Space domain identification method, system and device based on min-max mutual information

Abstract

The present application relates to the technical field of bioinformatics, in particular to a spatial domain recognition method, system and device based on minimum maximum mutual information; the method of the present application firstly preprocesses spatial transcriptome data to construct an original spatial transcriptome graph; then, based on an information separation strategy, two enhancements are implemented on the original spatial transcriptome graph, including perturbation expression reservation topology and changing topology to highlight expression, to obtain a first enhanced spatial transcriptome graph and a second enhanced spatial transcriptome graph; then, the node feature similarity with the original spatial transcriptome graph is used to perform adaptive evolution graph topology on the first enhanced spatial transcriptome graph, and encode multi-view feature embedding, so as to improve feature expression accuracy and reduce computational burden; finally, the multi-view features are constrained by minimum maximum mutual information, the effective information reservation is maximized, the representation redundancy between views is minimized, and the supervised learning is reconstructed by decoding, so as to realize accurate spatial domain recognition.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics technology, specifically to a spatial domain identification method, system, and device based on minimum-maximum mutual information. Background Technology

[0002] The rise of spatial transcriptomics (ST) has greatly advanced research in the biomedical field, particularly in understanding how genes are functionally arranged in specific spatial locations, achieving unprecedented progress. Deciphering spatial domains is a crucial step in spatial transcriptomics analysis, aiming to allocate spatial transcriptome data into a series of meaningful spatial domains, each with different biological functions. Understanding the relative positions of different cells within tissues and their relationships is essential for deciphering spatial domains, as different cells may exhibit different gene expression patterns in specific spatial environments, leading to their specific roles in tissue function and development.

[0003] In recent years, the emergence of deep learning has promoted the development of spatial transcriptomics. Although existing deep learning methods have made some progress, three core problems still exist: First, there is no effective ST graph construction strategy to balance global and local information. This imbalance leads to over-reliance on local or global information, affecting downstream task analysis. Second, when fusing gene expression and spatial structure information, it usually relies directly on the graph structure inherent in the data, which may contain some unimportant connections, limiting the accuracy of feature expression and increasing the computational burden. Third, without restrictions on mutual information between ST graphs, relying on maximizing mutual information between ST graphs can lead to the model capturing too much repetitive information and some noisy data being mistakenly identified as valid information, resulting in a decrease in the quality of the final feature embedding learning, thus affecting downstream task analysis. Summary of the Invention

[0004] The purpose of this invention is to provide a spatial domain identification method, system, and device with minimum and maximum mutual information.

[0005] The technical solution of this invention is as follows: A spatial domain identification method based on minimum-maximum mutual information includes the following operations: S1. Obtain spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points and edges are spatial proximity relationships between spatial points. S2. Based on the information separation strategy, the original spatial transcriptome map is subjected to data enhancement of the first map and the second map respectively to obtain the first enhanced spatial transcriptome map and the second enhanced spatial transcriptome map. During the data augmentation process of the first graph, the topological structure of the original spatial transcriptome graph is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first augmented spatial transcriptome graph. During the data augmentation process of the second graph, the gene expression feature matrix is ​​kept unchanged, and the topology of the original spatial transcriptome graph is changed to obtain the second augmented spatial transcriptome graph. S3. Based on the node feature similarity with the original spatial transcriptome map, the first enhanced spatial transcriptome map is subjected to adaptive graph topology evolution to obtain the first weighted spatial transcriptome map. The original spatial transcriptome map, the first weighted spatial transcriptome map, and the second enhanced spatial transcriptome map were encoded to obtain multi-view feature embeddings. S4. Multi-view feature embedding, after minimum-maximum mutual information constraint processing, yields mutual information constraint feature embedding, which is then used by the decoder to reconstruct gene expression features, resulting in a reconstructed gene expression feature matrix. This matrix is ​​then used for spatial domain recognition to obtain the spatial domain recognition result.

[0006] The specific steps for obtaining the first enhanced spatial transcriptome map in S2 are as follows: keeping the topological structure of the original spatial transcriptome map unchanged, adding a noise perturbation of a preset amplitude to the gene expression feature matrix of the original spatial transcriptome map, normalizing the noise perturbation according to its norm, and obtaining the perturbed gene expression feature matrix; and generating the first enhanced spatial transcriptome map based on the perturbed gene expression feature matrix and the adjacency matrix of the original spatial transcriptome map.

[0007] In S2, the operation to obtain the second enhanced spatial transcriptome map is as follows: keeping the gene expression feature matrix unchanged, removing the topological connections in the original spatial transcriptome map to obtain the second enhanced spatial transcriptome map.

[0008] In S3, the adaptive graph topology evolution operation is as follows: the original spatial transcriptome graph and the first enhanced spatial transcriptome graph are processed by graph convolutional networks to obtain the first node embedding representation and the second node embedding representation; based on the first node embedding representation and the second node embedding representation, the cosine similarity between nodes is calculated and normalized to obtain the normalized similarity; the edges in the first enhanced spatial transcriptome graph are filtered according to the normalized similarity, and only the edges with a normalized similarity greater than the similarity threshold are retained; the retained edges are weighted according to the normalized similarity to obtain a weighted adjacency matrix, and a weighted spatial transcriptome graph is generated as the first weighted spatial transcriptome graph.

[0009] In S3, the operation of encoding the original spatial transcriptome map and the first weighted spatial transcriptome map is implemented through a multi-layer GCN network; the original spatial transcriptome map and the first weighted spatial transcriptome map that retains topological information share the GCN network parameters.

[0010] The operation of minimizing and maximizing mutual information constraints in S4 includes: The feature embeddings of the original spatial transcriptome map and the feature embeddings of the first enhanced spatial transcriptome map are used to construct a first positive sample pair; the feature embeddings of the original spatial transcriptome map and the feature embeddings of the second enhanced spatial transcriptome map are used to construct a second positive sample pair; a mutual information maximization loss is constructed based on the first positive sample pair and the second positive sample pair; the feature embeddings of the first enhanced spatial transcriptome map and the feature embeddings of the second enhanced spatial transcriptome map are used to construct a negative sample pair; a mutual information minimization loss is constructed based on the negative sample pair.

[0011] In S1, the preprocessing operations are as follows: from the initial gene expression matrix corresponding to the spatial transcriptome data, genes with mutations greater than the mutation threshold are screened out, and after normalization and logarithmic transformation, they are scaled to obtain the gene expression feature matrix; the two-dimensional spatial coordinates of each spatial point in the spatial transcriptome data are obtained to obtain the spatial location information.

[0012] A spatial domain identification system based on minimum-maximum mutual information, used in the aforementioned spatial domain identification method based on minimum-maximum mutual information, includes: The original spatial transcriptome map generation module is used to acquire spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points, and edges are spatial proximity relationships between spatial points; The enhanced spatial transcriptome map generation module is used to perform first-map data enhancement and second-map data enhancement on the original spatial transcriptome map based on an information separation strategy, resulting in a first-enhanced spatial transcriptome map and a second-enhanced spatial transcriptome map. During the first-map data enhancement process, the topological structure of the original spatial transcriptome map is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first-enhanced spatial transcriptome map. During the second-map data enhancement process, the gene expression feature matrix is ​​kept unchanged, and the topological structure of the original spatial transcriptome map is changed to obtain the second-enhanced spatial transcriptome map. The multi-view feature embedding generation module is used to perform adaptive graph topology evolution on the first enhanced spatial transcriptome map based on the node feature similarity with the original spatial transcriptome map to obtain the first weighted spatial transcriptome map; the original spatial transcriptome map, the first weighted spatial transcriptome map and the second enhanced spatial transcriptome map are encoded respectively to obtain the multi-view feature embedding. The spatial domain recognition result generation module is used for multi-view feature embedding. After minimum-maximum mutual information constraint processing, mutual information constraint feature embedding is obtained. Gene expression feature is reconstructed by the decoder to obtain the reconstructed gene expression feature matrix. After spatial domain recognition, spatial domain recognition result is obtained.

[0013] A spatial domain identification device based on minimum-maximum mutual information includes a processor and a memory, wherein the processor implements the above-described spatial domain identification method based on minimum-maximum mutual information when executing a computer program stored in the memory.

[0014] A computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the above-described spatial domain identification method based on minimum-maximum mutual information.

[0015] The beneficial effects of this invention are as follows: This invention provides a spatial domain identification method based on minimum-maximum mutual information. First, gene expression feature matrices and spatial location information are obtained by preprocessing spatial transcriptome data. Based on this, an original spatial transcriptome graph is constructed with spatial points as nodes and spatial proximity relationships as edges. The spatial domain identification task is modeled as a graph node classification problem, laying a data foundation that considers both molecular features and spatial topology for subsequent multi-view learning. Then, based on an information separation strategy, two types of graph data augmentation are applied to the original spatial transcriptome graph: one maintains the topological structure while perturbing gene expression features to preserve spatial topological relationships; the other maintains the gene expression features while altering the topological structure to highlight the node's own expression characteristics. This results in a first-enhanced spatial transcriptome graph and a second-enhanced spatial transcriptome graph. This allows the two enhanced views to capture complementary information from different angles of the spatial transcriptome data, providing richer supervision signals for comparative learning. Next... Based on the node feature similarity with the original spatial transcriptome graph, the first augmented graph undergoes adaptive graph topology evolution, dynamically pruning redundant edges while retaining important connections. Simultaneously, multi-view feature embeddings are encoded, effectively improving the accuracy of feature representation and the clarity of spatial domain boundaries while reducing computational burden. Finally, the multi-view feature embeddings are subjected to minimum-maximum mutual information constraints. Maximizing the mutual information between the original and augmented graphs preserves effective biological information, while minimizing the mutual information between different augmented views reduces representational redundancy. Gene expression features are then reconstructed via a decoder, ultimately yielding high-quality spatial domain recognition results. This invention effectively addresses the problems of imbalanced graph construction strategies, redundant connection interference, and decreased feature learning quality due to lack of mutual information through the synergistic effect of information separation enhancement, dynamic topology evolution, and bidirectional mutual information constraints. This significantly improves the accuracy, boundary clarity, and clustering stability of spatial domain recognition. Attached Figure Description

[0016] The solutions and advantages of this application will become clear to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0017] In the attached diagram: Figure 1 For the example, a histological image and a true label image of section 151672; Figure 2 As shown in the embodiment, the different spatial domain identification methods are visualized on slice 151672; Figure 3 As shown in the example, a visualization of the six different methods on slice 151672; Figure 4 As shown in the example, developmental trajectory diagrams for six different methods; Figure 5 This is a real labeling image of human breast cancer in the example; Figure 6 This is a visualization comparing the ARI of different spatial domain identification methods in the embodiment; Figure 7 As shown in the embodiment, a visualization of spatial domain identification using eight different methods; Figure 8 As shown in the embodiment, the method of this embodiment is compared with the real label in spatial domain 2 and spatial domain 12; Figure 9 As shown in the example, a heatmap analysis of the first three differentially expressed genes in IDC_2, DCIS / LCIS_4, IDC_4, and Tumor_edge_2 is presented. Figure 10 This is a real label image of the mouse coronal brain in the example; Figure 11 As shown in the example, a visualization comparing the ARI of nine different methods; Figure 12 As shown in the embodiments, spatial domain identification visualizations of 7 different methods are presented. Figure 13 As shown in the embodiment, spatial domains 5, 7, 10, and 12 are compared with the actual labels; Figure 14 As an example, a heatmap analysis of the first three differentially expressed genes in Cortex_1, Cortex_3, Hippocampus, and Thalamus_2 is shown. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the exemplary embodiments of this application clearer, the technical solutions in the exemplary embodiments of this application are described clearly and completely below. Obviously, the described exemplary embodiments are only some embodiments of this application, and not all embodiments.

[0019] This embodiment provides a spatial domain identification method based on minimum-maximum mutual information, characterized by the following operations: S1. Obtain spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points and edges are spatial proximity relationships between spatial points. S2. Based on the information separation strategy, the original spatial transcriptome map is augmented with first and second data enhancements to obtain a first enhanced spatial transcriptome map and a second enhanced spatial transcriptome map. During the first data enhancement process, the topological structure of the original spatial transcriptome map is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first enhanced spatial transcriptome map. During the second data enhancement process, the gene expression feature matrix is ​​kept unchanged, and the topological structure of the original spatial transcriptome map is changed to obtain the second enhanced spatial transcriptome map. S3. Based on the node feature similarity with the original spatial transcriptome map, the first enhanced spatial transcriptome map is subjected to adaptive graph topology evolution to obtain the first weighted spatial transcriptome map; the original spatial transcriptome map, the first weighted spatial transcriptome map and the second enhanced spatial transcriptome map are encoded respectively to obtain multi-view feature embeddings; S4. Multi-view feature embedding, after minimum-maximum mutual information constraint processing, yields mutual information constraint feature embedding, which is then used by the decoder to reconstruct gene expression features, resulting in a reconstructed gene expression feature matrix. This matrix is ​​then used for spatial domain recognition to obtain the spatial domain recognition result. The specific steps are detailed below.

[0020] S1. Obtain spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points and edges are spatial proximity relationships between spatial points.

[0021] First, spatial transcriptome data is acquired and preprocessed to obtain gene expression feature matrices and spatial location information. The preprocessing steps are as follows: from the initial gene expression matrix corresponding to the spatial transcriptome data, genes with variations exceeding a variation threshold are selected to obtain highly variable genes. After normalization and logarithmic transformation, these genes are scaled to obtain the gene expression feature matrix. Additionally, the two-dimensional spatial coordinates of each spatial point in the spatial transcriptome data are obtained as spatial location information.

[0022] Then, based on the gene expression feature matrix and spatial location information, an original spatial transcriptome graph is constructed. In the original spatial transcriptome graph, nodes are spatial points, and edges represent the spatial proximity relationships between spatial points. Simultaneously, based on the spatial location information, the Euclidean distance between spatial points is calculated to obtain a distance matrix. For each spatial point, the k nearest spatial points are selected as neighboring nodes, and an original adjacency matrix is ​​generated based on the neighboring node relationships. To ensure the undirectedness of the original spatial transcriptome graph, this embodiment performs symmetry processing on the original adjacency matrix of the original spatial transcriptome graph, i.e. , The (new) adjacency matrix of the original spatial transcriptome map. This is the original adjacency matrix of the original spatial transcriptome map. This is a transpose of the original adjacency matrix of the original spatial transcriptome graph, and values ​​greater than 1 are restricted to 1. This ensures that the graph structure can not only describe the adjacency relationships of spatial cells, but also guarantees that the connections are bidirectional.

[0023] S2. Based on the information separation strategy, the original spatial transcriptome map is augmented with the first map data and the second map data respectively to obtain the first augmented spatial transcriptome map and the second augmented spatial transcriptome map.

[0024] By processing gene expression features and spatial adjacency relationships separately, two semantically complementary enhanced views are generated, thereby better capturing potential ST information in spatial transcriptome data.

[0025] In the first data augmentation process, the topological structure of the original spatial transcriptome map is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first augmented spatial transcriptome map. Specifically, while keeping the topological structure of the original spatial transcriptome map unchanged, noise perturbation of a preset amplitude is added to the gene expression feature matrix of the original spatial transcriptome map. Norm normalization is then performed on the noise perturbation to obtain the perturbed gene expression feature matrix. Based on the perturbed gene expression feature matrix and the adjacency matrix of the original spatial transcriptome map, specifically, the perturbed gene expression feature matrix is ​​combined with the adjacency matrix of the original spatial transcriptome map to obtain the first augmented spatial transcriptome map. (Noise perturbation) , , For the first i The expression feature vector of a gene, .

[0026] In the second data augmentation process, the gene expression feature matrix is ​​kept unchanged, while the topology of the original spatial transcriptome map is altered. Specifically, the topological connections in the original spatial transcriptome map are removed to obtain the second augmented spatial transcriptome map. This is achieved by preserving the gene expression features of cells while removing topological information; that is, the spatial position of cells is ignored, and the map is constructed solely based on gene expression information.

[0027] By employing the aforementioned information separation strategy, different enhanced spatial transcriptome maps can retain different types of spatial transcriptome information, thereby providing a complementary perspective for subsequent comparative learning.

[0028] S3. Based on the node feature similarity with the original spatial transcriptome map, the first enhanced spatial transcriptome map is subjected to adaptive graph topology evolution to obtain the first weighted spatial transcriptome map; the original spatial transcriptome map, the first weighted spatial transcriptome map and the second enhanced spatial transcriptome map are encoded respectively to obtain multi-view feature embedding.

[0029] First, based on the node feature similarity with the original spatial transcriptome graph, an adaptive graph topology evolution is performed on the first enhanced spatial transcriptome graph to obtain the first weighted spatial transcriptome graph. Specifically, the original spatial transcriptome graph and the first enhanced spatial transcriptome graph are processed by graph convolutional networks to obtain a first node embedding representation and a second node embedding representation. Based on the first node embedding representation and the second node embedding representation, the cosine similarity between nodes is calculated and normalized to obtain a normalized similarity. Spatial adjacency edges in the first enhanced spatial transcriptome graph are filtered according to the normalized similarity, retaining only edges with a normalized similarity greater than a similarity threshold, pruning edges with low similarity, and retaining edges with high similarity. Weights are assigned to the retained edges based on their corresponding normalized similarity to generate a weighted adjacency matrix. Based on the weighted adjacency matrix and the perturbed gene expression feature matrix, a weighted spatial transcriptome graph is generated, which serves as the first weighted spatial transcriptome graph.

[0030] During the weight assignment process, this embodiment discards edges with weights less than a weight threshold according to the proportion of edges, and then the initial weighted adjacency matrix is... Flattened A dimensional vector in the initial weighted adjacency matrix Extract the previous k The edge with the largest weight generates a new adjacency matrix. , , For the new adjacency matrix nodes i With nodes j Edge weights between them For nodes i With nodes j The normalized cosine similarity is finally based on and This yields a new adjacency matrix containing the weights, which serves as the weighted adjacency matrix. , This indicates that gradient operations are stopped. Through the above mechanism, the learning process dynamically evaluates the feature associations between cells in each forward propagation, adaptively preserving important connections and pruning redundant topological noise.

[0031] Preferably, after generating the weighted adjacency matrix, a gradient-stopping operation is performed on the weighted adjacency matrix to block gradient backpropagation during the topology update process, so that the graph topology evolution and feature embedding learning are coordinated and do not interfere with each other.

[0032] Then, the original spatial transcriptome map, the first weighted spatial transcriptome map, and the second enhanced spatial transcriptome map are encoded to obtain multi-view feature embeddings.

[0033] Encoding the original spatial transcriptome map and the first weighted spatial transcriptome map separately is achieved through a multi-layer GCN network with shared network parameters, yielding the original embedding features and the first embedding features. Encoding the second enhanced spatial transcriptome map is achieved through a multi-layer MLP encoder, yielding the second embedding features. The original spatial transcriptome map and the first weighted spatial transcriptome map, which preserves topological information, share GCN network parameters to achieve synergistic optimization between feature learning and topological evolution. Specifically, for the original spatial transcriptome map, its adjacency matrix and transcriptome data are used. The spatial transcriptome data is preprocessed to obtain a gene expression feature matrix, which is then input into... In the layered GCN network, generation Layer feature embedding, processed by a projection head, serves as the original embedding features. For the first weighted spatial transcriptome map, the adjacency matrix is ​​a weighted adjacency matrix learned based on similarity edge weights, and the gene expression information is a perturbed gene expression feature matrix. This is input into the same database as the original spatial transcriptome map. In the layered GCN network, the enhanced feature embeddings are obtained and processed by the projection head to serve as the first embedding feature. For the second enhanced spatial transcriptome map, the gene expression information is the gene expression feature matrix of the original spatial transcriptome map. Since topological information has been removed, there is no adjacency matrix. The layer MLP encoder obtains the learned feature embedding, which is then processed by the projection head and used as the second embedding feature.

[0034] The original embedding feature, the first embedding feature, and the second embedding feature together form the multi-view feature embedding.

[0035] S4. Multi-view feature embedding, after minimum-maximum mutual information constraint processing, yields mutual information constraint feature embedding, which is then used by the decoder to reconstruct gene expression features, resulting in a reconstructed gene expression feature matrix. This matrix is ​​then used for spatial domain recognition to obtain the spatial domain recognition result.

[0036] First, the multi-view feature embedding is subjected to minimum-maximum mutual information constraint processing to obtain the multi-view mutual information feature embedding. After concatenation processing, the mutual information constraint feature embedding is obtained.

[0037] The operation of minimizing and maximizing mutual information constraint processing includes constructing a first positive sample pair by combining the feature embeddings of the original spatial transcriptome map with the feature embeddings of the first enhanced spatial transcriptome map, i.e., constructing the original embedding features and the first embedding features as a first positive sample pair; constructing a second positive sample pair by combining the feature embeddings of the original spatial transcriptome map with the feature embeddings of the second enhanced spatial transcriptome map, i.e., constructing the original embedding features and the second embedding features as a second positive sample pair; constructing a mutual information maximizing loss based on the first positive sample pair and the second positive sample pair; and constructing a mutual information minimizing loss based on the feature embeddings of the first enhanced spatial transcriptome map with the feature embeddings of the second enhanced spatial transcriptome map, i.e., constructing the first embedding features and the second embedding features as a negative sample pair.

[0038] Meanwhile, to minimize the mutual information between the first and second embedding features, reduce representational redundancy between different enhanced views, and promote the learning of complementary spatial transcriptome information, this embodiment designs the following loss function calculation formula: ,in M This represents the total number of spatial points in the original spatial transcriptome map. It's a temperature parameter. It is the cosine similarity function. z t , i For the second embedded feature, the first i Feature embedding of a spatial point z f,i The first enhanced spatial transcriptome diagram i Feature embedding of a spatial point z f,j The first enhanced spatial transcriptome diagram j Feature embedding of a spatial point.

[0039] Meanwhile, this embodiment is designed to maximize the mutual information between the original spatial transcriptome map and the first enhanced spatial transcriptome map by obtaining similar contrastive losses. The loss function calculation formula is as follows: , z i The first in the original spatial transcriptome map i Feature embeddings of spatial points are used to reduce representational redundancy between different augmented views, enabling the model to learn complementary spatial transcriptomic information.

[0040] Then, the mutual information-constrained feature embedding is used by the decoder to reconstruct gene expression features, which are then used to reverse the original gene expression space to obtain the reconstructed gene expression feature matrix. The decoder operation can be implemented using the following formula: , For the first t The gene expression features output from the second decoding step are used to reconstruct the gene expression feature matrix. For the normalized adjacency matrix, For the first t-1 Gene expression characteristics output by the second decoding step. For mutual information-constrained feature embedding, , Let be the first parameter and the second parameter that can be trained in the t-th decoding, respectively.

[0041] To fully utilize gene expression information, the decoder process incorporates a self-reconstruction loss that minimizes gene expression for supervised learning. The formula for calculating the self-reconstruction loss is as follows: , , They are spatial points The original gene expression characteristics and reconstructed gene expression characteristics, N spot This represents the total number of spatial points.

[0042] Based on mutual information maximization loss, mutual information minimization loss, and self-reconstruction loss, a total loss function is constructed. When the loss value of the total loss function is less than the preset loss value, the reconstructed gene expression feature matrix is ​​output.

[0043] Finally, based on the reconstructed gene expression feature matrix, spatial domain identification is performed to obtain the spatial domain identification results.

[0044] To verify the effectiveness of the method in this embodiment, the following experiment was conducted.

[0045] Datasets. Experiments were conducted on three benchmark ST datasets: human dorsolateral prefrontal cortex (DLPFC), human breast cancer, and mouse brain coronal, to validate performance. In all three datasets, existing human annotations were used as ground truth labels, and the adjusted RAND index (ARI) and normalized mutual information (NMI) were employed to evaluate the spatial domain recognition results, providing a complete data foundation for subsequent modeling and analysis.

[0046] Parameter settings. In the experiment, this embodiment uses a four-layer GCN and MLP network as encoders for different ST graphs. The hidden layer dimensions are set to 3000-1024-256-64 respectively to compress high-dimensional gene expression features layer by layer and extract compact feature embeddings. The decoder structure is symmetrical with the encoder and is used for low-dimensional embedding reconstruction learning. During model training, the Adam optimizer is used for parameter updates, and the learning rate is set to 15e. -3 And introduce a weight decay of 15e -4 In the final total loss function, Set to 5e-1, Set to 1e -1 , Setting the parameter to 10 yielded the best performance on the three ST datasets. All comparison methods were configured with parameters according to the recommended settings in the original paper. In terms of implementation, this experiment used the PyTorch 1.12.0 framework for model building and training. The experimental environment was a server platform equipped with an NVIDIA GeForce RTX 3090 graphics card, an Intel(R) Core(TM) i5-13400F processor, and 32GB of RAM.

[0047] Comparative Analysis of Experimental Results. To better demonstrate the effectiveness of the spatial domain recognition method in this embodiment (hereinafter referred to as this embodiment), comparisons were made with other comparative methods. Existing methods include: the Louvain method (hereinafter referred to as Louvain in the accompanying drawings and below), a traditional spatial domain recognition method based on community detection; the stLearn method (hereinafter referred to as stLearn in the accompanying drawings and below), which can combine gene expression, spatial location, and tissue morphology information to correct the expression matrix by extracting image tissue features; the Spatial-MGCN method (hereinafter referred to as Spatial-MGCN in the accompanying drawings and below), which designs a multi-view graph convolutional network to extract specific and general embeddings from genes and spatial structures respectively, and maintains local consistency through spatial regularization constraints; the SEDR method (hereinafter referred to as SEDR in the accompanying drawings and below), which learns the low-dimensional latent representation of gene expression through a depth mask autoencoder, then embeds spatial information with the help of a variational graph autoencoder, and jointly optimizes the encoder to generate latent representations; and the MuCoST method (hereinafter referred to as MuCoST in the accompanying drawings and below), which uses message passing and aggregation operations of a multi-layer GCN to extract... Gene expression profiles and spatial location information for each spot; the GraphST method (hereinafter referred to as GraphST in the attached figure) proposes a graph self-supervised contrastive learning framework, generating a disrupted graph by randomly shuffling the gene expression vectors of the ST graph without changing the original adjacency matrix; the STAGATE method (hereinafter referred to as STAGATE in the attached figure) adaptively learns the similarity between spots and assigns different connection weights based on the GAT attention mechanism in the encoder and decoder; the stDCL method (hereinafter referred to as stDCL in the attached figure) adaptively integrates gene expression data and spatial information through a graph embedding autoencoder, thereby preserving key information in the latent embedding representation; the MCGAE method (hereinafter referred to as MCGAE in the attached figure) maps gene expression features, spatial topology, and histological features to independent graph views, and combines a contrastive learning mechanism to shorten the distance between consistent views, achieving deep alignment and effective denoising of cross-view information. Among these, the spatial clustering performance of different methods on the human dorsolateral prefrontal cortex (DLPFC) dataset is shown in the figure. Figure 1-14 As shown in Tables 1 and 2. The human dorsolateral prefrontal cortex (DLPFC) dataset contains 12 slices, each slice being like... Figure 1 Similarly, morphological features and marker genes are used for annotation. In the experiment, ARI and NMI were used as evaluation metrics for the spatial domain recognition accuracy of DLPFC.

[0048] Figure 2The image shows the performance of 10 different methods for spatial domain recognition on 12 DLPFC slices, along with the median ARI score. The x-axis represents the ARI value, and the y-axis represents the different methods. It can be seen that the method in this embodiment achieved the highest median ARI score of 0.66. GraphST achieved a median ARI score of 0.60, MCGAE achieved 0.49, stDCL achieved 0.56, SEDR achieved 0.54, MuCoST achieved 0.53, Spatial-MGCN achieved 0.56, stLearn achieved 0.35, and Louvain achieved an average ARI score of 0.34. Louvain had the lowest average ARI score, which is attributed to the lack of spatial information integration. Other methods that incorporated spatial information performed significantly better than Louvain. Apart from the method in this embodiment and GraphST, the average ARI score of other methods did not exceed 0.60, which indicates that the average ARI score of the method in this embodiment on 12 slices is higher than that of the compared methods.

[0049] In order to better demonstrate the spatial domain recognition performance of the method in this embodiment, Figure 3 Visualizations of spatial domain identification on slice 151672 are shown for stLearn, Louvain, SEDR, GraphST, MuCoST, and the method of this embodiment. Louvain only recovered Layer 6 and WM layers, and there was severe cell confusion between layers, with cells from Layer 3 infiltrating between other layers. stLearn, like Louvain, also suffered from severe cell confusion, with blurred and jagged boundaries between layers, significantly deviating from the annotation map. In SEDR, Layer 3 was separated by Layer 4, resulting in a layer gap, and cells from Layer 5 exceeded the clusterable boundaries in the annotation map. GraphST and MuCoST both employed contrastive learning strategies to identify spatial domains layer by layer, but the spatial domain of Layer 3 significantly deviated from the annotation map. Only the method of this embodiment identified a spatial domain that closely matched the annotation map, achieving the highest ARI of 0.76 and the highest NMI of 0.78, making it the best performing method among all methods. It clearly distinguished different layers (Layers 3-6 and WM), with clearer layer boundaries. exist Figure 4 The diagram shows the spatial domain developmental UMAP and PAGA plots for each method. Figure 4The upper colored image for each method is the spatial domain developmental UMAP map, and the lower topological map is the PAGA map. Different colors represent different spatial domains. The spatial domain developmental UMAP map and PAGA map can reflect the developmental trajectory of the tissue. It can be seen that most methods show the correct developmental trajectory, but Louvain's developmental trajectory does not start from Layer 3, which is significantly different from other methods. This also shows the importance of effectively utilizing spatial information in spatial domain identification.

[0050] Table 1. ARI results of different methods on the DLPFC dataset

[0052] Table 2. NMI results of different methods on the DLPFC dataset

[0054] Furthermore, the human breast cancer dataset was used in the experiments to validate the performance of the method in this embodiment in detecting heterogeneity of cancerous tissue. The human breast cancer dataset was annotated into 20 regions, each corresponding to... Figure 7 The legends with different numbers corresponding to different colors are mainly divided into four types: DCIS / LCIS, Healthy, IDC, and Tumor_edge. Figure 5 The different colors in the diagram correspond to the names of various spatial domains, which are predefined in the Human Dorsolateral Prefrontal Cortex (DLPFC) dataset. Figure 6 , Figure 7 In the results, it can be observed that the method in this embodiment achieved the highest ARI score of 0.65, followed closely by MuCoST and MCGAE with ARIs of 0.59 and 0.61 respectively. Only MCGAE and this embodiment exceeded 0.6. It can be seen that compared to other dispersed spatial domains, this embodiment exhibits several significantly clustered spatial domains, namely domains 4, 11, 2, and 12. Domain 4 is a Healthy_1 organization. The method in this embodiment can clearly identify spatial domains similar to the annotations, while MuCoST identifies smaller domains within the Healthy_1 organization. GraphST identifies larger domains than MuCoST, and other methods fail to identify Healthy_1, appearing fragmented. To further investigate domains 2 and 12, they are identified separately and compared with the annotations, such as... Figure 8 As shown, Figure 8The left image represents the real spatial domain map (provided by the dataset), while the right image shows the results of this embodiment correctly identifying these two spatial domains. It can be seen that the identification results of this embodiment's method in these two spatial domains are similar to the annotations, with smooth and fluid boundaries. In contrast, existing methods perform poorly, either resulting in fragmented spatial domains or coarse boundaries. Figure 9 This is a heatmap analysis of the first three differentially expressed genes in IDC_2, DCIS / LCIS_4, IDC_4, and Tumor_edge_2. The X-axis represents the locus, the Y-axis represents the gene name expressed at the locus, and the center represents the expression level. Figure 9 By comparing the first three differentially expressed genes (DEGs) in domains 2 (IDC_2), 12 (DCIS / LCIS_4), 11 (IDC_4), and 15 (Tumor_edge_2), significant spatial heterogeneity of these DEGs can be observed. In cancer research, these DEGs play an important role in disease progression, prognosis, and cancer treatment.

[0055] To further verify the effectiveness of the identification method proposed in this invention, the method of this embodiment, along with eight spatial domain identification methods, was applied to mouse brain tissue. Real labels were as follows: Figure 10 As shown, Figure 10 The different colors in the diagram represent the names of various spatial domains, predefined in the human dorsolateral prefrontal cortex (DLPFC) dataset. These include structures such as the cerebral cortex (Cortex 1-5), hippocampus, thalamus (Thalamus 1-2), hypothalamus (Hypothalamus 1-2), striatum, fiber tracts, and lateral ventricles. Figure 11 and Figure 12 As shown, the spatial domain recognition results and ARI scores of various methods are presented. It can be intuitively seen that the method in this embodiment achieved the highest ARI score of 0.65 on this dataset, and exhibited clearer, more continuous recognition results in spatial domain visualization that are highly consistent with the known label structure. This is due to the effective pruning of noisy links in this embodiment, constructing more refined adjacency relationships, and reducing the interference of erroneous spatial connections on model learning from the source. Figure 13 and Figure 14 As shown, four spatial domains were extracted, corresponding to area 1 of the cerebral cortex (corresponding to...). Figure 13 Cortex_1 in the brain and area 3 of the cerebral cortex (corresponding to) Figure 13 Cortex_3 in the middle), hippocampus (corresponding to Figure 13 Hippocampus and thalamus area 2 (corresponding to) Figure 13Thalamus_2 in the dataset, and a heatmap analysis of the genes in these four regions was performed. Figure 13 The left figure is the actual spatial domain, and the right figure shows the spatial domain result that the method of this embodiment can correctly identify. Figure 14 Heatmap analysis of the first three differentially expressed genes in Cortex_1, Cortex_3, Hippocampus, and Thalamus_2 shows the X-axis as the locus, the Y-axis as the gene name expressed at that locus, and the center as the expression level. Highly expressed genes in spatial domain 5 include Nrsn1, Mef2c, and Satb1. These genes play important roles in neuronal differentiation, cortical development, and synaptic organization, indicating that this spatial domain is a neuronal-dominated functional region closely related to cortical tissue structure. Highly expressed genes in spatial domain 10 (Hippocampus) include Cabp7, Ttr, and Spink8. These genes have been reported to be closely related to calcium signaling pathways and cerebrospinal fluid-related structures, suggesting that this spatial domain may be spatially adjacent to the ventricular system or thalamic-related regions. Highly expressed genes in spatial domain 12 (Cortex_3) include Tbr1, Ttc9b, and Ipcef1. These genes are classic markers of deep cortical projection neurons, reflecting a clear laminar tissue feature in cortical structure. Heatmap analysis of spatial domain-specific genes not only helps to deepen our understanding of the layered structure and functional regions of the brain, but also provides assistance in studying the roles of different brain regions in development, information transmission, and disease-related processes.

[0056] This embodiment also provides a spatial domain identification system based on minimum-maximum mutual information, used in the above-described spatial domain identification method based on minimum-maximum mutual information, including: The original spatial transcriptome map generation module is used to acquire spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points, and edges are spatial proximity relationships between spatial points; The enhanced spatial transcriptome map generation module is used to perform first-map data enhancement and second-map data enhancement on the original spatial transcriptome map based on an information separation strategy, resulting in a first-enhanced spatial transcriptome map and a second-enhanced spatial transcriptome map. During the first-map data enhancement process, the topological structure of the original spatial transcriptome map is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first-enhanced spatial transcriptome map. During the second-map data enhancement process, the gene expression feature matrix is ​​kept unchanged, and the topological structure of the original spatial transcriptome map is changed to obtain the second-enhanced spatial transcriptome map. The multi-view feature embedding generation module is used to perform adaptive graph topology evolution on the first enhanced spatial transcriptome map based on the node feature similarity with the original spatial transcriptome map to obtain the first weighted spatial transcriptome map; the original spatial transcriptome map, the first weighted spatial transcriptome map and the second enhanced spatial transcriptome map are encoded respectively to obtain the multi-view feature embedding. The spatial domain recognition result generation module is used for multi-view feature embedding. After minimum-maximum mutual information constraint processing, mutual information constraint feature embedding is obtained. Gene expression feature is reconstructed by the decoder to obtain the reconstructed gene expression feature matrix. After spatial domain recognition, spatial domain recognition result is obtained.

[0057] This embodiment also provides a spatial domain identification device based on minimum and maximum mutual information, including a processor and a memory, wherein the processor implements the above-described spatial domain identification method based on minimum and maximum mutual information when executing a computer program stored in the memory.

[0058] This embodiment also provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the above-described spatial domain identification method based on minimum and maximum mutual information.

[0059] This embodiment provides a spatial domain identification method based on minimum-maximum mutual information. First, gene expression feature matrices and spatial location information are obtained by preprocessing spatial transcriptome data. Based on this, an original spatial transcriptome graph is constructed with spatial points as nodes and spatial proximity relationships as edges. The spatial domain identification task is modeled as a graph node classification problem, laying a data foundation that takes into account both molecular features and spatial topology for subsequent multi-view learning. Then, based on an information separation strategy, two types of graph data augmentation are performed on the original spatial transcriptome graph: one maintains the topological structure while perturbing gene expression features to preserve spatial topological relationships, and the other maintains the gene expression features while changing the topological structure to highlight the expression characteristics of the nodes themselves. This results in a first-enhanced spatial transcriptome graph and a second-enhanced spatial transcriptome graph, allowing the two enhanced views to capture complementary information of spatial transcriptome data from different angles, providing richer supervision signals for comparative learning. Next... Based on the node feature similarity with the original spatial transcriptome graph, the first enhanced graph undergoes adaptive graph topology evolution, dynamically pruning redundant edges while retaining important connections. Simultaneously, multi-view feature embeddings are encoded, effectively improving the accuracy of feature representation and the clarity of spatial domain boundaries while reducing computational burden. Finally, the multi-view feature embeddings are subjected to minimum-maximum mutual information constraints. Maximizing the mutual information between the original and enhanced graphs preserves effective biological information, while minimizing the mutual information between different enhanced views reduces representational redundancy. Gene expression features are then reconstructed via a decoder, ultimately yielding high-quality spatial domain recognition results. This invention effectively addresses the problems of imbalanced graph construction strategies, redundant connection interference, and decreased feature learning quality due to missing mutual information through the synergistic effect of information separation enhancement, dynamic topology evolution, and bidirectional mutual information constraints. This significantly improves the accuracy, boundary clarity, and clustering stability of spatial domain recognition.

[0060] While exemplary embodiments of the invention have been described herein, many other variations or modifications conforming to the principles of the invention can be directly determined or derived from the disclosure of the invention without departing from its spirit and scope. Therefore, the scope of the invention should be understood and recognized to cover all such other variations or modifications.

Claims

1. A spatial domain identification method based on minimum-maximum mutual information, characterized in that, This includes the following operations: S1. Obtain spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; in the original spatial transcriptome map, nodes are spatial points and edges are spatial proximity relationships between spatial points. S2. Based on the information separation strategy, the original spatial transcriptome map is subjected to data enhancement of the first map and the second map respectively to obtain the first enhanced spatial transcriptome map and the second enhanced spatial transcriptome map. During the data augmentation process of the first graph, the topological structure of the original spatial transcriptome graph is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first augmented spatial transcriptome graph. During the data augmentation process of the second graph, the gene expression feature matrix is ​​kept unchanged, and the topology of the original spatial transcriptome graph is changed to obtain the second augmented spatial transcriptome graph. S3. Based on the node feature similarity with the original spatial transcriptome map, the first enhanced spatial transcriptome map is subjected to adaptive graph topology evolution to obtain the first weighted spatial transcriptome map. The original spatial transcriptome map, the first weighted spatial transcriptome map, and the second enhanced spatial transcriptome map were encoded to obtain multi-view feature embeddings. S4. Multi-view feature embedding, after minimum-maximum mutual information constraint processing, yields mutual information constraint feature embedding, which is then used by the decoder to reconstruct gene expression features, resulting in a reconstructed gene expression feature matrix. This matrix is ​​then used for spatial domain recognition to obtain the spatial domain recognition result.

2. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, In S2, the operation to obtain the first enhanced spatial transcriptome map is as follows: keeping the topological structure of the original spatial transcriptome map unchanged, adding a noise perturbation of a preset amplitude to the gene expression feature matrix of the original spatial transcriptome map, normalizing the noise perturbation according to the norm, and obtaining the perturbed gene expression feature matrix; based on the perturbed gene expression feature matrix and the adjacency matrix of the original spatial transcriptome map, the first enhanced spatial transcriptome map is generated.

3. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, In S2, the operation to obtain the second enhanced spatial transcriptome map is as follows: keeping the gene expression feature matrix unchanged, removing the topological connections in the original spatial transcriptome map to obtain the second enhanced spatial transcriptome map.

4. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, In S3, the operation of adaptive graph topology evolution is as follows: the original spatial transcriptome graph and the first enhanced spatial transcriptome graph are processed by graph convolutional networks to obtain the first node embedding representation and the second node embedding representation. Based on the first node embedding representation and the second node embedding representation, the cosine similarity between nodes is calculated and normalized to obtain the normalized similarity. The edges in the first enhanced spatial transcriptome graph are filtered according to the normalized similarity, and only the edges with a normalized similarity greater than the similarity threshold are retained. The retained edges are weighted according to the normalized similarity to obtain a weighted adjacency matrix, and a weighted spatial transcriptome graph is generated as the first weighted spatial transcriptome graph.

5. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, In S3, the operation of encoding the original spatial transcriptome map and the first weighted spatial transcriptome map is implemented through a multi-layer GCN network; the original spatial transcriptome map and the first weighted spatial transcriptome map that retains topological information share the GCN network parameters.

6. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, The operation of minimizing and maximizing mutual information constraints in S4 includes: The feature embeddings of the original spatial transcriptome map and the feature embeddings of the first enhanced spatial transcriptome map are used to construct a first positive sample pair; the feature embeddings of the original spatial transcriptome map and the feature embeddings of the second enhanced spatial transcriptome map are used to construct a second positive sample pair; a mutual information maximization loss is constructed based on the first positive sample pair and the second positive sample pair; the feature embeddings of the first enhanced spatial transcriptome map and the feature embeddings of the second enhanced spatial transcriptome map are used to construct a negative sample pair; a mutual information minimization loss is constructed based on the negative sample pair.

7. The spatial domain identification method based on minimum-maximum mutual information according to claim 1, characterized in that, In S1, the preprocessing operation is as follows: from the initial gene expression matrix corresponding to the spatial transcriptome data, genes with variations greater than the variation threshold are screened out, and after normalization and logarithmic transformation, they are scaled to obtain the gene expression feature matrix. Two-dimensional spatial coordinates of each spatial point in the spatial transcriptome data are obtained to acquire spatial location information.

8. A spatial domain identification system based on minimum-maximum mutual information, used to implement the spatial domain identification method based on minimum-maximum mutual information as described in claim 1, characterized in that, include: The original spatial transcriptome map generation module is used to acquire spatial transcriptome data, preprocess the spatial transcriptome data to obtain gene expression feature matrix and spatial location information, and construct the original spatial transcriptome map; In the original spatial transcriptome diagram, nodes are spatial points, and edges represent the spatial proximity relationships between spatial points; The enhanced spatial transcriptome map generation module is used to perform first-map data enhancement and second-map data enhancement on the original spatial transcriptome map based on an information separation strategy, resulting in a first-enhanced spatial transcriptome map and a second-enhanced spatial transcriptome map. During the first-map data enhancement process, the topological structure of the original spatial transcriptome map is kept unchanged, and the gene expression feature matrix is ​​perturbed to obtain the first-enhanced spatial transcriptome map. During the second-map data enhancement process, the gene expression feature matrix is ​​kept unchanged, and the topological structure of the original spatial transcriptome map is changed to obtain the second-enhanced spatial transcriptome map. The multi-view feature embedding generation module is used to perform adaptive graph topology evolution on the first enhanced spatial transcriptome map based on the node feature similarity with the original spatial transcriptome map to obtain the first weighted spatial transcriptome map; the original spatial transcriptome map, the first weighted spatial transcriptome map and the second enhanced spatial transcriptome map are encoded respectively to obtain the multi-view feature embedding. The spatial domain recognition result generation module is used for multi-view feature embedding. After minimum-maximum mutual information constraint processing, mutual information constraint feature embedding is obtained. Gene expression feature is reconstructed by the decoder to obtain the reconstructed gene expression feature matrix. After spatial domain recognition, spatial domain recognition result is obtained.

9. A spatial domain identification device based on minimum-maximum mutual information, characterized in that, It includes a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the spatial domain identification method based on minimum-maximum mutual information as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the spatial domain identification method based on minimum-maximum mutual information as described in any one of claims 1-7.

Images