A method for constructing a clustering framework for single-cell multi-omics data

Abstract

The present invention belongs to the field of bioinformatics technology, and in particular relates to a method for constructing a single-cell multi-omics data clustering framework. The framework in the present invention makes full use of the correlation between cells, and further strengthens the feature interaction between different omics data of the same cell to achieve efficient clustering of multi-omics data. In order to make full use of the topological information between cells, the present invention designs a graph autoencoder and a feature information enhancement module under different omics to achieve the extraction and information enhancement of cell features. At the same time, the contrastive learning technology is introduced to strengthen the interaction between different omics features of the same cell, and finally the single-cell multi-omics clustering is achieved through the multi-omics deep collaborative clustering module.

Description

Technical Field

[0001] The present invention belongs to the technical field of bioinformatics, and in particular relates to a method for constructing a single-cell multi-omics data clustering framework. Background Art

[0002] Single-cell multi-omics clustering integrates multiple omics data to analyze cellular heterogeneity, which is crucial for revealing complex biological processes and disease mechanisms. However, existing single-cell multi-omics clustering methods often neglect the full utilization of intercellular relationships and the interactions and synergies between different omics features, resulting in poor clustering results.

[0003] With the rapid development of single-cell sequencing technologies, massive amounts of single-cell sequencing data have provided valuable opportunities to study cellular heterogeneity and the mechanisms of complex diseases at the molecular level. Specifically, single-cell RNA sequencing (scRNA-seq) quantifies the mRNA abundance of genes in each cell, single-cell transposase-accessible chromatin sequencing (scATAC) characterizes the accessibility of cis-regulatory elements in nearby genes, and single-cell ADT assays (scADTs) quantify the abundance of cell-surface proteins. Joint analysis of single-cell multi-omics data, including scRNA-seq, scATAC, and scADTs, can enhance key genetic information from different omics and decipher gene regulatory relationships associated with cellular heterogeneity. However, because single-cell sequencing data are typically unlabeled, clustering analysis of single cells is crucial for a variety of downstream tasks, including studying cell differentiation, reconstructing developmental trajectories, discovering disease cell subpopulations, and identifying pathogenic factors.

[0004] Since single-cell multi-omics data can reflect the state information of cells from different angles, joint analysis of single-cell multi-omics data can utilize the consistency and complementary information provided by multi-omics data to improve clustering performance. Therefore, a large number of clustering methods based on single-cell multi-omics data have been proposed. For example, a jumping aggregation architecture ScEMC uses transform to fuse scRAN data with scATAC data, and performs single-cell multi-omics clustering based on the ZINB model. Although considerable progress has been made in single-cell multi-omics clustering, the above methods mainly focus on learning cell representations from the original feature space of multi-omics data, without explicitly representing the relationship between cells. Therefore, the learned representation may not be conducive to effective cell clustering.

[0005] Complex topological relationships between cells reveal intercellular interactions, providing rich contextual information for accurately identifying similar populations and thus being of great significance for cell clustering. To exploit neighborhood relationships between cells and integrate attribute information with neighborhood information for cell representation learning, numerous graph-based clustering methods have been proposed to cluster multi-omics data. For example, a cross-view multi-omics information aggregation framework, scMFC, employs random walk techniques to capture high-order topological relationships on cell graphs and designs a cross-view information aggregation mechanism to integrate single-cell multi-omics data for single-cell clustering. These studies demonstrate the benefits of considering cell neighborhood information when clustering single-cell multi-omics data. However, most studies simply combine cell topology information with attributes, potentially resulting in insufficient information integration. Furthermore, when integrating single-cell multi-omics data, existing methods fail to fully consider the interactions between features extracted from different omics, failing to effectively utilize complementary information from different omics, resulting in poor cell clustering results. Summary of the Invention

[0006] The present invention proposes a method for constructing a single-cell multi-omics data clustering framework, which solves the problem in the existing technology that the interaction of different omics extraction features cannot be fully considered and the complementary information of different omics cannot be well utilized, resulting in poor cell clustering effect.

[0007] The technical solution of the present invention is achieved as follows:

[0008] A method for constructing a single-cell multi-omics data clustering framework, named scMDCL, is described as follows:

[0009] (1) Cell graph construction and feature extraction based on graph autoencoders: We constructed a cell similarity network under each omics, and designed a cell omics feature extraction module based on graph autoencoders. By utilizing the correlation between cells, we can extract cell-specific features under different omics.

[0010] (2) Feature information enhancement module using neighborhood message passing: Based on the feature information enhancement module of neighborhood message passing, the topological structure of the cell similarity network is integrated with the extracted cell features to further enhance the cell embedding information obtained by the graph autoencoder and enrich the cell feature information in the network;

[0011] (3) Omic feature interaction based on contrastive learning: A multi-omic feature interaction module based on contrastive learning was designed. By using contrastive learning technology, the similarities and differences of cell features obtained from different omics perspectives were compared to achieve information interaction of different omics features.

[0012] (4) Multi-omics deep collaborative supervision of cell clustering: A multi-omics deep collaborative supervision clustering strategy is proposed to enhance the information interaction between different omics, thereby producing better clustering results.

[0013] Optionally, in cell graph construction and feature extraction based on graph autoencoder, first input cell omics features , where N is the number of samples, The cells are The number of features under omics, for any two cells ,calculate and The Euclidean distance between:

[0014] ;

[0015] Then, a K-NN neighbor cell graph is constructed according to the K nearest neighbor algorithm to represent the similarity between cells. The adjacency matrix It can be expressed as:

[0016] ;

[0017] in, Represents cells The first K nearest neighbor nodes, K is an adjustable hyperparameter; after obtaining the adjacency matrix Finally, in order to better utilize the inter-cell correlation information, for the v-th genome data, a graph autoencoder is used to extract the potential representation of the cell from the constructed cell graph;

[0018] The feature representation learned by the graph encoder can be defined as:

[0019] ;

[0020] in, represents the cell embedding representation learned by the mth layer of the graph autoencoder under the vth omics, and d represents the embedding dimension of the graph autoencoder; The adjacency matrix The normalized adjacency matrix is ​​defined as ; Here D is the adjacency matrix The degree matrix of , It is an N*N identity matrix, indicating that each node has a self-loop structure; represents the learnable weight matrix of the mth layer of the encoder under omics v; The function represents the Tanh activation function.

[0021] Optionally, in the feature information enhancement module using neighborhood message passing, the local structure within the data is considered to embed different omics Make enhancements;

[0022] ;

[0023] in, Indicates the autoencoder embedding in different omics v Feature embedding after information enhancement using local structure domain message passing mechanism;

[0024] In the information enhancement feature After that, the representation learned by the h-th layer of the graph autoencoder-decoder can be defined as:

[0025] ;

[0026] in, is the decoder function of the graph autoencoder, It is still the normalized adjacency matrix. is the output embedding of the decoder layer h-1 in the graph autoencoder, where , Represented as the reconstructed feature matrix of the encoder's final output; represents the learnable weight matrix of the hth layer of the decoder under omics v;

[0027] In order to minimize the reconstruction loss function on the weighted attribute matrix and the adjacency matrix, the graph autoencoder adopts a minimized hybrid loss function. The graph autoencoder loss is expressed as:

[0028] ;

[0029] in, and They represent the autoencoder feature reconstruction and graph reconstruction losses under different omics. is a predefined hyperparameter;

[0030] Feature reconstruction loss under different omics and graph reconstruction loss It can be defined as:

[0031] ;

[0032] ;

[0033] It represents the reconstructed weighted feature matrix. is the reconstructed adjacency matrix generated by the inner product of multiple layers of representation in the graph autoencoder.

[0034] Optionally, in the interaction of omics features based on contrastive learning, feature embeddings under different omics conditions are obtained by graph autoencoders. , the scRNA-omics feature representation is represented as an anchor point as Z, where there are N samples, and To represent the index of each sample, the contrast loss is formed It can be expressed as:

[0035] ;

[0036] in, represents the fth sample in Z, Other omics data corresponding to the same sample, represented as sample f, are considered as sample Positive samples of Represents the set of all other sample indexes of non-target node f under other omics, which are considered as samples Negative samples of Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, Represents a vector With vector The inner (dot) product of .

[0037] Alternatively, in multi-omics deep collaborative supervision of cell clustering, Student's t distribution is used as the kernel to measure the similarity between cells and the initial cluster center, and its soft assignment matrix is The definition is as follows:

[0038] ;

[0039] in, Indicates that it is in v Cells under Omics i The embedding representation of represents the b-th cluster center under omics v, Represents all cluster centers, B is the number of cluster centers, It can be interpreted as the probability of assigning the i-th cell in the v-th group to the b-th cluster;

[0040] After obtaining the soft assignment matrix After that, we can use the soft allocation matrix The matching target gets the target assignment , to enhance the confidence of cluster assignment, specifically defined as follows:

[0041] ;

[0042] in, is the soft clustering frequency of soft clustering;

[0043] At the same time, the embedding of each cell under different omics based on the graph autoencoder was calculated The distribution of soft allocation ; Then, using the enhanced confidence target distribution To guide the update of these two soft assignment distributions, the multi-clustering loss is defined as follows:

[0044] ;

[0045] The multi-co-supervised clustering loss is defined as follows:

[0046] ;

[0047] in, represents the target distribution in the reference group. The soft-assigned labels of the two omics are averaged to obtain the final clustering result, which is defined as follows:

[0048] ;

[0049] in, represents the predicted cluster label of the i-th cell;

[0050] The overall loss can be defined as follows:

[0051] ;

[0052] in, There are two hyperparameters used to control the loss of different parts. is the feature interaction contrast loss, Feature reconstruction and graph reconstruction losses of graph autoencoders under different omics.

[0053] After adopting the above technical solution, the beneficial effects of the present invention are:

[0054] This paper proposes a method for constructing a single-cell multi-omics data clustering framework, scMDCL, which fully utilizes the correlation between cells and further strengthens the feature interaction between different omics data of the same cell to achieve efficient clustering of multi-omics data. To fully utilize the topological information between cells, the present invention designs a graph autoencoder and feature information enhancement module under different omics to extract and enhance the cell features. At the same time, contrastive learning technology is introduced to strengthen the interaction between different omics features of the same cell. Finally, single-cell multi-omics clustering is achieved through a multi-omics deep collaborative clustering module.

[0055] The technical solutions in the present invention are mainly used in the field of precision medicine, especially in the analysis of single-cell multi-omics data in oncology and genomics research. In the field of precision medicine, especially in tumor research, gene expression and phenotypic differences at the single-cell level are crucial for understanding the occurrence and development of tumors and their microenvironment. However, due to the complexity and heterogeneity of different omics data, how to effectively integrate and analyze a variety of omics information has become the key to solving problems such as tumor heterogeneity and treatment response. The present invention uses deep collaborative comparative learning technology to accurately process and fuse data from different omics, thereby improving the accuracy and effectiveness of single-cell multi-omics data clustering. This technical solution can not only improve the understanding of tumor cell heterogeneity, but also provide more accurate cell population division and feature identification for the formulation of personalized treatment plans. It has important application value and can effectively promote the development of precision medicine and disease diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 is the scMDCL flow chart;

[0058] Figure 2 is the running time cost of various single-cell clustering methods on eight real datasets with different cell numbers. DETAILED DESCRIPTION

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0060] The present application discloses a method for constructing a single-cell multi-omics data clustering framework. Example

[0061] according to Figure 1-Figure 2 As shown in Figure 2, a method for constructing a single-cell multi-omics data clustering framework is shown in Figure 2. The specific content is as follows:

[0062] 1. Introduction

[0063] 1.1 Overview of scMDCL

[0064] This paper proposes a method for constructing a single-cell multi-omics data clustering framework, named scMDCL. The overall process is as follows: Figure 1 As shown. In order to make full use of the correlation between cells and further strengthen the feature interaction between different omics data of the same cell, scMDL designed modules such as omics feature extraction based on graph autoencoder, omics feature interaction based on comparative learning, and multi-omics deep collaborative clustering. Its framework mainly includes the following four steps: the first step, cell graph construction and feature extraction based on graph autoencoder; the second step, feature information enhancement module using neighborhood message passing; the third step, omics feature interaction based on comparative learning; the fourth step, cell clustering under multi-omics deep collaborative supervision. Specifically, in step one, the present invention constructs a cell similarity network under each omics (including scRNA, scATAC / ADT), and designs a cell omics feature extraction module based on graph autoencoder, making full use of the correlation between cells to realize the extraction of cell-specific features under different omics; in step two, the feature information enhancement module based on neighborhood message passing fuses the topological structure of the cell similarity network with the extracted cell features, aiming to further enhance the cell embedding information obtained by the graph autoencoder and enrich the cell feature information in the network. In step three, to further enhance the information interaction between cell features under different omics, the present invention designed a multi-omics feature interaction module based on contrastive learning. This technology compares the similarities and differences of cell features obtained from different omics perspectives, thus achieving information interaction between different omics features. Finally, the present invention proposes a multi-omics deep collaborative supervised clustering strategy to enhance information interaction between different omics, thereby producing better clustering results.

[0065] 1.2 Cell Graph Construction and Feature Extraction Based on Graph Autoencoder

[0066] For each genomic data, in addition to the original cell feature matrix, the present invention also constructs a cell graph to capture the neighborhood relationship between cells, which helps to explore the similarity between cells. For each cell, first find the K cells that are most similar to its neighbors based on the Euclidean distance, and then connect them with the neighbors. Specifically, first input the cell omics feature , where N is the number of samples, The cells are The number of features under omics. For any two cells ,calculate and The Euclidean distance between:

[0067] ; (1)

[0068] Then, a K-NN neighbor cell graph is constructed according to the K nearest neighbor algorithm to represent the similarity between cells. The adjacency matrix It can be expressed as:

[0069] ; (2)

[0070] in, Represents cells The first K nearest neighbor nodes, K is an adjustable hyperparameter. Finally, to better utilize the inter-cell association information, for the vth genome data, a graph autoencoder (GAE) is used to extract the latent representation of the cell from the constructed cell graph. GAE is an unsupervised feature extraction method that can effectively utilize the cell graph structure and extract node information. It uses a symmetric structure and simultaneously reconstructs the weighted feature matrix and adjacency matrix. Specifically, the feature representation learned by the graph encoder can be defined as:

[0071] ; (3)

[0072] in, represents the cell embedding representation learned by the mth layer of the graph autoencoder under the vth omics, and d represents the embedding dimension of the graph autoencoder; The adjacency matrix The normalized adjacency matrix is ​​defined as ; Here D is the adjacency matrix The degree matrix of , It is an N*N identity matrix, indicating that each node has a self-loop structure; represents the learnable weight matrix of the mth layer of the encoder under omics v; The function represents the Tanh activation function.

[0073] 1.3 Feature Information Enhancement Module Using Neighborhood Message Passing

[0074] After obtaining the feature embeddings of different omics obtained by the graph autoencoder, in order to further mine the local results within the data and enhance the information of the features extracted by the graph autoencoder, the present invention uses a graph convolution-like operation (i.e., message passing operation) to process the combined information. The message propagation mechanism of the graph can make good use of the local topological structure of the graph and enhance the information of different nodes. By using cell embedding By propagating messages on the cell graph, we can not only use the local topological structure of the cell graph to enhance the information interaction of adjacent cell embeddings, but also enable the graph encoder to retain the association of the original data to a certain extent, and enhance the feature information encoded by the graph autoencoder. Specifically, the present invention considers the local structure within the data and embeds different omics To enhance:

[0075] ; (4)

[0076] in, Indicates the autoencoder embedding in different omics v Feature embedding after information enhancement using local structure domain message passing mechanism.

[0077] In the information enhancement feature After that, the present invention can reconstruct the weighted feature matrix and adjacency matrix by introducing the following decoder part. The representation learned by the hth layer of the graph autoencoder decoder can be defined as:

[0078] ; (5)

[0079] in, is the decoder function of the graph autoencoder, It is still the normalized adjacency matrix. is the output embedding of the decoder layer h-1 in the graph autoencoder, where , Represented as the reconstructed feature matrix of the encoder's final output; Represents the learnable weight matrix of the hth layer of the decoder under omics v. In order to minimize the reconstruction loss function on the weighted attribute matrix and the adjacency matrix, the graph autoencoder adopts the minimization of the hybrid loss function. The graph autoencoder loss is expressed as:

[0080] ; (6)

[0081] in, and They represent the autoencoder feature reconstruction and graph reconstruction losses under different omics. It is a predefined hyperparameter used to balance the weights of the two reconstruction loss functions. Specifically, the feature reconstruction loss under different omics and graph reconstruction loss It can be defined as:

[0082] ; (7)

[0083] ; (8)

[0084] In formula (7), represents the weighted feature matrix for reconstruction. In formula (8), is the reconstructed adjacency matrix generated by the inner product of the multi-layer representation in the graph autoencoder. Formula (7) uses the reconstruction loss minimized on the weighted feature matrix, which helps to mine structure-based attribute information and improve the generalization ability of the framework. In this way, the latent representation can inherit more attributes from the feature space of the cell graph, which helps to retain representative features for better clustering.

[0085] Through the feature information enhancement module based on the graph autoencoder feature extraction module and the module neighborhood message passing, the local and global structures between cells can be considered, and the relationship between cells can be fully utilized to enhance the intra-class closeness.

[0086] 1.4 Omics feature interaction based on contrastive learning

[0087] Strengthening the interaction between different omics data features from the same cell helps fully utilize the complementary information from different omics, providing valuable insights for the overall understanding of biological systems. The resurgence of contrastive learning research has led to significant progress in self-supervised representation learning. This approach effectively leverages the mutual information between different data views to maximize the construction of a contrastive loss that connects features from different views. This contrast is formed between similar and dissimilar pairs, aiming to bring similar samples closer together and separate dissimilar samples.

[0088] The present invention uses a contrastive learning strategy to integrate different omics data, ensuring that the feature embeddings of the same cell under different omics are as similar as possible, while the feature embeddings of different cells under different omics are separated from each other. The present invention uses a self-supervised contrastive loss to maximize the mutual information between the anchor omics cell features and other omics features of the same cell. This loss is applied to different cell feature embeddings in two views during training to enhance the interaction between different omics features.

[0089] Specifically, in order to obtain the feature embeddings under different omics obtained by the graph autoencoder , the present invention uses the scRNA-omics feature representation as an anchor point represented by Z, where there are N samples, and To represent the index of each sample. Then the contrast loss is formed It can be expressed as:

[0090] ; (9)

[0091] in, represents the fth sample in Z, Other omics data corresponding to the same sample, represented as sample f, are considered as sample Positive samples of Represents the set of all other sample indexes of non-target node f under other omics, which are considered as samples Negative samples of Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, Represents a vector With vector Contrastive learning is used to encourage scMDCL to maximize the similarity between different omics representations of the same source cells while reducing the correlation between different omics of different cells. This strengthens the interaction between omics features, fully utilizes the complementary information between different omics, and better extracts features.

[0092] 1.5 Cell clustering with multi-omics deep collaborative supervision

[0093] In order to combine the representation learning of different omics for clustering and strengthen the joint collaboration of different omics, the present invention designs a multi-cooperative supervised clustering strategy. Specifically, the present invention extracts the features of different omics data through graph autoencoders and uses information enhancement, contrastive learning and other modules to obtain representations. Finally, the present invention uses a method similar to DEC and uses Student's t distribution as the kernel to measure the similarity between cells and the initial cluster center. Its soft assignment matrix The definitions are as follows:

[0094] ; (10)

[0095] in, Indicates that it is in v Cells under Omics i The embedding representation of represents the b-th cluster center under omics v, Represents all cluster centers, and B is the number of cluster centers. It can be interpreted as the probability of assigning the i-th cell in the v-th group to the b-th cluster.

[0096] After obtaining the soft assignment matrix After that, we can use the soft allocation matrix The matching target gets the target assignment , to enhance the confidence of cluster assignment, specifically defined as follows:

[0097] ; (11)

[0098] in, is the soft clustering frequency of soft clustering.

[0099] At the same time, the embedding of each cell under different omics based on the graph autoencoder is calculated according to formula (10) The distribution of soft allocation Then, the enhanced confidence target distribution obtained based on formula (11) is used To guide the update of these two soft assignment distributions. The multi-clustering loss is defined as follows:

[0100] ; (12)

[0101] Multi-omics data provide characterization of cell states from different perspectives. However, optimizing the multi-clustering loss The cluster assignment is only learned from each omics separately, ignoring the consistency and complementary information between different omics. In order to take advantage of the consistency and complementary information inherent in multiple omics data, the present invention adopts a method of collaborative training of different omics, rather than simply using the target distribution to guide the soft assignment distribution in the same omics data. Specifically, during the framework training process, each omics data is used as a reference omics in turn to guide the clustering process of all omics data. When a group data is selected as a reference group, the Represents its target distribution, which is used to guide the update of the soft distribution of all groups. In this way, accurately predicted cells in the reference group may correct incorrectly predicted cells in other groups. At the same time, there may also be some incorrectly predicted cells in the reference group, which may mislead other groups. Therefore, the present invention alternates the reference group during training to allow multiple groups to supervise each other. The multi-co-supervised clustering loss is defined as follows:

[0102] ; (13)

[0103] in, Represents the target distribution in the reference group. The final clustering result can be obtained by averaging the soft-assigned labels of the two omics, which is defined as follows:

[0104] ; (14)

[0105] in, represents the predicted cluster label for the i-th cell. This multi-collaborative supervised clustering strategy promotes the mutual optimization between representation learning and clustering, making representation learning more suitable for clustering tasks. Furthermore, through information interaction, the intrinsic differences between cells are explored from a multi-omics perspective, further enhancing the clustering effect.

[0106] In summary, the overall loss of the scMDCL framework can be defined as follows:

[0107] ; (15)

[0108] in, There are two hyperparameters used to control the loss of different parts. is the feature interaction contrast loss, Feature reconstruction and graph reconstruction losses of graph autoencoders under different omics.

[0109] 2. Verification

[0110] 2.1 Data

[0111] To validate the effectiveness of our framework, we collected eight real-world single-cell multi-omics datasets from different data platforms. These included a human peripheral blood mononuclear cell (PBMC) dataset; adult mouse cerebral cortex data (GSE12607 (Chen-2019) downloaded from the GEO database; the mouse CITE-seq splenic lymph node dataset (SLN206); and the mouse tissue dataset Ma-2020. For the SLN206 dataset, we collected two batches of cell data, named CITEseq_lymph206-1 and CITEseq_lymph206-2; and for the Ma-2020 dataset, we collected four batches of cell data, named Ma2020-1, Ma-2020-2, Ma-2020-3, and Ma-2020-4.

[0112] The above datasets contain single-cell data from various omics categories. The CITEseq_lymph206-1 and CITEseq_lymph206-2 datasets contain matched scRNA-seq and ADT data, while the other six datasets contain matched scRNA-seq and scA TAC-seq data. Details of these datasets are shown in Table 1.

[0113]

[0114] 2.2 Data Preprocessing

[0115] The present invention first uses the SCANPY pipeline, a tool commonly used to process scRNA-seq data, to preprocess scRNA-seq data. Specifically, the present invention first selects the top 3,000 highly variable genes, then normalizes the data to eliminate the impact of technical variations (such as count depth), and uses logarithmic transformation and scaling to mitigate the impact of extreme values ​​in the data matrix. In addition, the present invention performs principal component analysis (PCA) on the scRNA-seq data separately. For scATAC-seq data, the present invention uses latent semantic indexing (LSI) to preprocess the data to reduce the dimensionality of the original data. For ADT data, due to the low dimensionality of ADT data, the present invention retains all ADT data and only uses preprocessing by performing normalization and scaling.

[0116] 2.3 Comparison methods and evaluation indicators

[0117] This paper compares the scMDCL framework with eight state-of-the-art clustering methods, including a classical clustering method (i.e., K-means), two single-omics clustering methods for clustering scRNA-seq data (scziDesk and scGAE), and five deep learning-based multi-omics clustering methods (DCCA, DEMOC, scMFC, scEMC, and scMIC). Because K-means, scziDesk, and scGAE are designed for clustering single genomes, these algorithms were applied separately to different omics data sets. Multi-omics clustering methods such as DCCA, DEMOC, scMFC, scEMC, and scMIC were applied directly to the multi-omics data sets. Parameters for each algorithm were set according to the respective publications.

[0118] To evaluate the performance of scMDCL, we used four widely used clustering metrics, including the adjusted Rand index (ARI), normalized mutual information (NMI), adjusted mutual information (AMI), and accuracy (ACC). Specifically, ARI measures the similarity between predicted labels and true labels and is defined as follows:

[0119] ; (16)

[0120] Among them, a i and b i denotes the number of cells in the ith true cluster and the ith predicted cluster, n ij represents the number of cells shared by the i-th true cluster and the j-th predicted cluster. Expressed as a binomial coefficient, .

[0121] Let Y = {y1,y2,…,y n} and P={p1, p2,…, p n} represent the true label and predicted label of the cell respectively. NMI is also used to evaluate the consistency between the predicted label and the true label, which is defined as follows:

[0122] ; (17)

[0123] Among them, I(Y,P) represents the mutual information between the true label and the predicted label, H(Y) and H(P) represent the information entropy of the true label and the information entropy of the predicted label, respectively.

[0124] Adjusted Mutual Information (AMI) is an improvement to Normalized Mutual Information (NMI) that aims to eliminate the impact of randomness on clustering evaluation. AMI adjusts the expected mutual information value to make it more robust to clustering randomness. The calculation formula of AMI is as follows:

[0125] ; (18)

[0126] Among them, E[I(Y,P)] represents the expectation of the mutual information between the true label and the predicted label, which is used to adjust the mutual information deviation caused by randomness; max(H(Y),H(P)) represents the maximum value of the true label information entropy and the predicted label information entropy.

[0127] ACC measures the percentage of cells that are correctly predicted, and the specific calculation formula is as follows:

[0128] ; (19)

[0129] in, is an indicator function, when hour, ,otherwise ; It is a Hungarian Algorithm that maps predicted labels to equivalent true labels.

[0130] 3. Results

[0131] To fully compare the performance of the scMDCL framework with other advanced clustering methods, comparative experiments were conducted on eight public datasets. During the framework training process, each method was run 10 times and the average of the evaluation metrics was taken as the experimental results. Extensive experiments on different datasets demonstrated the superior performance of the scMDCL framework. Furthermore, a series of experiments, including framework performance experiments using different omics combinations, framework ablation experiments, parameter analysis experiments, and runtime experiments of different methods, also demonstrated the effectiveness of the scMDCL framework.

[0132] 3.1 Clustering Results

[0133] We compared scMDCL with eight leading clustering methods, with the results shown in Tables 2 and 3. These results clearly demonstrate that scMDCL outperformed all evaluation metrics across the eight single-cell multi-omics datasets, achieving significant improvements over other methods. For example, on the PBMC-10k dataset (Table 2), scMDCL achieved an ARI of 0.8774, a NMI of 0.8780, an AMI of 0.8772, and an ACC of 0.8923, surpassing the runner-up by 2.7%, 1.49%, 1.51%, and 5.05% in ARI, NMI, AMI, and ACC, respectively. On the Ma-2020-1 dataset (Table 3), scMDCL achieved improvements of 11.09%, 2.64%, 2.66%, and 8.09% in ARI, NMI, AMI, and ACC, respectively, over the runner-up.

[0134] Table 2 Performance of different methods on the PBMC-10k dataset

[0135]

[0136] Table 3 Performance of different methods on the Ma-2020-1 dataset

[0137]

[0138] The results in the table also show that due to the more severe noise and missing data in scATAC data, the performance of several single-omics clustering methods on scATAC-seq data is significantly lower than that on scRAN-seq data. For ADT data, single-omics clustering methods exhibit competitive performance, likely due to the fact that protein signatures better approximate the clustering results. Furthermore, compared to other multi-omics clustering methods, scMDCL effectively handles the correlations between different omics data, resulting in superior performance compared to other baseline methods.

[0139] 3.2 Ablation Results

[0140] In order to fully understand the impact of the components of the scMDCL framework on clustering tasks, we further conducted ablation studies on the three important components of the scMDCL framework on eight datasets. Specifically, we ablated the three important components of the scMDCL framework, namely, the feature information enhancement module based on neighborhood propagation (FIRND), the omics information interaction module based on contrastive learning (FeCL), and the soft distribution removal module. The multi-supervisory strategy module (MIGAE) based on

[15] is used to perform the multi-supervisory strategy module (MIGAE) and compared with the proposed method scMDCL. The experimental results are shown in Table 4.

[0141] Through the experimental results, we can observe the following: (1) The classification effect of the results after the ablation of any module is reduced, which effectively proves that all modules play an important role in scMDCL; (2) When the FIRND module is ablated, the experimental effect on most datasets shows a significant decline, which shows that the FIRND module can make full use of the relationship between cells to enhance the closeness within the class. (3) Thanks to the information enhancement module (FIRND) and the contrastive learning feature interaction module (FeCL), the proposed framework produces better results on most datasets, proving the rationality and effectiveness of each component.

[0142] Table 4 Ablation experimental results of different modules of scMDCL

[0143]

[0144] 3.3 Runtime Comparison

[0145] In order to compare the differences in the running time of different methods, the running time of scMDCL and seven other single-cell clustering methods based on deep learning were compared on eight real datasets. Among them, for the single-omics clustering method, the present invention ran it on two omics data respectively and took the average running time on the two omics as its framework running time. The results are shown in Figure 2. Figure 2 shown.

[0146] from Figure 2 As can be seen from the figure, scMDCL's runtime increases approximately linearly with the number of cells. Furthermore, except for some datasets where scMDCL runtime is slightly higher than that of the single-omics clustering method DCCA and the multi-omics clustering method scMIC, scMDCL's runtime cost is significantly lower than that of other single-cell clustering methods. Overall, scMDCL demonstrates efficient runtime while achieving excellent clustering performance.

[0147] In this article, the present invention proposes a method for constructing a single-cell multi-omics data clustering framework, scMDCL. This framework makes full use of the correlation between cells, and further strengthens the feature interaction between different omics data of the same cell, thereby achieving efficient and accurate cell clustering. Specifically, the present invention designs modules such as omics feature extraction based on graph editors, comparative learning omics feature interaction, and multi-omics deep collaborative clustering, so as to strengthen the connection between different omics while fully extracting the cell features of different omics and improve the cell clustering effect. Through extensive experiments on eight public datasets, including human peripheral blood mononuclear cell dataset (PBMC-10k), adult mouse cerebral cortex data (Chen-2019), mouse CITE-seq splenic lymph node dataset (SLN206), and mouse tissue dataset Ma-2020 dataset, scMDCL has good performance compared with the current advanced single-cell clustering methods.

[0148] Furthermore, we conducted experiments on the effectiveness of scMDCL using different omics combinations. These results demonstrate the necessity of integrating diverse omics data to improve cell clustering performance in biomedical applications. Furthermore, extensive experiments, including ablation experiments, hyperparameter experiments, and framework runtime comparisons, demonstrate the superiority and effectiveness of the proposed framework.

[0149] From a theoretical analysis, the reasons why scMDCL has good stability and interpretability are as follows: First, the present invention makes full use of the correlation between cells under different omics, designs a feature extraction module based on graph autoencoders and a feature information enhancement module based on domains, and realizes the effective extraction of cell features. On the other hand, the present invention uses contrastive learning to integrate different omics data of single cells and strengthen the interaction of cell features under different omics, making full use of the complementary information under different omics, and bringing valuable insights to the overall understanding of biological systems. Finally, the present invention designs a multi-cooperative supervised clustering strategy, which explores the intrinsic differences of cells from a multi-omics perspective through the interaction of different omics information, further enhancing the clustering effect.

[0150] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a single-cell multi-omics data clustering framework, characterized in that: The framework is named scMDCL and its contents are as follows: (1) Cell graph construction and feature extraction based on graph autoencoders: We constructed a cell similarity network under each omics, and designed a cell omics feature extraction module based on graph autoencoders. By utilizing the correlation between cells, we can extract cell-specific features under different omics. (2) Feature information enhancement module using neighborhood message passing: Based on the feature information enhancement module of neighborhood message passing, the topological structure of the cell similarity network is integrated with the extracted cell features to further enhance the cell embedding information obtained by the graph autoencoder and enrich the cell feature information in the network; (3) Omic feature interaction based on contrastive learning: A multi-omic feature interaction module based on contrastive learning was designed. By using contrastive learning technology, the similarities and differences of cell features obtained from different omics perspectives were compared to achieve information interaction of different omics features. (4) Multi-omics deep collaborative supervision of cell clustering: A multi-omics deep collaborative supervision clustering strategy is proposed to enhance the information interaction between different omics, thereby producing better clustering results; In multi-omics deep collaborative supervision of cell clustering, Student's t distribution is used as the kernel to measure the similarity between cells and the initial cluster center. Its soft assignment matrix The definition is as follows: ； in, Indicates that it is in v Cells under Omics i The embedding representation of represents the b-th cluster center under omics v, Represents all cluster centers, B is the number of cluster centers, is the probability of assigning the i-th cell in the v-th group to the b-th cluster; After obtaining the soft assignment matrix Then, according to the soft allocation matrix The matching target gets the target assignment , to enhance the confidence of cluster assignment, specifically defined as follows: ； in, is the soft clustering frequency of soft clustering; At the same time, the embedding of each cell under different omics based on the graph autoencoder was calculated The distribution of soft allocation ; Then, using the enhanced confidence target distribution To guide the update of these two soft assignment distributions, the multi-clustering loss is defined as follows: ； The multi-co-supervised clustering loss is defined as follows: ； in, represents the target distribution in the reference group, and the soft-assigned labels of the two omics are averaged to obtain the final clustering result, which is defined as follows: ； in, represents the predicted cluster label of the i-th cell; The overall loss is defined as follows: ； in, There are two hyperparameters used to control the loss of different parts. is the feature interaction contrast loss, Feature reconstruction and graph reconstruction losses of graph autoencoders under different omics.

2. The method for constructing a single-cell multi-omics data clustering framework according to claim 1, characterized in that: In the construction of cell graph and feature extraction based on graph autoencoder, the cell omics features are first input , where N is the number of samples, The cells are The number of features under omics, for any two cells ,calculate and The Euclidean distance between: ； Then, a K-NN neighbor cell graph is constructed according to the K nearest neighbor algorithm to represent the similarity between cells. The adjacency matrix It can be expressed as: ； in, Represents cells The first K nearest neighbor nodes, K is an adjustable hyperparameter; after obtaining the adjacency matrix Finally, in order to better utilize the inter-cell correlation information, for the v-th genome data, a graph autoencoder is used to extract the potential representation of the cell from the constructed cell graph; The feature representation learned by the graph encoder is defined as: ； in, represents the cell embedding representation learned by the mth layer of the graph autoencoder under the vth omics, and d represents the embedding dimension of the graph autoencoder; The adjacency matrix The normalized adjacency matrix is ​​defined as ; Here D is the adjacency matrix The degree matrix of , It is an N*N identity matrix, indicating that each node has a self-loop structure; represents the learnable weight matrix of the mth layer of the encoder under omics v; The function represents the Tanh activation function.

3. The method for constructing a single-cell multi-omics data clustering framework according to claim 2, characterized in that: In the feature information enhancement module using neighborhood message passing, the local structure within the data is considered to embed different omics Make enhancements; ； in, Indicates the autoencoder embedding in different omics v Feature embedding after information enhancement using local structure domain message passing mechanism; In the information enhancement feature After that, the representation learned by the hth layer of the graph autoencoder decoder is defined as: ； in, is the decoder function of the graph autoencoder, It is still the normalized adjacency matrix. is the output embedding of the decoder layer h-1 in the graph autoencoder, where , Represented as the reconstructed feature matrix of the encoder's final output; represents the learnable weight matrix of the hth layer of the decoder under omics v; In order to minimize the reconstruction loss function on the weighted attribute matrix and the adjacency matrix, the graph autoencoder adopts a minimized hybrid loss function. The graph autoencoder loss is expressed as: ； in, and They represent the autoencoder feature reconstruction and graph reconstruction losses under different omics. is a predefined hyperparameter; Feature reconstruction loss under different omics and graph reconstruction loss Defined as: ； ； It represents the reconstructed weighted feature matrix. is the reconstructed adjacency matrix generated by the inner product of multiple layers of representation in the graph autoencoder.

4. The method for constructing a single-cell multi-omics data clustering framework according to claim 3, characterized in that: In the interaction of omics features based on contrastive learning, feature embeddings under different omics conditions are obtained by graph autoencoders. , the scRNA-omics feature representation is represented as an anchor point as Z, where there are N samples, and To represent the index of each sample, the contrast loss is formed Expressed as: ； in, represents the fth sample in Z, Other omics data corresponding to the same sample, represented as sample f, are considered as sample Positive samples of Represents the set of all other sample indexes of non-target node f under other omics, which are considered as samples Negative samples of Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, Represents a vector With vector The inner (dot) product of .

Images