neighbor matrix, is the value of the jth row and ith column of the spatial neighbor matrix; Step 1.2: Feature view is composed of feature neighbor matrix and the original gene expression matrix X, based on the k-nearest neighbor algorithm to select and spot i The k spots with the smallest cosine distance are taken as its neighbors. If spot j It's spot i 's neighbors, then otherwise in, is the value of the i-th row and j-th column of the feature neighbor matrix; Step 1.3: Enhanced view by weighted neighbor matrix and enhanced gene expression matrix First, according to the neighbors of each spot screened out by the spatial view in step 1.1, the cosine distance between adjacent spots is calculated, and this distance is transformed into a similarity matrix through exponential transformation Weighted neighbor matrix A w Calculated according to the following formula: S ij =exp(2-cosine_dist(spot i ,spot j )); Among them, S ij for spot i With spot j Feature similarity coefficient, is the value of the i-th row and j-th column of the weighted neighbor matrix; Finally, the enhanced gene expression of each spot is obtained by comparing and learning the shared information of neighbors, thereby constructing the enhanced gene expression matrix, which is calculated according to the following formula: X a =X+βXA w ; where β is an adjustable parameter that can be manually set to control the impact of spatial neighborhood similarity on the spatial domain.

3. The spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1: The feature view, spatial view, and enhanced view obtained in step 1 are used as the feature convolution network FGCN, the spatial convolution network SGCN, and the enhanced convolution network AGCN to learn the embedded features of each view. The feature convolution network embeds H f , spatial convolutional network embedding H s , enhanced convolutional network embedding H a , calculated according to the following formula: in, is the output of the l+1th convolutional layer of view ι, is the output of the l-th convolutional layer of view ι, is the trainable parameter matrix of the l-th layer convolution of view ι, view ι takes the value of {s, f, a}, and the initial value of the convolution network is set σ is the activation function in the convolutional network, yes The corner matrix of is the angle matrix The result of taking the reciprocal of the power is is an adjacency matrix with self-loops added, where I N is an N×N identity matrix; Step 2.2: Based on the three views obtained in step 1, a co-convolutional network CoGCN is constructed to extract and construct the co-embedded representation between the three views. The propagation rule of the co-convolutional network is defined as follows: in, is the latent embedding extracted from the l+1th layer of the co-convolutional network for view ρ, is the trainable parameter matrix of the lth layer of the co-convolutional network, is the potential embedding extracted from the l-th layer of the co-convolutional network for view ρ, where the value of view ρ is {s, f, a} and the initial layer is set to yes The corner matrix of is an adjacency matrix with self-loops added, where I N is an N×N identity matrix, is the angle matrix The result of taking the reciprocal of the power; Step 2.3: Based on the co-convolutional network in step 2.2, the feature co-embedding of the lth layer is obtained. Spatial co-embedding Enhanced co-embedding The co-embedding of the lth layer is calculated according to the following formula Step 2.4: Introduce the attention mechanism for adaptively learning the contribution of each embedding and integrate the feature embedding H f , spatial embedding H s , Enhanced Embedding H a and co-embedded H c , the collaborative embedding H is obtained to achieve fine-grained recognition in the spatial domain, and the embedding contribution of each view is calculated according to the following formula: x ν =softmax(W ν ·σ(WH ν +b)); Among them, σ is the activation function, W is the trainable weight matrix, b is the bias vector, H ν represents the embedding of each view, where ν is {s, f, a, c}, ξ ν is the contribution coefficient of view ν to the collaborative embedding H. The final collaborative embedding H is obtained by combining the embeddings of each view, which is calculated according to the following formula: in, is a single linear layer for learning highly variable features of embeddings; Step 2.5: Use the ZINB distribution model to simulate the distribution of potential features and capture the characteristics of co-embedding, that is, use the distribution parameters of the co-embedding matrix to reconstruct the original gene expression matrix X data: ZINB(X|π,μ,θ)=π·δ0(x)+(1-π)·NB(X|μ,θ); where μ and θ represent mean and dispersion, π controls the probability of the zero-value production process, NB(X|μ,θ) is the negative binomial distribution part, which represents the distribution in the non-zero generation process; Γ(X+θ) is the gamma function value of X+θ, Γ(θ) is the gamma function value of θ, X! is the factorial of X, and δ0(x) is an indicator function used to represent the zero-value generation process; Step 2.6: After obtaining the co-embedding, connect 3 fully connected layers to learn the parameters corresponding to the ZINB model and use the negative log-likelihood reconstruction loss L zinb , defined as follows: L zinb = ∑-log(ZINB(X|π,μ,θ)).

4. The spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1: Embed the space into H s , feature embedding H f , Enhanced Embedding H a and the collaborative embedding H is input into the weight-sharing pseudo-label classifier for cluster prediction to generate the corresponding cluster distribution matrix, Y s =gc(H s ), Y f =gc(H f ), Y a =gc(H a ), Y = gc(H), gc is a weight-sharing pseudo-label classifier, C is the number of clusters, and for ease of expression, we define Represents Y s The cluster distribution vector of the jth column, Y f ,Y a ,Y and Y s To express unity, in, Represents Y s The probability vector of being assigned to the jth cluster, Y s Nj is the spot in the spatially embedded cluster distribution matrix i The probability value of being assigned to the jth cluster; Step 3.2: Calculate feature embedding H f , spatial embedding H s and enhanced embedding H a The contrast loss between the cluster distribution vectors of each cluster in , by minimizing this loss, effectively reduces the ambiguity of the clustering results, calculated according to the following formula: in, Denotes the computational space embedding H s The contrast loss of the j-th cluster is, Denotes the computational feature embedding H f The contrast loss of the j-th cluster is, Denotes the computationally enhanced embedding H a The contrast loss of the j-th cluster is, for and The exponential result of the similarity function between for and The exponential result of the similarity function between for and The exponential result of the similarity function between them, τ is the cluster-level weight parameter that controls the softness, and the total contrast loss of clustering is expressed as follows: in, represents information entropy, is the maximum entropy, is the distribution probability of the t-th sample in the j-th cluster of the spatially embedded cluster distribution matrix, T(Y f ) is Y f The information entropy of a ) is Y a The information entropy of f ) and T(Y a ) and T(Y s ) is calculated in the same way; Step 3.3: Based on the four cluster distribution matrices, the maximum cluster selection strategy is adopted. For each spot, the maximum value of the probability of belonging to each cluster is selected from the four matrices to determine the target cluster of the spot, and then the target distribution matrix Q is constructed. i The cluster soft label is calculated according to the following formula: Step 3.4: Soft label q based on step 3.3 ij To improve the high confidence of the collaborative embedding H, the target distribution matrix Q is normalized so that the sum of all cluster probabilities of each spot is 1, calculated as follows: Among them, p ij is the normalized probability value, ensuring that the sum of all cluster probabilities of each sample is 1. is the maximum probability value selected from the four cluster distribution matrices, which is used to determine the target cluster for each sample; Step 3.5, the normalized target distribution matrix P is used as an auxiliary guide for clustering results, and the optimization target is calculated according to the following formula: Among them, KL(Y||P) represents the KL divergence between the cluster distribution matrix Y and the target distribution matrix P, y ij is the probability that the i-th sample in the cluster distribution matrix Y is in the j-th cluster.

5. The spatial transcriptomics multi-view clustering method based on spatial expression enhancement and high-confidence guidance according to claim 1, characterized in that: Step 4 specifically includes the following steps: Step 4.

1. Calculate the cosine similarity matrix and spatial neighbor matrix A of the co-embedding H s The cross entropy loss ensures that the co-embedding of each spot during model training is as similar as possible to its neighboring spots in space. The spatial consistency constraint loss is calculated as follows: Where cosine_dist(H i ,H j ) means spot i With spot j Cosine similarity calculated based on collaborative embedding, δ i It's spot i The spatial neighbor set, H i for spot i The spatial embedding vector of j for spot j The spatial embedding vector of Step 4.2: Jointly optimize the high-confidence clustering guidance loss, ZINB reconstruction loss, and spatial consistency constraint loss. The total loss target of stMHCG is defined as follows: L=ε1L reg +ε2L clu +ε3L hcg +ε4L zinb ; Among them, L reg is the spatial consistency constraint, L clu is the clustering loss, L hcg is the guidance loss for high confidence clustering, L zinb is the ZINB reconstruction loss, and ε1, ε2, ε3, and ε4 are weighting factors that weigh the impact of the loss function.

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