Single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization

Abstract

The application discloses a single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization. The method uses a K-means method to generate cluster centers as initial anchor points for single-cell multi-omics data, uses a multi-view subspace method to establish specific omics anchor graphs and shared anchor graphs, designs a graph convolution network and an anchor point learning collaborative optimization strategy to adaptively update anchor points, so that the learned anchor points can better adapt to the multi-view features of the data and accurately represent the omics information, and designs a hierarchical graph attention module to mine the complex relationship of features from shared anchor graph data to enrich the obtained omics representation. In the commonality fusion and completion module, the shared high-order information graph representation is used to complete the omics specific anchor graph representation, and the final result is obtained after clustering the fused results. The application can integrate single-cell RNA data and ATAC data, and good results can be obtained in downstream tasks such as cell type annotation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bioinformatics and machine learning, in particular to a single-cell multi-omics integration method based on anchor selection and graph learning collaborative optimization, mainly applied to the fields of cell type and subpopulation identification, epigenetic and transcriptional regulation research, cross-omics data integration and disease mechanism research, drug target discovery and verification, etc. BACKGROUND

[0002] With the continuous development of sequencing technology, researchers can capture multiple omics data in the same cell, such as transcriptome, epigenome, proteome, and metabolome, etc. The combination of these single-cell multi-omics technologies can analyze the molecular characteristics and regulation mechanisms of individual cells from multiple perspectives, breaking through the limitations of traditional single-omics research. By integrating these multi-omics data, researchers can more comprehensively reveal the complex regulatory network of cells, identify new cell types or subpopulations by analyzing cell heterogeneity, reconstruct more accurate cell differentiation trajectories by combining multi-omics data, analyze key regulatory nodes and signaling pathways, reveal cell components and their interactions in the tumor microenvironment, and help elucidate the mechanisms of tumor occurrence and progression. It can also analyze the dynamic functional state of immune cells and provide support for the development of immunotherapy targets.

[0003] Capturing multiple omics in the same cell provides multiple perspectives for the same biological system, thus forming multi-view data. Existing multi-view methods are mainly based on graph networks. These graph networks aggregate multi-view information while their computational cost grows exponentially, requiring high computational resources and making it difficult to apply them to large-scale data sets. In addition, existing clustering methods do not fully utilize the view information and do not fully exploit the rich biological information.

[0004] To improve efficiency, researchers in the field of multi-view have proposed using the relationship between anchors and data to represent the relationship between all data points. Currently, anchor selection mainly adopts two strategies: heuristic sampling and adaptive sampling. Heuristic sampling is a method of selecting anchors based on prior knowledge, empirical rules, or specific heuristic functions. It is simple to calculate, but its effectiveness is highly dependent on the accuracy of prior knowledge. If the prior information is insufficient, the anchor points may be biased, affecting subsequent analysis. Adaptive sampling dynamically adjusts the sampling strategy and parameters during the sampling process based on the distribution characteristics of the data and the analysis target to gradually find the optimal anchor set. It usually first randomly selects a small number of initial anchors from the data set, then analyzes the effectiveness of these anchors based on certain evaluation indicators, and adjusts the anchors based on the analysis results, iteratively optimizing until the preset stopping condition is met.

[0005] However, these methods cannot be fully applied in the field of single-cell multi-omics. First, in the learning process, such methods only learn the structural information of the graph, while in the single-cell field, the main reliance is on features (genes, peaks) to distinguish cell types; second, the method learns shared representations from different views, completely ignoring the differences between views; in addition, in the field of multi-omics, the feature expression of cells is very different at different molecular levels, and the measurement scale, data distribution and noise level of different omics data are very different, and direct integration will mask the real biological signal. SUMMARY

[0006] To solve the above problems in the prior art, a single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization is proposed, which is applied to the fields of cell type and subpopulation identification, epigenetic and transcriptional regulation research, etc., and is suitable for processing scRNA-seq and scATAC-seq data from the same cell; the method establishes specific omics anchor graphs and shared anchor graphs through a multi-view subspace method, designs a graph convolution network and an anchor point learning collaborative optimization strategy to adaptively update the anchor points, obtains omics-specific graph information and shared graph information; a hierarchical graph attention network is used to mine the potential relationship between omics features (genes and peaks), obtain high-order shared information, and finally organically fuse the specific graph representation and the high-order shared representation to improve the clustering accuracy of cell subtypes and effectively integrate single-cell multi-omics data.

[0007] The single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization proposed in the application comprises the following steps:

[0008] Step one: obtaining scRNA-seq data from a single-cell multi-omics data set , scATAC-seq data and its feature splicing data as multi-view data;

[0009] Step a1: ensuring that the scRNA-seq data and the scATAC-seq data are one-to-one corresponding;

[0010] Step a2: defining the scRNA-seq data and the scATAC-seq data , wherein represents the view data with a feature dimension of and a cell number of , and represents the feature splicing view data with a feature dimension of and a cell number of n ;

[0011] Step 2: Use the K-means method to generate each view Each cluster center serves as the initialization anchor point;

[0012] Step 3: Using the initial anchor points obtained in Step 2, construct a specific omics anchor map. and And calculate the corresponding specific omics anchor graph representation based on anchor graph subspace clustering. and ;

[0013] Define the anchor map for scRNA-seq specific omics Anchor map of scATAC-seq specific omics Then, scRNA-seq anchor map representations are obtained by clustering the anchor map subspace. and scATAC-seq anchor diagram representation

[0014]

[0015] in, and for and The unique anchor point matrix, It is a column vector consisting entirely of 1s, guaranteeing and Each column adds up to 1. It is the Frobenius norm;

[0016] Step 4: Adaptively update the anchor graphs of specific omics and their specific omics anchor graph representations using a co-optimization strategy of graph convolutional networks and anchor point learning. and Specifically, it includes the following steps:

[0017] Step b1: Use a graph convolutional network to learn the scRNA-seq graph hidden layer representation. Preserve omics-specific information

[0018]

[0019] in, , It is the adjacency matrix of the scRNA-seq graph. It is the identity matrix. In this way, graph convolution can capture the specificity of each omics view and preserve its important information in the graph;

[0020] Step b2: Similarly, use a graph convolutional network to learn the scATAC-seq graph hidden layer representation. ;

[0021] Step b3: update the corresponding omics anchor graph representation using the graph convolutional network to get the graph hidden layer representation and :

[0022]

[0023] Step b4: update the variables using the method of control variables in the anchor graph subspace ， optimization;

[0024]

[0025]

[0026] wherein is the trace of a matrix;

[0027] Step b5: repeat steps b1 to b4 until convergence;

[0028] Step five: in order to make the information of omics fully integrated, get the shared information between views; define the anchor point projection matrix to align the shared anchor points the feature dimension of the original omics data of the view ; according to the initialized anchor points, use anchor graph subspace clustering to get the shared anchor graph representation ;

[0029]

[0030] wherein, is the number of input views, is the weight coefficient for balancing the influence between views, is the column vector formed by , and is the shared anchor point between views. is the shared anchor graph representation, and the shared anchor graph is formed ;

[0031] Step six: use the graph convolutional network and anchor point to learn the strategy of collaborative optimization to update the shared anchor graph and the shared anchor graph representation adaptively , the specific implementation steps are as follows:

[0032] Step c1: use the graph convolutional network to learn the feature splicing graph hidden layer representation

[0033]

[0034] wherein, , is the adjacency matrix of the feature stitching graph, is the identity matrix;

[0035] Step c2: update the shared anchor graph representation between shared anchors and cells using the graph convolution network to obtain the graph hidden layer representation

[0036]

[0037] Step c3: update the variables , , and respectively using the method of control variables, the specific implementation process is as follows:

[0038] Fix , and , optimize the anchor point projection matrix of each view while ensuring is an orthogonal matrix to ensure the stability and consistency of the anchor point mapping.

[0039]

[0040] Since is independent of each view, simplifying the above formula can obtain

[0041]

[0042] where is the trace of the matrix, fix , optimize , and the anchor graph subspace clustering can be simplified as

[0043]

[0044] Fix , and , optimize :

[0045]

[0046] Fix , optimize :

[0047]

[0048] Define To find the weight coefficient of each view so that the contribution among all views is balanced, the best ;

[0049]

[0050] Step c4: Repeat steps c1 to c3 until convergence;

[0051] Step seven: Design a hierarchical graph attention network for the shared anchor graph to learn high-order shared representations of genes and peaks in the shared anchor graph features The specific implementation process is as follows:

[0052] Step d1: The input of the graph attention layer is the node feature set of the shared graph The output of the k layer is , where are the input and output node embeddings respectively, is the dimension of the input and output node embeddings, and the normalized input and output node embeddings can be represented as:

[0053]

[0054] Step d2: Calculate the weight for each neighbor node, and apply the shared weight of the layer to each node, and the attention coefficient is as follows:

[0055]

[0056] where, is the importance of the kth layer vertex to the vertex , denotes the correlation measure function. In order to compare the weight coefficients between different vertices in the neighborhood, the function is used to normalize :

[0057]

[0058] The transformed features of vertex and vertex are spliced to obtain a feature vector, which is then input into a feedforward neural network and activated by a LeakyReLU function. The final weight coefficient is ;

[0059]

[0060] is the normalized parameter matrix of the relevance measure function. is the neighborhood of a node in the graph, is the concatenation operation. Get the representation of node ;

[0061]

[0062] Step d3: In order to enhance the expression ability and stability of the model, the multi-head attention mechanism is used, and the representation of node under multi-head attention is obtained by averaging ;

[0063]

[0064] wherein, is the number of multi-head attention heads. By calculating the representation of each node, the high-order shared representation of genes and peaks in the final shared anchor graph feature ;

[0065] Step eight: a common fusion completion operator is designed to integrate to integrate and high-order shared representation to enrich specific omics;

[0066]

[0067] wherein, denotes the Hadamard operator, and is the specific graph representation after completion, and finally , is and between the weight distribution parameters:

[0068]

[0069] Step eight: output the specific graph representation after completion , , , and use the K-means method to cluster .

[0070] ​The application has the following characteristics: (1) the rich biological information contained in the complex relationship between cells, cells and characteristics, and characteristics and characteristics in single-cell multi-omics data is fully considered, the expressiveness of the single-cell multi-omics graph learning model is enhanced through comprehensive fusion of multi-level relationships, and the resolution of cell subpopulations is improved; (2) the multi-view subspace anchor point collaborative optimization module simultaneously considers specific information and shared information of each omics, dynamically updates specific anchor graphs and shared anchor graphs, effectively reduces the sparsity problem of multi-omics data, and enhances the complementarity between multi-omics, so that different omics data can be more closely related to each other; (3) the hierarchical graph attention module is designed to fully mine the complex relationship between cross-omics characteristic genes and peaks, more accurately capture key biological information between characteristic genes and omics peaks, and optimize node representation learning.

[0071] The application is mainly applied to the fields of cell type and subpopulation identification, epigenetic and transcriptional regulation research, cross-omics data integration and disease mechanism research, drug target discovery and verification, can improve cell clustering effect, effectively mine the complex relationship between cross-omics characteristic genes and peaks, and lay a foundation for subsequent development of regulation mechanism analysis, biomarker discovery and function research in multi-omics data integration. BRIEF DESCRIPTION OF DRAWINGS

[0072] The application will be further described below with reference to the drawings and examples;

[0073] Figure 1 The figure is a structural schematic diagram of the single-cell multi-omics integration method of the application. DETAILED DESCRIPTION

[0074] In order to have a clearer understanding of the technical features, objects and effects of the application, the specific implementation modes of the application will be described in detail with reference to the drawings; different sizes of single-cell multi-omics data sets are used to show the implementation effect of the application, and the data set size is from 1000 to 120000.

[0075] Figure 1 The figure is a structural schematic diagram of the single-cell multi-omics integration method of the application, mainly including a multi-view subspace anchor point collaborative optimization module, a hierarchical graph attention module and a common fusion completion module. The multi-view subspace anchor point collaborative optimization module uses K-means algorithm to calculate cluster centers as initial anchor points in different omics and characteristic spliced omics data, constructs omics specific graph and shared graph with initial anchor points and cells as nodes, minimizes the Frobenius norm loss between original nodes and anchor points, and learns node representation and updates anchor points by using graph convolution network. The hierarchical graph attention module extracts omics high-order shared representation The common fusion completion operator of the common fusion completion clustering module is completion Information obtained , the fusion is clustered.

[0076] (1) Parameter setting

[0077] To ensure the universality of the comparison method, the parameters of all comparison methods follow the settings in their respective paper algorithms; the experiment uses Python 3.9 programming language, and a memory capacity of 24G GPU+64G CPU is used to carry out the experiment. All algorithms are repeated 10 times, and the average value is taken as the final performance of the model. The present application uses the K-means method to generate cluster centers as initialization anchor points, initializes the pre-trained graph convolutional network, sets the scRNA-seq hidden layer feature dimension to 500, the scATAC-seq hidden layer feature dimension to 1000, and the number of graph convolutional layers to 2. The initial learning rate is 0.01, the iteration number is 1000 times, the weight decay is set to 5e-3, and the Adam optimizer is used for learning. The number of anchor points needs to be determined in the range of [10k, 20k, 30k, 40k, 50k, 60k, 70k], where k represents the number of cell types in the dataset. The multi-head attention of the graph attention network is set to 3 by default, and the weight distribution parameter is set to 0.5.

[0078] (2) 4 kinds of data sets

[0079] Four data sets were selected for the experiment to evaluate the performance of the proposed algorithm. The data set size varies from 1000 to 120000. The data set name, cell number, gene number, peak number and cell class number are shown in Table 1.

[0080] Table 1: Information statistics of data sets

[0081]

[0082] CellMix: A small data set containing paired 1047 cell scRNA-seq and scATAC-seq data from SNARE-seq mixed culture human BJ, H1, K562 and GM12878 cell lines. The Seurat package is used to retain the top 500 genes expressed in 1047 cells in the scRNA-seq data set, and 7136 peaks within 100 kb upstream and downstream of the genes in the scATAC-seq.

[0083] PBMC-3K: The PBMC-3K dataset contains paired scRNA-seq and scATAC-seq of 3012 cells. First, 200 poor quality cells (mitochondrial proportion greater than 25%, threshold less than 200) were removed. Then 2900 cells were predicted using Azimuth software, and cell type data with less than 5 cells were removed, finally obtaining 2874 cells and 14 cell types. To improve efficiency, the Seurat package was used to retain the top 1500 genes in the scRNA-seq dataset and 11063 peaks within 100 kb upstream and downstream of genes in the scATAC-seq dataset.

[0084] Mouse-Skin: A large dataset containing 34774 cells. SHARE-seq REF _Ref186911119 \r \h \* MERGEFORMAT

[55] Data of paired scRNA-seq and scATAC-seq from adult mouse skin; the dataset has been pre-processed and no further operation is performed.

[0085] Human bone marrow mononuclear cells (BMMC): BMMC can be publicly downloaded from the National Center for Biotechnology Information (NCBI), with gene expression (GEO) accession number GSE194122, the dataset includes single cells extracted from human bone marrow mononuclear cells from 12 different donors, and measured using 10X multi-group and 10x3' single cell gene expression technology.

[0086] (3) 4 clustering indicators

[0087] The experiment selected accuracy (Accuracy, ACC), normalized mutual information (Normalized Mutual Information, NMI), macro F1 score (Macro F1-score, F1), precision rate (Precision Rate, Precision), recall rate (Recall Rate, Recall), adjusted rand index (Adjusted Rand Index, ARI) and silhouette coefficient (Silhouette Coefficient, SC) as evaluation indicators of clustering effect.

[0088] (4) 18 clustering algorithms

[0089] The embodiments were tested on 4 single-cell multi-omics datasets, and the single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization was compared with 14 commonly used clustering algorithms. The specific introduction of each algorithm is as follows:

[0090] K-means: A traditional clustering method mentioned by Ahmed M, Seraj R, Islam SM in the paper The k-means algorithm: A comprehensive survey and performance evaluation, Electronics. 2020. pp. 1-12.

[0091] Liger: A single-cell multi-omic integration method based on non-negative matrix factorization mentioned by Welch J D, Kozareva V, Ferreira A in the paper Single-cell multi-omic integration compares and contrasts features of brain cell, Cell. 2019. pp. 1873-1887.

[0092] MOFA+: A single-cell multi-omic analysis method based on multi-omics factor analysis proposed by Argelaguet R, Arnol D, Bredikhin D in the paper MOFA+: a statistical framework for comprehensive integration of multi-modal single-cell data, Genome Biology. 2020. pp. 1-17.

[0093] scAI: A method that assumes a weighted linear function of the shared latent space of the data matrices of transcriptome and epigenome, thus inferring the latent cell types; proposed by Jin S, Zhang L, Nie Q in the paper scAI: an unsupervised approach for the integrative analysis of parallel single-cell transcriptomic and epigenomic profiles, Genome Biology. 2020. pp. 21-25.

[0094] UnionCom: Project multi-omics data into a common embedding space and match complex nonlinear features through a global scale parameter. Cluster cells or other biological entities in the embedding space. Proposed by Cao K, Bai X, Hong Y in Unsupervised topological alignment for single-cell multi-omics integration. Bioinformatics. 2020. pp.48-56.

[0095] DCCA: Project different omics into corresponding low-dimensional spaces and use a "Teacher-Student" mechanism to integrate multi-omics data. Proposed by Zuo C, Dai H, Chen L in Deep cross-omics cycle attention model for joint analysis of single-cell multi-omics data. Bioinformatics. 2021. pp. 4091-4099.

[0096] scMVAE: scMVAE model uses three strategies to learn joint latent features for data integration and clustering. scMVAE-Direct connects the original features of each omic, scMVAE-NN integrates low-dimensional features extracted from different omics, and scMVAE-PoE combines multiple expert models to estimate the joint posterior distribution. Proposed by Zuo C, Chen L in Deep-joint-learning analysis model of single cell transcriptome and open chromatin accessibility data. Briefings in Bioinformatics. 2021. Pp. 1-13.

[0097] JSNMF: Semi-orthogonal non-negative matrix factorization of different omics data into different latent spaces and learn consistent information of multi-omics data through consensus. Proposed by Ma Y, Sun Z, Zeng P in JSNMF enables effective and accurate integrative analysis of single-cell multi-omics data. Briefings In Bioinformatics. 2022. pp.1-13.

[0098] scMVP: A single-cell multi-view profiler that automatically learns a common latent representation of scRNA-seq and scATAC-seq data by utilizing a multi-view variational autoencoder model (VAE) with cluster consistency constraints; proposed by Li G, Fu S, Wang S in the paper A deep generative model for multi-view profiling of single-cell RNA-seq and ATAC-seq data, Genome biology. 2022. pp.1-23.

[0099] EOMSC-CA: An efficient one-pass multi-view subspace clustering with consensus anchors method that learns consistent information for clustering by utilizing information from different views; proposed by Liu S, Wang S, Zhang P in the paper Efficient one-pass multi-view subspace clustering with consensus anchors, Proceedings of the AAAI Conference on Artificial Intelligence. 2022. pp.7576-7584.

[0100] scMCs: A single-cell multi-omics data integration and multiple clusterings framework that models the distribution of common and specific features of single-cell transcriptomic and epigenetic data; proposed by Ren L, Wang J, Li Z in the paper scMCs: a framework for single-cell multi-omics data integration and multiple clusterings, Bioinformatics. 2023. pp. 1-7.

[0101] scICML: Information-theoretic co-clustering-based multi-view learning for the integrative analysis of single-cell multi-omics data. Zeng P C, Lin Z X. IEEE-ACM transactions on computational biology and bioinformatics. 2023. pp. 1-10.

[0102] The comparative experimental results of CellMix, PBMC-3k, Mouse-skin, and BMMC datasets are shown in Tables 2-5. “-” indicates that the algorithm faces a memory shortage problem, underlined indicates a suboptimal result, and bold indicates the optimal result.

[0103] Table 2 Comparative experiments on the CellMix dataset

[0104]

[0105] Table 3 Comparative experiments on the PBMC-3k dataset

[0106]

[0107] Table 4 Comparative experiments on the Mouse-skin dataset

[0108]

[0109] Table 5 Comparative experiments on the BMMC dataset

[0110]

[0111] Compared with other algorithms, the integration performance of the present application on single-cell multi-omics dataset is the best, and the learned graph representation is significantly better than other methods. On small and medium-sized datasets, compared with the suboptimal method scMCs, scAGCI improves the ACC, NMI, F1-score, Precision, Recall, ARI and SC indicators by 1.34%, 4.02%, 1.83%, 2.32%, 1.35%, 1.31% and 5.99% respectively; on the PBMC-3k dataset, compared with the suboptimal method scMVAE-NN, the ACC, NMI, F1-score, Precision, Recall, ARI and SC are improved by 5.77%, 8.49%, 2.59%, 4.01%, 1.23%, 2.42% and 0.45% respectively.

[0112] On large datasets, the advantages of the present application are still obvious. For example, on the Mouse-skin dataset, compared with the suboptimal method scMVAE-POE, the present application improves the ACC, NMI, F1-score, Precision, Recall and ARI by 1.68%, 0.89%, 2.18%, 2.02%, 2.37%, 2.67% and 36.72% respectively; on the large dataset BMMC containing more than 100,000 single cells, compared with the suboptimal method scMVAE, the ACC, NMI, F1-score, Precision, Recall and ARI are improved by 2.78%, 0.15%, 1.63%, 0.91%, 2.30%, 6.60% and 2.03% respectively. The excellent performance of the present application is mainly due to its effective extraction and full fusion of specific omics information and high-order shared information. In contrast, scMCs also considers shared and specific information, but ignores high-order shared information; other methods focus more on the extraction and use of single-omics information.

[0113] In addition, the application effectively alleviates the sparsity problem. Taking the CellMix dataset as an example, the ARI of the scAI and UnionCom based on matrix decomposition is 0.5450 and 0.6420 respectively. The scMVAE and scMCs methods using the ZINB decoder to reconstruct the data obtain an ARI value higher than 0.8, while the ARI of the application reaches 0.9522; the lower ARI indicates that these methods perform poorly in solving the sparsity of the single-cell dataset; the application achieves better sparsity alleviation effect through the multi-view subspace anchor point collaborative optimization method, further improving the clustering distinguishability of the integrated embedding; significant effects are also observed on the PBMC, Mouse-skin and BMMC datasets. Compared with ACC and NMI, ARI measures the consistency of the distribution of the original data and the distribution of the data after being processed by the algorithm, and F1 comprehensively considers the precision and recall rate, which can better reflect the clustering effect.

[0114] The application considers three types of single-cell multi-omics information. The first is the structural information, i.e., the connection between cells, which is often taken in previous work. The second problem is the feature information of each omics, for example, the gene features in scRNA-seq data and the peak features in scATAC-seq data. The last one is the high-order information they share, such as the relationship between genes and peaks, which is rarely seen in existing research but is of great significance to the integration of single-cell multi-omics. Compared with only one piece of information, this combined information more fully represents the single-cell multi-omics; they are used to construct the specific graph of each omics and the shared high-order graph; in order to optimize the specific representation and shared representation of single-cell multi-omics, the application designs a graph convolution network and an anchor point learning collaborative optimization strategy, which optimizes the anchor points of each and shared omics and their anchor graphs through a unified and bidirectional cycle; it effectively reduces the sparsity of omics data. The application has excellent performance on the single-cell multi-omics integration task.

[0115] From the above examples, it can be seen that the application has excellent performance in single-cell multi-omics integration, and further illustrates that the application effectively extracts the specific information and shared information of single-cell multi-omics by utilizing the multi-omics characteristics and considering the rich data information in multi-omics data, and effectively solves the technical difficulties in the process of practical application in the field.

[0116] The embodiments of the application are described above in combination with the drawings, but the application is not limited to the above specific embodiments, the above specific embodiments are only illustrative, not limiting, and those skilled in the art can make many forms under the inspiration of the application without departing from the purpose of the application and the scope protected by the claims, which are all within the protection of the application.

Claims

1. A single-cell multi-omics integration method based on anchor point selection and graph learning collaborative optimization, characterized in that, The method comprises the following steps: Step one: Obtain scRNA-seq data from single-cell multi-omics dataset , scATAC-seq data and its feature concatenation data as multi-view data; Step two: Use K-means method to generate one cluster center from each view as initialization anchor points; Step three: Constructing the omics anchor graph using the initialized anchor points from step two and and computing its corresponding anchor graph representation based on the anchor graph subspace clustering and The method is specifically as follows: Anchors for defining scRNA-seq specific omics Anchors for scATAC-seq specific omics Anchors for scRNA-seq and scATAC-seq specific omics Anchors for scRNA-seq and scATAC-seq specific omics : where , and are the specific anchor matrices of and , is a column vector of all ones, ensuring that and each column of and adds up to 1, is the Frobenius norm; Step four: design a graph convolutional network and anchor learning collaborative optimization strategy to update the anchor graph of specific omics and the corresponding anchor graph representation adaptively and ; Step five: To make the information of omics fully integrated, get the shared information between views, define anchor projection matrix To align the shared anchors Feature dimension of original omics data of views According to the initialized anchor, get the shared anchor graph representation using shared anchor graph subspace clustering wherein, is the number of input views, is a weight coefficient balancing the influence between views, is a column vector formed, is a shared anchor point between views, is a shared anchor graph representation between anchors and omics, forming a shared anchor graph ; Step six: design a graph convolutional network and anchor learning collaborative optimization strategy to update the shared anchor graph and shared anchor graph representation adaptively ; Step seven: design a hierarchical graph attention network for shared anchor graph to learn high-order shared representation of genes and peaks in shared anchor graph features ; Step eight: integrate with a common fusion completion operator and high-order sharing representations to enrich the specific omics; wherein, denotes the Hadamard operator, and is the completed specific graph representation, and finally : wherein, is and a weight distribution between the outputs of the specific graph representations , , and using a K-means method to cluster .

2. The method of claim 1, wherein, The strategy of step four cooperatively optimizes the specific omics anchor graph and the corresponding anchor graph representation by adaptively updating the specific omics anchor graph and The strategy deeply mines the hidden features of omics information through the graph convolution network, and combines with anchor learning to achieve adaptive updating of the specific omics anchor graph and the corresponding anchor graph representation and The cooperative optimization mechanism dynamically adjusts the anchor graph structure and representation to capture the inherent correlation of omics data, and the calculation is as follows: Step bl: Learning scRNA-seq graph hidden layer representations using a graph convolutional network , preserving the specificity information of the omics; wherein, , is an adjacency matrix of the scRNA-seq graph, is an identity matrix, in this way, the graph convolution can capture the specificity of each omics view and preserve its important information in the graph; Step b2: Similarly, a graph convolutional network is used to learn the scATAC-seq graph hidden layer representation ; Step b3: updating the corresponding anchor graph representation with the graph hidden layer representation obtained with the graph convolutional network and : Step b4: Update variables using the method of control variables in the anchor graph subspace ， Optimizing; wherein is the trace of the matrix; Step b5: repeating steps b1 to b4 until convergence.

3. The method of claim 1, wherein, The strategy of collaborative optimization of the design graph convolutional network and anchor learning adaptively updates the shared anchor graph and the shared anchor graph representation in step six Unlike step four, the strategy extracts specific information of each omics data respectively by using a graph convolutional network, introduces a balance weight coefficient for coordinating information interaction between different views, organically fuses these information, dynamically adjusts the contribution degree of each omics data, and ensures the shared anchor graph and its representation The calculation is as follows: Step cl: Learning feature graph hidden layer representations using a graph convolutional network ; wherein , is an adjacency matrix of the feature stitching map, is an identity matrix; Step c2: updating the shared anchor graph representation with the graph hidden layer representation obtained with the graph convolutional network ; Step c3: update the variables , , and using the method of control variables, respectively; step c4: repeat steps cl to c3 until convergence.

4. The method of claim 1, wherein, In step seven, a hierarchical graph attention network is designed for the shared anchor graph to learn high-order shared representations of genes and peaks in the shared anchor graph features . Specifically, the network models the features of genes and peaks from different levels through a multi-layer attention mechanism, reveals the deep relationship between them, and deeply mines the interaction patterns between genes and peaks and captures their high-order correlations in the learning process of high-order shared representations . The specific implementation process is as follows: Step d1 : Graph attention layer input shared node feature set of graph , the first k layer output is , wherein are the input and output node embeddings, respectively, is the node embedding dimension of the input and output, and the normalized input node embedding and output node embedding can be represented as: Step d2: Compute weight for each neighbor node by the first Shared weight of the layer Apply to each node, the attention coefficient is as follows: wherein, is the k Layer vertex pair of importance, denotes a relevance measure function, for the sake of comparing the weight coefficients between different vertices in the neighborhood, the function is used to normalize: ​ The vertices and the vertices Transformed features are spliced to obtain a feature vector, which is then input into a feedforward neural network and activated by a LeakyReLU function, and the weight coefficient of the last is ; is a normalized parameter matrix of the relevance measure function, is a neighborhood of a node in the graph, is a series operation resulting in a representation of a node ; ​ Step d3: In order to enhance the expression ability and stability of the model, the multi-head attention mechanism is used, and the nodes under the multi-head attention are averaged again representations ; wherein, is the number of multi-head attention heads, the representation of each node is calculated, and the high-order shared representation of genes and peaks in the final shared anchor map feature can be obtained .

5. The method of claim 1, wherein, Step eight, the common fusion completion operator is used to integrate and high-order shared representation The common fusion completion operator fuses three types of single-cell multi-omics information, the first is the structural information, i.e., the connection between cells; the second is the feature information of each omics, the gene features in scRNA-seq data and the peak features in scATAC-seq data; the last is the high-order information they share, the relationship between genes and peaks, the common fusion completion operator fuses the high-order shared representation of genes and peaks in the shared anchor graph features learned by the hierarchical graph attention network in step seven , the specific omics representation obtained in step four and , respectively, to complete the information of the two omics, obtaining , and finally design the parameter to organically integrate .

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