Spatial multi-omics structural domain identification method and system based on Taylor linear attention graph convolution

Abstract

The invention relates to a spatial multi-omics structural domain identification method and system based on Taylor linear attention map convolution. The method comprises the following steps: collecting a spatial transcriptome, a proteome and an apparent group, and respectively carrying out standardization treatment; constructing a mixed space-feature map based on the processed multi-omics data; a hybrid encoder composed of a graph neural network and Taylor linear attention is adopted to independently encode data of each group, and independent potential representation of each group is generated; self-adaptive weighted fusion is carried out through the learnable weight coefficient, low-dimensional potential feature representation is generated and input into a clustering algorithm, and spatial multi-omics structural domain division based on molecular expression and spatial position unification is achieved. Wherein the graph neural network is used for extracting local space neighborhood features, the Taylor linear attention is used for capturing a global dependency relationship, a framework model for realizing efficient integration of multi-omics data is formed, efficient fusion of information can be realized, and the structural domain division precision is improved.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics engineering technology, and in particular to a spatial multi-omics structural domain recognition method and system based on Taylor linear attention map convolution. Background Technology

[0002] With the rapid development of life sciences and sequencing technology, single-cell sequencing technology has enabled high-resolution analysis of cellular heterogeneity and tissue molecular characteristics. Traditional single-cell omics (such as transcriptomics, proteomics, and epigenomics) mainly focuses on changes at the molecular level, but neglects the spatial relationships between cells and the influence of the tissue microenvironment. The emergence of spatial transcriptomics technology allows researchers to preserve the spatial location information of genes while measuring gene expression, providing a new opportunity to reveal the spatial pattern of gene regulation in tissues. Spatial multi-omics technologies integrate multiple modalities such as transcription, protein, epigenetics, and even metabolism, enabling the acquisition of multi-level molecular maps from a single tissue slice. Examples include DBiT-seq, SPOTS, MISAR-seq, and spatial-CITE-seq, which provide the possibility of constructing a tissue-scale multimodal molecular landscape.

[0003] Traditional spatial multi-omics domain identification methods mainly include unimodal spatial analysis methods, multimodal integration methods, and various linear or kernel-based attention methods. Unimodal spatial analysis methods often focus on a single omics level (such as spatial transcriptomics), utilizing clustering, graph convolutional networks, or self-supervised learning to delineate spatial regions. For example, GraphST and stDCL use contrastive learning to model spatial relationships, while Spatial-MGCN introduces an attention mechanism to enhance spatial neighborhood modeling. In multimodal integration methods, Spatial-Glue constructs a K-nearest neighbor graph using spatial coordinates and employs a dual attention mechanism to achieve intermodal alignment; SSGATE designs a dual-channel graph attention autoencoder structure to integrate single-cell and spatial data; COSMOS uses multi-layer embedding and attention aggregation to achieve cross-modal representation learning; and PRAGA introduces a learnable spatial aggregation graph to achieve adaptive fusion of information between modalities. These methods mark a new stage in deep learning-driven spatial multi-omics integration. Regarding attention mechanism optimization, various linear or kernel-based attention (Kernel / Linear Attention) methods have emerged to improve computational efficiency in high-dimensional sparse data. Linformer simplifies the soft-max attention matrix through low-rank projection, Nyströmformer achieves global dependency modeling based on landmark sampling, Performer approximates dot product attention by using kernel function mapping, and TaylorShift introduces Taylor expansion into tensor operations to achieve efficient attention approximation.

[0004] However, due to the high sparsity and heterogeneity of spatial multi-omics data, traditional spatial multi-omics structural domain identification methods often suffer from low information integration and poor recognition function due to incomplete global information capture, low computational efficiency, and insufficient modality fusion. Summary of the Invention

[0005] In order to solve the above technical problems, a spatial multi-omics structural domain recognition method and system based on Taylor linear attention map convolution is provided, which can achieve efficient information fusion and improve the accuracy of structural domain segmentation.

[0006] A spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution, the method comprising:

[0007] Spatial transcriptome, spatial proteome, and spatial epigenome data were collected and standardized to obtain processed multi-omics data.

[0008] Based on the processed multi-omics data, a spatial adjacency graph is constructed by calculating the Euclidean distance using the two-dimensional coordinates of spatial points, and a feature graph is constructed based on the cosine similarity of molecular feature vectors; the spatial adjacency graph and the feature graph are fused to generate a weighted adjacency matrix, forming a hybrid spatial-feature graph;

[0009] Based on the hybrid space-feature map structure, a hybrid encoder consisting of a graph neural network and Taylor linear attention is used to independently encode each omics data, generating independent latent representations for each omics. The graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; the Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise.

[0010] Based on the latent representations of each omics, adaptive weighted fusion is performed through learnable weight coefficients to generate low-dimensional latent feature representations;

[0011] The low-dimensional latent feature representation is input into the clustering algorithm to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location.

[0012] In one embodiment, spatial transcriptome, spatial proteome, and spatial epigeneome data are collected and standardized separately, including:

[0013] The spatial transcriptome was subjected to low-expression gene removal, high-variance gene screening, normalization, and logarithmic transformation.

[0014] The spatial proteome was subjected to center-log ratio normalization.

[0015] The spatial appearance group is subjected to high-variability feature screening, TF-IDF transformation, log normalization, and truncated SVD dimensionality reduction.

[0016] In one embodiment, based on the processed multi-omics data, a spatial adjacency graph is constructed by calculating Euclidean distance using the two-dimensional coordinates of spatial points, and a feature graph is constructed based on the cosine similarity of molecular feature vectors, including:

[0017] Based on the processed multi-omics data, the spatial coordinates corresponding to each spatial point are determined.

[0018] Calculate the Euclidean distance between each of the spatial coordinates, and construct a spatial adjacency graph by selecting each neighbor point for each of the spatial points.

[0019] Calculate the cosine similarity between molecular feature vectors, and construct a feature map based on the neighboring points determined by the cosine similarity.

[0020] In one embodiment, based on the hybrid space-feature map structure, a hybrid encoder consisting of a graph neural network and Taylor linear attention is used to independently encode each omics data, generating independent latent representations for each omics, including:

[0021] Extract the standardized molecular feature matrix from the processed multi-omics data, find the corresponding mixed space-feature map weighted adjacency matrix, and perform matrix alignment processing;

[0022] Based on the hybrid spatial-feature map, a graph neural network is used to perform iterative computation of graph convolutional layers based on the aligned matrix to obtain a local spatial feature representation.

[0023] Taylor linear attention is used to perform feature mapping and normalization on the homogenized matrix. After kernel transformation and global bias optimization, global dependencies are captured in linear complexity, and a global spatial feature representation is output.

[0024] The local spatial feature representation and the global spatial feature representation are fused by residual connection to generate independent potential representations for each omics.

[0025] In one embodiment, based on the latent representations of each omics, adaptive weighted fusion is performed using learnable weight coefficients to generate low-dimensional latent feature representations, including:

[0026] Determine the potential representations for each omics and identify learnable weight parameters;

[0027] By using learnable weight coefficients to fuse the latent representations of various omics, a low-dimensional latent feature representation is generated.

[0028] The learnable weight coefficients are automatically adjusted during training to achieve modal balance.

[0029] In one embodiment, the method further includes:

[0030] The low-dimensional latent feature representation is mapped back to the original space of each modality by the decoder, and the reconstruction error is calculated using the mean squared error to obtain the reconstruction loss function.

[0031] By constraining the distribution of the low-dimensional latent features to be consistent with the target clustering distribution using KL divergence, a clustering regularization loss function is obtained.

[0032] A dual loss function, comprising reconstruction loss and clustering regularization loss, is constructed. The low-dimensional latent feature representation is used as the optimization object, and a graph convolutional neural network model guided by Taylor attention mechanism is obtained through end-to-end training.

[0033] In one embodiment, the method further includes:

[0034] The processed multi-omics data and hybrid space-feature map are input into the graph convolutional neural network model guided by the Taylor attention mechanism;

[0035] The recognition results of spatial multi-omics structural domains are obtained by regularizing the dual loss function in the graph convolutional neural network model guided by the Taylor attention mechanism.

[0036] In one embodiment, the method further includes:

[0037] The RAND index, homogeneity score, and adjusted mutual information were selected as quantitative indicators.

[0038] Qualitative analysis was performed on the identification results of the spatial multi-omics structural domain based on the quantitative indicators, and the verification results of the graph convolutional neural network model guided by the Taylor attention mechanism were obtained.

[0039] In one embodiment, the low-dimensional latent feature representation is input into a clustering algorithm to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location, including:

[0040] Input the low-dimensional latent feature representation of each spatial point in the latent space into the clustering algorithm;

[0041] The clustering algorithm described above is used to divide spatial multi-omics structures with consistent molecular expression patterns and spatial locations based on feature separability and spatial consistency.

[0042] A spatial multi-omics structural domain recognition system based on Taylor linear attention map convolution, the system comprising:

[0043] The data processing module is used to collect spatial transcriptome, spatial proteome, and spatial epigenome data and perform data standardization processing to obtain processed multi-omics data.

[0044] The hybrid space-feature map generation module is used to construct a spatial adjacency graph based on the processed multi-omics data by calculating the Euclidean distance through the two-dimensional coordinates of spatial points, and construct a feature map based on the cosine similarity of molecular feature vectors; the spatial adjacency graph and the feature map are fused to generate a weighted adjacency matrix, forming a hybrid space-feature map;

[0045] The latent representation generation module is used to independently encode each omics data using a hybrid encoder composed of a graph neural network and Taylor linear attention, based on the hybrid space-feature map structure, to generate independent latent representations for each omics. The graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; the Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise.

[0046] The low-dimensional latent feature generation module is used to generate low-dimensional latent feature representations based on the latent representations of various omics through adaptive weighted fusion using learnable weight coefficients.

[0047] The spatial multi-omics structural domain partitioning module is used to input the low-dimensional latent feature representation into the clustering algorithm to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location.

[0048] The aforementioned spatial multi-omics structural domain recognition method and system based on Taylor linear attention graph convolution independently encodes each omics data through a hybrid encoder composed of graph neural network and Taylor linear attention. The graph neural network is used to extract local spatial neighborhood features, and Taylor linear attention is used to capture global dependencies, forming a framework model that achieves efficient integration of multi-omics data. This enables efficient information fusion and improves the accuracy of structural domain partitioning. Attached Figure Description

[0049] Figure 1 This is an application environment diagram of a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution in one embodiment;

[0050] Figure 2 This is a flowchart illustrating a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution in one embodiment.

[0051] Figure 3 This is a flowchart illustrating the efficient integration of multiple omics data from the same slice in one embodiment.

[0052] Figure 4 This is a schematic diagram illustrating the effect on the Human Lymph Node A1 dataset in one embodiment;

[0053] Figure 5This is a block diagram of a spatial multi-omics structural domain recognition system based on Taylor linear attention map convolution in one embodiment.

[0054] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0056] The spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution provided in this application can be applied to, for example... Figure 1 The application environment shown. For example... Figure 1 As shown, the application environment includes computer equipment 110. Computer device 110 can collect spatial transcriptome, spatial proteome, and spatial epigeneome data and perform data standardization processing respectively to obtain processed multi-omics data. Based on the processed multi-omics data, computer device 110 can construct a spatial adjacency graph by calculating Euclidean distance using two-dimensional coordinates of spatial points, and construct a feature graph based on the cosine similarity of molecular feature vectors. The spatial adjacency graph and feature graph are fused to generate a weighted adjacency matrix, forming a hybrid spatial-feature graph. Using the hybrid spatial-feature graph as a structural basis, computer device 110 can independently encode each omics data using a hybrid encoder composed of a graph neural network and Taylor linear attention, generating independent latent representations for each omics. The graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise. Based on the latent representations of each omics, computer device 110 can perform adaptive weighted fusion using learnable weight coefficients to generate low-dimensional latent feature representations. Computer device 110 can input the low-dimensional latent feature representations into a clustering algorithm to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location. Among them, computer equipment 110 may include, but is not limited to, various personal computers, laptops, smartphones, robots, tablets and other devices.

[0057] In one embodiment, such as Figure 2 As shown, a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution is provided, including the following steps:

[0058] Step 202: Collect spatial transcriptome, spatial proteome, and spatial epigenome data and perform data standardization processing respectively to obtain processed multi-omics data.

[0059] Before data integration, spatial transcriptomics, spatial proteomics, and spatial epigenomics data need to be standardized separately. Before integrating spatial multi-omics data, independent preprocessing operations can be performed on the data characteristics of different modalities.

[0060] In one embodiment, a spatial multi-omics domain identification method based on Taylor linear attention map convolution may further include a process of standardizing each data point. Specifically, this process includes: removing low-expression genes, screening high-variance genes, normalizing, and logarithmic transformation of the spatial transcriptome; performing centered logarithmic ratio normalization on the spatial proteome; and performing high-variance feature screening, TF-IDF transformation, logarithmic normalization, and truncated SVD dimensionality reduction on the spatial epigenetics.

[0061] In this study, low-expression genes in the spatial transcriptome data were removed, and high-variance genes were screened before normalization and logarithmic transformation. The spatial proteome data were normalized using the center-log ratio (CLR) method to reduce the influence of extreme values. The spatial epigenomic data underwent feature extraction and dimensionality reduction based on TF-IDF transformation and Latent Semantic Indexing (LSI). All modality data were ultimately standardized before being used for subsequent multi-omics integrated analysis.

[0062] Specifically, when performing data standardization, for spatial transcriptome data, low-expression genes expressed in fewer than 10 spatial points are first removed to reduce noise. Then, the 3000 genes with the highest variance are selected to retain key biological characteristics. Subsequently, the gene expression matrix is ​​normalized and logarithmically transformed to stabilize the variance, and the selected high-variance genes are retained after standardization for subsequent integration.

[0063] For spatial proteome data, the centered log-ratio normalization method is used to perform logarithmic transformation and geometric mean standardization on the protein expression levels at each spatial point, thereby reducing the influence of extreme values ​​and improving the comparability between different spatial points.

[0064] For the spatial appearance group data, the 3000 features with the highest variance were first selected, and then latent semantic indexing (LSI) analysis was performed using the Seurat v3 framework. Specifically, TF-IDF transformation was first performed on the data to adjust feature frequency and sparsity, followed by log normalization and truncated singular value decomposition (SVD) to achieve dimensionality reduction. The resulting LSI components were then centered and scaled for downstream analysis.

[0065] Step 204: Based on the processed multi-omics data, a spatial adjacency graph is constructed by calculating the Euclidean distance using the two-dimensional coordinates of spatial points, and a feature graph is constructed based on the cosine similarity of molecular feature vectors; the spatial adjacency graph and the feature graph are fused to generate a weighted adjacency matrix, forming a hybrid spatial-feature graph.

[0066] To simultaneously capture the spatial proximity and molecular feature similarity of cells in tissue sections, a hybrid space-feature map can be constructed. Specifically, for each spatial point, Euclidean distance is calculated based on its two-dimensional coordinates to establish spatial adjacency, and a feature map is constructed based on the cosine similarity of molecular feature vectors. Subsequently, the edge sets of the spatial map and the feature map are fused, and the importance of both is balanced by learnable weight coefficients to obtain the final weighted adjacency matrix. The constructed hybrid space-feature map preserves the spatial topological continuity of the tissue structure and effectively reflects the expression similarity at different molecular levels, providing a unified structural foundation for subsequent graph convolution and multimodal information fusion.

[0067] In one embodiment, a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution may further include a process of constructing a hybrid space-feature map. The specific process includes: determining the spatial coordinates corresponding to each spatial point based on the processed multi-omics data; calculating the Euclidean distance between each spatial coordinate and selecting each neighbor point to construct a spatial adjacency graph for each spatial point; calculating the cosine similarity between molecular feature vectors and determining neighbor points based on the cosine similarity to construct a feature map.

[0068] In this embodiment, it is assumed that the tissue slice contains N spatial spots. For each spatial spot... The known spatial coordinates of the spatial point are: ; and the molecular feature vectors corresponding to the spatial points. Here, M represents the omics layer (e.g., genes, proteins, or chromatin). For each omics modality M, an undirected K-nearest neighbor (KNN) graph can be constructed to simultaneously capture spatial proximity and molecular similarity. An undirected KNN graph is defined as follows: ; contains nodes ,side and weight .

[0069] The weights at the spatial or feature level can be expressed as: The combined weighted edge weights are: ;in, It is a scale parameter used to normalize spatial distance and feature distance; Used to balance the relative contributions of spatial edges and feature edges in the overall weight.

[0070] In this embodiment, the Euclidean distance between spatial coordinates can be calculated first, and the nearest coordinate for each spatial point can be selected. 1. 2. 3. 4. 5. 6. ... The feature map is constructed by merging the neighbors. Then, the edges of the two classes are merged, and a hybrid weight is assigned to each edge. This method of constructing adjacency matrices can effectively capture molecular-level similarities while maintaining spatial topological continuity, enabling multi-omics structure modeling under dual spatial-feature constraints.

[0071] Step 206: Based on the hybrid space-feature map structure, a hybrid encoder consisting of a graph neural network and Taylor linear attention is used to independently encode each omics data to generate independent latent representations for each omics. Among them, the graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise.

[0072] Each omics is encoded using an encoder consisting of a graph neural network (GNN) and a Taylor linear attention (TLA) mechanism. During the encoding phase, a hybrid encoder is employed, combining a GNN and a Taylor linear attention (TLA) mechanism. The GNN aggregates local spatial neighborhood information, extracting local structural features from the mixed spatial-feature map; while the TLA module uses a first-order Taylor expansion approximates softmax attention to capture long-range global dependencies and suppress sparse noise in a lightweight manner. The two are fused through residual connections to jointly model local and global information, thereby obtaining a stable and biologically interpretable latent representation.

[0073] In one embodiment, a spatial multi-omics structural domain recognition method based on Taylor linear attention graph convolution may further include a process for generating latent representations. Specifically, this process includes: extracting the standardized molecular feature matrix from the processed multi-omics data and finding the corresponding hybrid space-feature map weighted adjacency matrix, performing matrix alignment; based on the hybrid space-feature map, using a graph neural network to iteratively compute graph convolutional layers on the aligned matrix to obtain local spatial feature representations; using Taylor linear attention to perform feature mapping and normalization on the aligned matrix, followed by kernel transformation and global bias optimization, capturing global dependencies with linear complexity, and outputting global spatial feature representations; and fusing the local and global spatial feature representations through residual connections to generate independent latent representations for each omics.

[0074] In this embodiment, the encoder is residually connected using a graph convolutional neural network and a Taylor linear attention mechanism. The graph convolutional network receives a hybrid spatial feature map and omics representation information as input, which is then fed into the TLA proposed in this application. This TLA aims to approximate the standard softmax attention mechanism with linear complexity while maintaining stable convergence and global awareness. Given an input matrix... First, the input matrix is ​​linearly mapped to three sets of representations: query, key, and value (Q, K, V) to construct the basic space for attention. Then, to avoid gradient instability caused by excessively large inner product values, TLA applies a linear mapping to each pair of... conduct Normalization yields a value constrained to a unit sphere. Based on the kernelization concept, the feature mapping function is adopted. To approximate the exponential weights of softmax, the numerator of attention is rewritten as: The original quadratic complexity is transformed into linear aggregation through kernelization operations, allowing all key-value pairs to be accumulated and counted at once.

[0075] To further enhance numerical stability and global convergence speed, a global bias term is introduced at the molecule end to reflect the average contribution of the global context, i.e. Correspondingly, a bias term is also added to the denominator calculation to avoid division by zero, and the global normalization term is corrected: Where N is a small constant used to ensure stability. Therefore, the final TLA expression can be formalized as: The formalized formula essentially approximates the softmax kernel linearly through Taylor expansion, thus achieving [something] while maintaining global context sensitivity. Highly efficient attention computation. Compared to the traditional Transformer attention mechanism, TLA has significant advantages in numerical stability, memory usage, and convergence speed, making it particularly suitable for feature fusion scenarios involving large-scale multimodal and spatial multi-omics data. Then, a residual connection is made with the result of the preceding graph convolutional neural network to obtain the encoding of each omics.

[0076] Step 208: Based on the latent representations of each omics, adaptive weighted fusion is performed using learnable weight coefficients to generate low-dimensional latent feature representations.

[0077] After obtaining the latent representations of each omics modality, the embeddings of different modalities are adaptively fused using learnable weighting coefficients to generate a unified low-dimensional representation Z, i.e., a low-dimensional latent feature representation.

[0078] In one embodiment, a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution may further include a multimodal fusion process, specifically including: determining the latent representation of each omics and determining learnable weight parameters; performing feature fusion on the latent representation of each omics through learnable weight coefficients to generate low-dimensional latent feature representations; wherein the learnable weight coefficients are automatically adjusted during training to achieve modality balance.

[0079] Among them, the potential representations of each omics and The TLAGC model, consisting of a hybrid encoder comprising a graph neural network and Taylor linear attention, is derived from both omics approaches. It utilizes a learnable weighting coefficient. The features of the two modalities are fused, and the learnable weighting coefficients are automatically adjusted during training to achieve optimal modality balance. The final fused low-dimensional latent feature representation is denoted as Z, and its calculation form is: This linear fusion method based on learnable weights can achieve adaptive integration of cross-modal information while maintaining the independence of modal features, thereby obtaining a more robust and representative joint representation in downstream spatial domain recognition and phenotypic analysis tasks.

[0080] For achieving efficient integration of multi-omics data from the same slice, such as... Figure 3 As shown, the model first maps and encodes the data from the two omics modalities, and then fuses the two omics data. The core of the framework is a graph convolutional neural network module guided by TLA (TaylorLinear Attention). The two achieve joint modeling through residual connections, and finally perform weighted fusion through learnable weight coefficients to obtain a unified low-dimensional latent feature representation Z, which is used for spatial structural domain partitioning and downstream analysis.

[0081] In this embodiment, the latent space is constrained and structured by jointly optimizing the objectives of reconstruction regularization and clustering. This enhances the separability and spatial consistency of features while maintaining the integrity of information across modalities. The resulting unified representation supports spatial structural domain identification and provides a robust feature foundation for subsequent multi-omics downstream analysis.

[0082] In one embodiment, a spatial multi-omics structural domain recognition method based on Taylor linear attention graph convolution may further include a model training process, specifically including: mapping low-dimensional latent feature representations back to the original spaces of each modality through a decoder, and calculating the reconstruction error using mean squared error to obtain a reconstruction loss function; constraining the distribution of low-dimensional latent feature representations to be consistent with the target clustering distribution through KL divergence to obtain a clustering regularization loss function; constructing a dual loss function including reconstruction loss and clustering regularization loss, using low-dimensional latent feature representations as the optimization object, and obtaining a graph convolutional neural network model guided by Taylor attention mechanism through end-to-end training.

[0083] During model training, the reconstruction loss and clustering regularization term are jointly minimized to achieve structured optimization of the latent representation. First, the low-dimensional latent feature representation Z is mapped back to the original feature space of each modality using a decoder, and the reconstruction error is calculated to maintain information consistency between modalities. Then, a clustering regularization based on Kullback–Leibler (KL) divergence is introduced to constrain the consistency between the latent representation distribution and the target cluster distribution, thereby improving the discriminativeness and stability of the structural domain partitioning. The final optimization objective consists of a weighted sum of the two losses, achieving a synergistic improvement in reconstruction accuracy and clustering performance through end-to-end training.

[0084] Specifically, in multi-omics learning tasks, in addition to focusing on the similarity between latent representations, reconstruction regularization is introduced to enhance the reconstruction capabilities of each omics modality. Specifically, the final low-dimensional latent feature representation Z-pass GCN decoder is mapped back to the original feature space to obtain the reconstructed feature matrix. The reconstruction loss, calculated using the mean square error, can be expressed as: ;in, This represents the reconstructed feature matrix of mode M. For the original input, Weighting coefficients to control the contribution of reconstruction loss to different modes.

[0085] To further constrain the distribution of the latent representation, KL divergence is introduced to represent the final low-dimensional latent features. Mapped to a clustering space. Through a classifier. Using soft tags Regularize the clustering process. KL loss is defined as... ;in, This represents the sample probability distribution predicted by the model.

[0086] The final total loss is defined as the sum of two parts: The objective function achieves a balance between clustering accuracy and modality preservation by jointly optimizing cluster consistency and feature reconstructibility, thereby improving the overall multi-omics representation learning ability.

[0087] In one embodiment, a spatial multi-omics structural domain recognition method based on Taylor linear attention graph convolution may further include a process of using a model to recognize multi-omics structural domains. The specific process includes: inputting the processed multi-omics data and the mixed spatial-feature map into a graph convolutional neural network model guided by the Taylor attention mechanism; and performing regularization processing through the dual loss function in the graph convolutional neural network model guided by the Taylor attention mechanism to obtain the recognition result of the spatial multi-omics structural domain.

[0088] In one embodiment, a spatial multi-omics structural domain identification method based on Taylor linear attention graph convolution may further include a process for evaluating model performance. The specific process includes: selecting the Rand index, homogeneity score, and adjusted mutual information as quantitative indicators; performing qualitative analysis on the identification results of spatial multi-omics structural domains based on the quantitative indicators to obtain the verification results of the graph convolutional neural network model guided by the Taylor attention mechanism.

[0089] To verify the effectiveness of the model in spatial multi-omics domain identification, various quantitative metrics were used to evaluate the results. The main metrics employed were the Adjusted Rand Index (ARI), Homogeneity Score, and Adjusted Mutual Information (AMI) to measure the consistency between the model's clustering results and the ground truth labels, as well as the clarity of the cluster boundaries. Simultaneously, on an unlabeled dataset, spatial coherence and functional consistency analyses were used to qualitatively validate the identification results. Spatial coherence reflects the spatial continuity of cluster labels at adjacent locations, while functional consistency assesses the enrichment of molecular pathways and biological functions within each domain. These evaluation metrics collectively reflect the model's comprehensive performance in multimodal information integration, spatial consistency preservation, and domain partitioning accuracy.

[0090] Specifically, in terms of quantitative evaluation, the main indicators include adjusted RAND index, homogeneity score, and adjusted mutual information. Among them, ARI measures the degree of matching between cluster partitions and true labels, and corrects for random consistency, defined as: ;in This represents the number of intersection samples between the true category i and the clustering result j. These represent the total number of samples with the true and predicted labels, respectively.

[0091] Homogeneity measures whether samples within each cluster belong to the same true class, and is defined as: ;in Let K be the conditional entropy of class C given the clustering result K. Entropy of the category.

[0092] AMI is used to measure the degree of information overlap between the true labels and the clustering results, and to eliminate the influence of random factors. ;in Indicates mutual information, The expected mutual information under random partitioning.

[0093] In this embodiment, the proposed Taylor attention mechanism-guided graph convolutional neural network model (TLAGC) demonstrates significant superiority in spatial multi-omics data integration and structural domain identification. Quantitative experimental results on the Human Lymph Node A1 dataset are shown in the table below:

[0094]

[0095] As shown in the table above, TLAGC outperforms the baseline models (including COSMOS, SpatialGlue, and PRAGA) in all internal and external evaluation metrics. TLAGC achieves the highest scores in metrics such as whole Rand index, homogeneity score, and silhouette coefficient, demonstrating stronger clustering consistency and spatial boundary clarity. Its results in spatial domain partitioning are more coherent, accurately identifying subtle subregions of tissues, especially exhibiting higher spatial continuity in the medial cortex, and showing high consistency with the actual annotation results. The actual annotation results are as follows: Figure 4 As shown.

[0096] By leveraging the synergy of LocalGCN and TLA, efficient fusion of local spatial structure and global dependency information is achieved. GCN captures local topological relationships within the spatial neighborhood, while TLA models long-range dependencies through Taylor linear expansion, effectively mitigating the problem of limited feature propagation caused by spatial data sparsity.

[0097] In this embodiment, an ablation experiment was conducted, and the comparison results of the ablation experiments are shown in the table below:

[0098]

[0099] in, The table above indicates removal. This further verifies the complementarity of LocalGCN and TLA: removing either module leads to a significant decrease in model performance, especially in terms of preserving cluster boundaries and spatial continuity. This demonstrates that the dual-module design of LocalGCN and TLA is crucial for achieving high-quality spatial structure domain recognition.

[0100] Step 210: Input the low-dimensional latent feature representation into the clustering algorithm to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location.

[0101] In one embodiment, a spatial multi-omics structural domain identification method based on Taylor linear attention map convolution may further include a process of spatial multi-omics structural domain partitioning. The specific process includes: inputting the low-dimensional latent feature representation of each spatial point in the latent space into a clustering algorithm; and using the clustering algorithm to partition a spatial multi-omics structure with unified molecular expression patterns and spatial locations based on feature separability and spatial consistency.

[0102] After obtaining the low-dimensional latent feature representation Z, the Taylor attention mechanism-guided graph convolutional neural network model performs spatial multi-omics domain identification based on its embedded features. Specifically, the representation of each spatial point (spot) in the latent space is used as input, and a clustering algorithm is used to segment regions that are consistent in both molecular expression and spatial location, thereby revealing functionally related spatial domains in tissues.

[0103] It should be understood that although the steps in the flowchart above are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowchart above may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0104] In one embodiment, such as Figure 5 As shown, a spatial multi-omics structural domain recognition system based on Taylor linear attention map convolution is provided, including: a data processing module 510, a hybrid space-feature map generation module 520, a latent representation generation module 530, a low-dimensional latent feature generation module 540, and a spatial multi-omics structural domain partitioning module 550, wherein:

[0105] The data processing module 510 is used to collect spatial transcriptome, spatial proteome and spatial epigenome data and perform data standardization processing respectively to obtain processed multi-omics data.

[0106] The hybrid space-feature map generation module 520 is used to construct a spatial adjacency graph based on the processed multi-omics data by calculating the Euclidean distance of spatial points using two-dimensional coordinates, and to construct a feature map based on the cosine similarity of molecular feature vectors; the spatial adjacency graph and the feature map are fused to generate a weighted adjacency matrix, forming a hybrid space-feature map;

[0107] The latent representation generation module 530 is used to independently encode each omics data based on a hybrid spatial-feature map structure, using a hybrid encoder composed of a graph neural network and Taylor linear attention to generate independent latent representations for each omics. Among them, the graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise.

[0108] The low-dimensional latent feature generation module 540 is used to generate low-dimensional latent feature representations based on the latent representations of each omics through adaptive weighted fusion using learnable weight coefficients.

[0109] The spatial multi-omics structural domain partitioning module 550 is used to input low-dimensional latent feature representations into clustering algorithms to achieve spatial multi-omics structural domain partitioning based on the unity of molecular expression and spatial location.

[0110] In one embodiment, the data processing module 510 is further used to perform low-expression gene removal, high-variance gene screening, normalization, and logarithmic transformation on the spatial transcriptome; to perform centered logarithmic ratio normalization on the spatial proteome; and to perform high-variance feature screening, TF-IDF transformation, logarithmic normalization, and truncated SVD dimensionality reduction on the spatial epigenetics.

[0111] In one embodiment, the hybrid space-feature map generation module 520 is further configured to determine the spatial coordinates corresponding to each spatial point based on the processed multi-omics data; calculate the Euclidean distance between each spatial coordinate and select each neighbor point to construct a spatial adjacency graph for each spatial point; calculate the cosine similarity between molecular feature vectors and determine the neighbor points based on the cosine similarity to construct a feature map.

[0112] In one embodiment, the latent representation generation module 530 is further configured to extract the standardized molecular feature matrix of the processed multi-omics data, find the corresponding hybrid space-feature map weighted adjacency matrix, and perform matrix alignment processing; based on the hybrid space-feature map, a graph neural network is used to perform graph convolutional layer iterative calculation based on the aligned matrix to obtain the local spatial feature representation; Taylor linear attention is used to perform feature mapping and normalization on the aligned matrix, and after kernel transformation and global bias optimization, the global dependency is captured with linear complexity, and the global spatial feature representation is output; residual connections are performed on the local spatial feature representation and the global spatial feature representation to generate the independent latent representation of each omics.

[0113] In one embodiment, the low-dimensional latent feature generation module 540 is further configured to determine the latent representations of each omics and determine the learnable weight parameters; perform feature fusion on the latent representations of each omics through the learnable weight coefficients to generate low-dimensional latent feature representations; wherein the learnable weight coefficients are automatically adjusted during training to achieve modality balance.

[0114] In one embodiment, a spatial multi-omics structural domain recognition system based on Taylor linear attention graph convolution may further include a model training module, which is used to map the low-dimensional latent feature representation back to the original space of each modality through a decoder, and calculate the reconstruction error using mean squared error to obtain a reconstruction loss function; constrain the distribution of the low-dimensional latent feature representation to be consistent with the target clustering distribution through KL divergence to obtain a clustering regularization loss function; construct a dual loss function including reconstruction loss and clustering regularization loss, take the low-dimensional latent feature representation as the optimization object, and obtain a graph convolutional neural network model guided by Taylor attention mechanism through end-to-end training.

[0115] In one embodiment, the spatial multi-omics structural domain partitioning module 550 is further used to input the processed multi-omics data and the hybrid spatial-feature map into a graph convolutional neural network model guided by the Taylor attention mechanism; and to perform regularization processing through the dual loss function in the graph convolutional neural network model guided by the Taylor attention mechanism to obtain the recognition result of the spatial multi-omics structural domain.

[0116] In one embodiment, a spatial multi-omics structural domain recognition system based on Taylor linear attention graph convolution may further include a model evaluation module for selecting the Rand index, homogeneity score, and adjusted mutual information as quantitative indicators; and performing qualitative analysis on the recognition results of the spatial multi-omics structural domain based on the quantitative indicators to obtain the verification results of the graph convolutional neural network model guided by the Taylor attention mechanism.

[0117] In one embodiment, the spatial multi-omics structural domain partitioning module 550 is also used to input the low-dimensional latent feature representations of each spatial point in the latent space into the clustering algorithm; through the clustering algorithm, a spatial multi-omics structure with unified molecular expression patterns and spatial locations is partitioned based on feature separability and spatial consistency.

[0118] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0119] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0120] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution.

[0121] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of a spatial multi-omics structural domain recognition method based on Taylor linear attention map convolution.

[0122] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0123] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0124] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for spatial multi-omics domain identification based on Taylor linear attention map convolution, characterized in that, The method comprises: Collecting spatial transcriptome, spatial proteome, and spatial epigenome data and performing data standardization processing respectively to obtain processed multi-omics data; Based on the processed multi-omics data, a spatial adjacency graph is constructed by calculating the Euclidean distance of the two-dimensional coordinates of the spatial points, and a feature graph is constructed based on the cosine similarity of the molecular feature vectors; the spatial adjacency graph and the feature graph are fused to generate a weighted adjacency matrix, forming a hybrid spatial-feature graph; Based on the hybrid spatial-feature graph, a hybrid encoder composed of a graph neural network and a Taylor linear attention is used to independently encode each omics data to generate independent latent representations of each omics; wherein the graph neural network is used to aggregate local spatial neighborhood information and extract local structural features; the Taylor linear attention is used to capture long-range global dependencies and suppress sparse noise; Based on the latent representations of each omics, adaptive weighted fusion is performed through learnable weight coefficients to generate low-dimensional latent feature representations; The low-dimensional latent feature representations are input into a clustering algorithm to realize spatial multi-omics domain division based on the unification of molecular expression and spatial position.

2. The spatial multi-omic domain identification method based on Taylor linear attention map convolution according to claim 1, characterized in that, Collecting spatial transcriptome, spatial proteome, and spatial epigenome data and performing data standardization processing respectively, comprising: Performing low-expression gene removal, high-variable gene screening, normalization, and logarithmic conversion processing on the spatial transcriptome; Performing central logarithmic ratio normalization processing on the spatial proteome; Performing high-variable feature screening, TF-IDF conversion, logarithmic normalization, and truncated SVD dimensionality reduction processing on the spatial epigenome.

3. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 1, wherein, Based on the processed multi-omics data, a spatial adjacency graph is constructed by calculating the Euclidean distance of the two-dimensional coordinates of the spatial points, and a feature graph is constructed based on the cosine similarity of the molecular feature vectors, comprising: Based on the processed multi-omics data, the spatial coordinates corresponding to each spatial point are determined; The Euclidean distances between each of the spatial coordinates are calculated, and each of the spatial points is selected to construct a spatial adjacency graph with each neighbor point; The cosine similarity between the molecular feature vectors is calculated, and the neighbor points are determined based on the cosine similarity to construct a feature graph.

4. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 1, wherein, Based on the hybrid spatial-feature graph, a hybrid encoder composed of a graph neural network and a Taylor linear attention is used to independently encode each omics data to generate independent latent representations of each omics, comprising: The standardized molecular feature matrix of the processed multi-omics data is extracted, and the corresponding hybrid spatial-feature graph weighted adjacency matrix is searched for matrix alignment processing; Based on the hybrid spatial-feature graph, a graph convolution layer is iteratively calculated based on the aligned matrix using a graph neural network to obtain a local spatial feature representation; The Taylor linear attention is used to map and normalize the aligned matrix, and the kernel conversion and global bias optimization are performed, the linear complexity captures the global dependency, and the global spatial feature representation is output; The local spatial feature representation and the global spatial feature representation are fused by residual connection to generate independent latent representations of each omics.

5. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 1, wherein, Based on the latent representations of each omics, adaptive weighted fusion is performed through learnable weight coefficients to generate low-dimensional latent feature representations, comprising: determining potential representations of each omics, and determining learnable weight parameters; performing feature fusion on the potential representations of each omics through the learnable weight coefficients to generate a low-dimensional potential feature representation; wherein the learnable weight coefficients are automatically adjusted in a training process to achieve modal balance.

6. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 1, wherein, The method further comprises: mapping the low-dimensional potential feature representation back to the original space of each modality through a decoder, and calculating reconstruction error in a mean square error to obtain a reconstruction loss function; constraining the distribution of the low-dimensional potential feature representation to be consistent with a target clustering distribution through KL divergence to obtain a clustering regular loss function; constructing a double loss function comprising the reconstruction loss and the clustering regular loss, taking the low-dimensional potential feature representation as an optimization object, and obtaining the Taylor attention mechanism guided graph convolutional neural network model through end-to-end training.

7. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 6, wherein, The method further comprises: inputting the processed multi-omics data and the hybrid space-feature map into the Taylor attention mechanism guided graph convolutional neural network model; performing regularization processing on the hybrid space-feature map through the double loss function in the Taylor attention mechanism guided graph convolutional neural network model to obtain the recognition result of the spatial multi-omics domain.

8. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 7, wherein, The method further comprises: selecting the Lande index, homogeneity score and adjusted mutual information as quantitative indicators; performing qualitative analysis on the recognition result of the spatial multi-omics domain based on the quantitative indicators to obtain a verification result of the Taylor attention mechanism guided graph convolutional neural network model.

9. The Taylor linear attention map convolution-based spatial multi-omic domain identification method of claim 1, wherein, inputting the low-dimensional potential feature representation into a clustering algorithm to realize spatial multi-omics domain division based on unified molecular expression and spatial position, comprising: inputting the low-dimensional potential feature representation of each spatial point in the latent space into a clustering algorithm; dividing the spatial multi-omics domain with unified molecular expression and spatial position based on feature separability and spatial consistency through the clustering algorithm.

10. A spatial multi-omic domain identification system based on Taylor linear attention map convolution, characterized in that, The system comprises: a data processing module configured to collect spatial transcriptome, spatial proteome and spatial epigenome data and perform data standardization processing on the data respectively to obtain processed multi-omics data; a hybrid space-feature map generation module configured to construct a spatial adjacency graph based on the processed multi-omics data by calculating the Euclidean distance of spatial point two-dimensional coordinates, and construct a feature graph based on the cosine similarity of molecular feature vectors; fuse the spatial adjacency graph and the feature graph to generate a weighted adjacency matrix to form a hybrid space-feature map; a potential representation generation module configured to independently encode each omics data using a hybrid encoder composed of a graph neural network and a Taylor linear attention based on the hybrid space-feature map as a structure basis to generate independent potential representations of each omics; wherein the graph neural network is configured to aggregate local spatial neighborhood information and extract local structure features; and the Taylor linear attention is configured to capture long-range global dependencies and suppress sparse noise; a low-dimensional potential feature generation module configured to perform adaptive weighted fusion on the potential representations of each omics through learnable weight coefficients to generate a low-dimensional potential feature representation. The spatial multi-omics domain partitioning module is configured to input the low-dimensional latent feature representation into a clustering algorithm to realize spatial multi-omics domain partitioning based on unification of molecular expression and spatial position.

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