Single-cell multi-omics data clustering framework based on deep collaborative contrast learning

Abstract

The invention belongs to the technical field of bioinformatics, and particularly relates to a single-cell multi-omics data clustering framework based on deep collaborative contrast learning. According to the framework, the association relationship between cells is fully utilized, and meanwhile, the feature interaction of the same cell between different omics data is further enhanced, so that efficient clustering of multiple omics data is realized. In order to make full use of topological information between cells, a graph self-encoder and a feature information enhancement module under different omics are designed, and extraction and information enhancement of cell features are achieved. Meanwhile, a comparative learning technology is introduced to enhance interaction among different omics characteristics of the same cell, and finally single-cell multi-omics clustering is realized through a 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 single-cell multi-omics data clustering framework based on deep collaborative contrastive learning. 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 ignore 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 technology, massive single-cell sequencing data provide us with valuable opportunities to study the mechanisms of cellular heterogeneity and 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 openness of cis-regulatory elements in nearby genes, and single-cell ADT tests (scADTs) quantify the abundance of cell surface proteins. The joint analysis of single-cell multi-omics data such as scRNA-seq, scATAC and scADTs can enhance the key genetic information of different omics and decipher the gene regulatory relationships associated with cellular heterogeneity. However, since single-cell sequencing data are usually unlabeled, clustering analysis of single cells is crucial in a variety of downstream tasks such as studying cell differentiation, reconstructing developmental trajectories, discovering disease cell subpopulations, and determining 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 jump 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 characterizing the relationship between cells. Therefore, the learned representation may not be conducive to effective cell clustering.

[0005] The complex topological relationship between cells reveals the interaction between cells and provides rich contextual information for accurately identifying similar groups, which is of great significance for cell clustering. In order to utilize the neighborhood relationship between cells and integrate attribute information with neighborhood information for cell representation learning, many graph-based clustering methods have been proposed to cluster multi-omics data. For example, a cross-view multi-omics information aggregation framework scMFC uses random walk technology to capture high-order topological relationships on cell graphs, and designs a cross-view information aggregation mechanism to integrate single-cell multi-omics data to achieve single-cell clustering; these studies have demonstrated the benefits of considering cell neighborhood information when clustering single-cell multi-omics data, but most studies simply combine cell topological information with attributes, which may lead to insufficient information integration. On the other hand, when integrating single-cell different omics data, existing methods do not fully consider the interaction of different omics extracted features, and cannot make good use of different omics complementary information, resulting in poor cell clustering effect. Summary of the invention

[0006] The present invention proposes a single-cell multi-omics data clustering framework based on deep collaborative contrastive learning, which solves the problem that the prior art fails to fully consider the interaction of features extracted from different omics and fails to make good use of complementary information from different omics, resulting in poor cell clustering effect.

[0007] The technical solution of the present invention is achieved in this way:

[0008] A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning, the name of the framework is scMDCL, the specific contents are as follows:

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

[0010] (2) Feature information enhancement module using neighborhood message passing: Based on the feature information enhancement module based on neighborhood message passing, the topological structure of the cell similarity network is fused 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. Through contrastive learning technology, the similarities and differences of the features obtained from different omics perspectives of cells were compared to achieve information interaction of different omics features.

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

[0013] Optionally, in the cell graph construction and feature extraction based on the graph autoencoder, the cell omics features are first input Where N is the number of samples, M is v is the number of cell features under v-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 A v Finally, in order to make better use of the inter-cell correlation information, for the vth 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 group learning, and d represents the embedding dimension of the graph autoencoder encoding; The adjacency matrix A v The normalized adjacency matrix is ​​defined as Here D is the adjacency matrix A v The degree matrix of is an N*N identity matrix, indicating that each node has a self-loop structure; W v(m) represents the learnable weight matrix of the mth layer of the encoder under the omics v; the σ(·) function represents the Tanh activation function.

[0021] Optionally, in the feature information enhancement module using neighborhood message passing, the local structure inside 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 hth layer of the graph autoencoder-decoder can be defined as:

[0025]

[0026] Among them, f dec (·) is the decoder function of the graph autoencoder, 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 the 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, respectively. a1 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 obtained by graph autoencoders are obtained. The scRNA-omics feature representation is represented as an anchor point Z, where there are N samples, and f∈F={1,...,N} is used to represent the index of each sample, then the contrast loss L is formed cl It can be expressed as:

[0035]

[0036] Among them, z f represents the fth sample in Z, z p(f) The other omics data corresponding to the same sample represented as sample f are considered as sample z f A(f) = F\{f} represents the index set of all other samples of non-target node f under other omics, which is regarded as sample z f Negative samples of L f Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, z f z p(f) Represents vector z f With vector z p(f) The inner (dot) product of .

[0037] Optionally, in multi-omics deep collaborative supervised 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, represents the embedding representation of cell i under the v-th omics, represents the bth cluster center under omics v, b∧∈[1,...,B] 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 Q v After that, we can use the soft allocation matrix Q v The matching target gets the target assignment To enhance the confidence of cluster assignment, the specific definition is 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 P v 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] Among them, c i Represents the predicted cluster label of the i-th cell;

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

[0051]

[0052] Among them, α1 and α2 are two hyperparameters used to control the losses of different parts, L cl 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] The present invention proposes a single-cell multi-omics data clustering framework scMDCL based on deep collaborative contrastive learning, which 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 extract and enhance the characteristics of cells. At the same time, contrastive learning technology is introduced to strengthen the interaction between different omics features of the same cell, and 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 to 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 can accurately process and fuse data from different omics through deep collaborative comparative learning technology, and improve 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative labor.

[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 numbers of cells. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0060] The embodiments of the present application disclose a single-cell multi-omics data clustering framework based on deep collaborative contrastive learning.

[0061] Example

[0062] according to Figure 1-Figure 2 As shown in the figure, a single-cell multi-omics data clustering framework based on deep collaborative contrastive learning is presented. The specific contents are as follows:

[0063] 1. Introduction

[0064] 1.1 Overview of scMDCL

[0065] This paper proposes a single-cell multi-omics data clustering framework based on deep collaborative contrastive learning, 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 of the same cell between different omics data, scMDL designs modules such as omics feature extraction based on graph autoencoder, comparative learning omics feature interaction, 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, multi-omics deep collaborative supervised cell clustering. 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, in order to further enhance the information interaction of cell features under different omics, the present invention designs a multi-omics feature interaction module based on contrastive learning. Through contrastive learning technology, the similarities and differences of the features obtained by cells under different omics perspectives are compared to achieve information interaction of different omics features. Finally, the present invention proposes a multi-omics deep collaborative supervised clustering strategy to enhance the information interaction between different omics, thereby producing better clustering results.

[0066] 1.2 Cell Graph Construction and Feature Extraction Based on Graph Autoencoder

[0067] 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, M is v is the number of features of the cell under v-omics. For any two cells calculate and The Euclidean distance between:

[0068]

[0069] 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:

[0070]

[0071] in, Represents cells The first K nearest neighbor nodes, K is an adjustable hyperparameter. v Finally, in order to make better use of the inter-cell association information, for the vth genome data, a graph autoencoder (GAE) is used to extract the potential representation of the cell from the constructed cell graph. GAE is an unsupervised feature extraction method that can make better use of the cell graph structure and extract node information. It adopts a symmetric structure and reconstructs the weighted feature matrix and adjacency matrix at the same time. Specifically, the feature representation learned by the graph encoder can be defined as:

[0072]

[0073] in, represents the cell embedding representation learned by the mth layer of the graph autoencoder under the vth group learning, and d represents the embedding dimension encoded by the graph autoencoder; The adjacency matrix A v The normalized adjacency matrix is ​​defined as Here D is the adjacency matrix A v The degree matrix of is an N*N identity matrix, indicating that each node has a self-loop structure; W v(m) represents the learnable weight matrix of the mth layer of the encoder under the omics v; the σ(·) function represents the Tanh activation function.

[0074] 1.3 Feature Information Enhancement Module Using Neighborhood Message Passing

[0075] After obtaining the feature embeddings of different omics obtained by the graph autoencoder, in order to further mine the local results inside 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., a 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. Message propagation on the cell graph can not only utilize the local topological structure of the cell graph to strengthen 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 inside the data and embeds different omics To enhance:

[0076]

[0077] in, Indicates the autoencoder embedding in different omics v Feature embedding after information enhancement using local structure domain message passing mechanism.

[0078] In the information enhancement feature After that, the present invention can reconstruct the weighted feature matrix and the adjacency matrix by introducing the following decoder part. The representation learned by the hth layer of the graph autoencoder decoder can be defined as:

[0079]

[0080] Among them, f dec (·) is the decoder function of the graph autoencoder, 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 hybrid loss function. The graph autoencoder loss is expressed as:

[0081]

[0082] in, and They represent the feature reconstruction and graph reconstruction loss of the autoencoder under different omics, respectively. a1 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:

[0083]

[0084]

[0085] In formula (7), represents the weighted feature matrix for reconstruction. In formula (8), is the reconstructed adjacency matrix generated by the inner product of multiple layers of representation in the graph autoencoder. Among them, 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.

[0086] 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 compactness.

[0087] 1.4 Omics feature interaction based on contrastive learning

[0088] Strengthening the interaction of different omics data features of the same cell is conducive to making full use of the complementary information under different omics, and bringing valuable insights to the overall understanding of biological systems. The resurgence of contrastive learning research has made significant progress in self-supervised representation learning, which can better utilize the mutual information between different data views to maximize the construction of contrast loss so that the features of different views are connected. This contrast is formed between similar and dissimilar pairs, with the aim of bringing similar samples closer and separating different samples.

[0089] The present invention adopts a contrastive learning strategy to integrate different omics data to ensure 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.

[0090] Specifically, we obtain feature embeddings under different omics obtained by graph autoencoders. The present invention uses the scRNA-omics feature representation as an anchor point represented by Z, where there are N samples, and f∈F={1,...,N} is used to represent the index of each sample. The resulting contrast loss L cl It can be expressed as:

[0091]

[0092] Among them, z f represents the fth sample in Z, z p(f) The other omics data corresponding to the same sample represented as sample f are considered as sample z f A(f) = F\{f} represents the index set of all other samples of non-target node f under other omics, which is regarded as sample z f Negative samples of Lf Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, z f z p(f) Represents vector z f With vector z p(f) Contrastive learning is used to encourage scMDCL to maximize the similarity between different omics representations of the same source cells, while reducing the association between different cells in different omics, thereby strengthening the interaction between omics features, making full use of the complementary information between different omics, and better extracting features.

[0093] 1.5 Cell clustering with multi-omics deep collaborative supervision

[0094] 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 the representation Z v 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:

[0095]

[0096] in, represents the embedding representation of cell i under the v-th omics, represents the bth cluster center under omics v, b ∧ ∈[1,...,B] represents all cluster centers, and B is the number of cluster centers. can be interpreted as the probability of assigning the i-th cell in the v-th group to the b-th cluster.

[0097] After obtaining the soft assignment matrix Q v After that, we can use the soft allocation matrix Q v The matching target gets the target assignment To enhance the confidence of cluster assignment, the specific definition is as follows:

[0098]

[0099] in, is the soft clustering frequency of soft clustering.

[0100] 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 Pv obtained based on formula (11) is used 来 Guide the update of these two soft assignment distributions. The multi-clustering loss is defined as follows:

[0101]

[0102] Multi-omics data provide characterization of cell states from different perspectives. However, optimizing the multi-clustering loss L v The cluster assignment is only learned from each omics separately, ignoring the consistency and complementary information between different omics. In order to utilize the consistency and complementary information inherent in multiple omics data, the present invention adopts the method of co-training 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 of data is selected as the reference group, P is used. r Represents its target distribution, which is used to guide the update of the soft assignment distribution of all groups. In this way, the accurately predicted cells in the reference group may correct the 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 omics. Therefore, the present invention alternately changes the reference group during training to allow multiple groups to supervise each other. The multi-co-supervised clustering loss is defined as follows:

[0103]

[0104] 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:

[0105]

[0106] Among them, c i Represents the predicted cluster label of the ith cell. This multi-collaborative supervised clustering strategy promotes the mutual optimization between representation learning and clustering, making representation learning more suitable for clustering tasks. At the same time, through information interaction, the intrinsic differences of cells are explored from a multi-omics perspective, further enhancing the clustering effect.

[0107] In summary, the overall loss of the scMDCL framework can be defined as follows:

[0108]

[0109] Among them, α1 and α2 are two hyperparameters used to control the losses of different parts, L cl is the feature interaction contrast loss, Feature reconstruction and graph reconstruction losses of graph autoencoders under different omics.

[0110] 2. Verification

[0111] 2.1 Data

[0112] In this invention, in order to verify the effectiveness of the framework, eight real single-cell multi-omics datasets were collected from different data platforms, including human peripheral blood mononuclear cell (PBMC) dataset; adult mouse cerebral cortex data GSE12607 (Chen-2019) downloaded from the GEO database; mouse CITE-seq spleen lymph node dataset (SLN206) and mouse tissue dataset Ma-2020 dataset. Among them, for the SLN206 dataset, we collected two batches of cell data, named CITEseq_lymph206-1 and CITEseq_lymph206-2; for the Ma-2020 dataset, four batches of cell data were collected, named Ma2020-1, Ma-2020-2, Ma-2020-3 and Ma-2020-4.

[0113] The above datasets contain single-cell data of different omics, among which CITEseq_lymph206-1 and CITEseq_lymph206-2 datasets contain matched scRNA-seq and ADT data, and the other six datasets contain matched scRNA-seq and scA TAC-seq data. The detailed information of these datasets is shown in Table 1.

[0114]

[0115] Table 1: Single cell multi-omics data details

[0116] 2.2 Data Preprocessing

[0117] The present invention is first based on a tool commonly used to process scRNA-seq data, the SCANPY pipeline, for preprocessing scRNA-seq data. Specifically, the present invention first selects the top 3000 highly variable genes, then normalizes the data to eliminate the impact of technical changes (such as counting depth), and uses logarithmic transformation and scaling to reduce 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, since the ADT data has a low dimensionality, the present invention retains all ADT data and only uses preprocessing by performing normalization and scaling.

[0118] 2.3 Comparison methods and evaluation indicators

[0119] The present invention compares the scMDCL framework with 8 advanced clustering methods, including the classical clustering method (i.e., K-means), two single-omics clustering methods for clustering scRNA-seq data, i.e., scziDesk and scGAE, and five multi-omics clustering methods based on deep learning, i.e., DCCA, DEMOC, scMFC, scEMC, and scMIC. Since K-means, scziDesk, and scGAE are designed for single genome clustering, the present invention applies these algorithms to different omics data respectively. Multi-omics data clustering methods such as DCCA, DEMOC, scMFC, scEMC, and scMIC are directly applied to multi-omics data. The parameters of each algorithm are set with reference to its original text.

[0120] To evaluate the performance of scMDCL, this paper adopts four widely used evaluation measures for clustering, including the adjusted Rand index (ARI), normalized mutual information (NMI), adjusted mutual information (AMI), and accuracy (ACC). Specifically, ARI is used to measure the similarity between the predicted label and the true label, which is defined as follows:

[0121]

[0122] Among them, a i and b i Represents the number of cells in the ith true cluster and the ith predicted cluster, n ij represents the number of cells in common between the i-th true cluster and the j-th predicted cluster. Expressed as a binomial coefficient,

[0123] 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:

[0124]

[0125] 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.

[0126] Adjusted Mutual Information (AMI) is an improvement on Normalized Mutual Information (NMI) and 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:

[0127]

[0128] 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.

[0129] ACC measures the percentage of cells that are correctly predicted, and the specific calculation formula is as follows:

[0130]

[0131] Among them, θ(y,p) is an indicator function. When y=p, θ(y,p)=1, otherwise θ(y,p)=0; map(p i ) is a method that maps predicted labels to equivalent true labels through the Hungarian Algorithm.

[0132] 3. Results

[0133] In order to fully compare the performance of the scMDCL framework with other advanced clustering methods, comparative experiments were conducted on eight public datasets with eight other methods. During the framework training process, the present invention runs each method 10 times and takes the average value of its evaluation index as the experimental result. Extensive experiments on different datasets illustrate the superior performance of the scMDCL framework. At the same time, the implementation of a series of experiments such as framework performance experiments under different omics, framework ablation experiments, parameter analysis experiments, and running time experiments of different methods also demonstrates the effectiveness of the scMDCL framework.

[0134] 3.1 Clustering Results

[0135] The present invention compares scMDCL with eight advanced clustering methods, and the results are shown in Tables 2 and 3. From these results, it can be clearly seen that on eight single-cell multi-omics datasets, scMDCL is excellent in all evaluation indicators, and has a certain improvement over other methods. For example, on the PBMC-10k (Table 2) dataset, scMDCL has an ARI of 0.8774, an NMI of 0.8780, an AMI of 0.8772, and an ACC of 0.8923, which are 2.7%, 1.49%, 1.51%, and 5.05% higher than the second place ARI, NMI, AMI, and ACC, respectively. On the dataset Ma-2020-1 (Table 3), scMDCL's ARI, NMI, AMI, and ACC are 11.09%, 2.64%, 2.66%, and 8.09% higher than the second place, respectively.

[0136] Table 2 Performance of different methods on the PBMC-10k dataset

[0137]

[0138] Table 3 Performance of different methods on the Ma-2020-1 dataset

[0139]

[0140] At the same time, it can be seen from the table results that due to the more serious noise and missing problems of scATAC data, the performance of several single-omics clustering methods on scATAC-seq data is significantly reduced compared with scRAN-seq data. For ADT data, single-omics clustering methods show competitive performance, which may be due to the fact that protein markers can better approximate the clustering results. In addition, compared with other multi-omics clustering methods, scMDCL effectively handles the correlation between different omics data, thereby achieving better performance than other benchmark methods.

[0141] 3.2 Ablation Results

[0142] In order to fully understand the impact of the components of the scMDCL framework on clustering tasks, the three important components of the scMDCL framework were further ablated on eight datasets. Specifically, the present invention ablates 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 removal of soft distribution for clustering tasks. The multi-supervisory strategy module (MIGAE) on is used and compared with the proposed method scMDCL. The experimental results are shown in Table 4.

[0143] Through the experimental results, we can observe the following results: (1) The classification effect of the results after the ablation of any module is reduced, which can effectively prove that all modules play an important role in scMDCL; (2) When the FIRND module is ablated, the experimental effect on most data sets has 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 data sets, proving the rationality and effectiveness of each component.

[0144] Table 4 Ablation experimental results of different modules of scMDCL

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[0147] 3.3 Run time comparison

[0148] In order to compare the differences between the running times of different methods, the running times of scMDCL and seven other single-cell clustering methods based on deep learning were compared on eight real data sets. Among them, for the single-omics clustering method, the present invention runs it on two omics data respectively, and takes its average running time on the two omics as its framework running time. The results are shown in Figure 2. Figure 2 shown.

[0149] from Figure 2 As can be seen from the figure, the running time of scMDCL increases approximately linearly with the increase in the number of cells. In addition, except for the fact that the running time of scMDCL is slightly higher than that of the single-omics clustering method DCCA and the multi-omics clustering method scMIC on some data sets, the running time cost of scMDCL is significantly lower than that of other single-cell clustering methods. In general, scMDCL demonstrates efficient running time while achieving excellent clustering performance.

[0150] In this article, the present invention proposes a single-cell multi-omics data clustering framework based on deep collaborative contrastive learning, 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, omics feature interaction based on contrastive learning, and multi-omics deep collaborative clustering, so as to strengthen the connection between different omics while fully extracting the cell features of different omics, thereby improving 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 spleen lymph node dataset (SLN206), and mouse tissue dataset Ma-2020 dataset, scMDCL has good performance compared with the current advanced single-cell clustering methods.

[0151] At the same time, the present invention conducted experiments on the effect of scMDCL under different omics combinations, and the experimental results proved the necessity of integrating various types of omics data to improve the cell clustering performance in biomedical applications. At the same time, ablation experiments, hyperparameter experiments, framework running time comparison and other rich experiments showed the superiority and effectiveness of the proposed framework.

[0152] 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 fields, 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, and further enhances the clustering effect.

[0153] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning, characterized by: The name of the framework is scMDCL, and its specific contents are as follows: (1) Cell graph construction and feature extraction based on graph autoencoder: We constructed a cell similarity network under each omics, and designed a cell omics feature extraction module based on graph autoencoder. We used the correlation between cells to extract cell-specific features under different omics. (2) Feature information enhancement module using neighborhood message passing: Based on the feature information enhancement module based on neighborhood message passing, the topological structure of the cell similarity network is fused 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. Through contrastive learning technology, the similarities and differences of the features obtained from different omics perspectives of cells were compared to achieve information interaction of different omics features. (4) Multi-omics deep collaborative supervised cell clustering: A multi-omics deep collaborative supervised clustering strategy is proposed to enhance the information interaction between different omics, thereby producing better clustering results.

2. A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning according to claim 1, characterized in that: In the construction of cell graphs and feature extraction based on graph autoencoders, the cell omics features are first input Where N is the number of samples, M is v is the number of cell features under v-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 A v Finally, in order to make better use of the inter-cell correlation information, for the vth 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 can be defined as: in, represents the cell embedding representation learned by the mth layer of the graph autoencoder under the vth group learning, and d represents the embedding dimension of the graph autoencoder encoding; The adjacency matrix A v The normalized adjacency matrix is ​​defined as Here D is the adjacency matrix A v The degree matrix of is an N*N identity matrix, indicating that each node has a self-loop structure; W v(m) represents the learnable weight matrix of the mth layer of the encoder under the omics v; the σ(·) function represents the Tanh activation function.

3. A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning according to claim 2, characterized in that: In the feature information enhancement module using neighborhood message passing, the local structure inside 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 can be defined as: Among them, f dec (·) is the decoder function of the graph autoencoder, 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 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, respectively. a1 is a predefined hyperparameter; Feature reconstruction loss under different omics and graph reconstruction loss It can be 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. A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning according to claim 3, characterized in that: In the interaction of omics features based on contrastive learning, feature embeddings under different omics obtained by graph autoencoders are obtained. The scRNA-omics feature representation is represented as an anchor point Z, where there are N samples, and f∈F={1,...,N} is used to represent the index of each sample, then the contrast loss L is formed cl It can be expressed as: Among them, z f represents the fth sample in Z, z p(f) The other omics data corresponding to the same sample represented as sample f are considered as sample z f A(f) = F\{f} represents the set of all other sample indexes of non-target node f under other omics, which is regarded as sample z f Negative samples of L f Represents the loss of contrastive learning for a certain sample; is a scalar temperature parameter in contrastive learning, z f z p(f) Represents vector z f With vector z p(f) The inner (dot) product of .

5. A single-cell multi-omics data clustering framework based on deep collaborative contrastive learning according to claim 4, characterized in that: In multi-omics deep collaborative supervised 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, represents the embedding representation of cell i under the v-th omics, represents the bth cluster center under omics v, b ∧ ∈[1,...,B] 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; After obtaining the soft assignment matrix Q v After that, we can use the soft allocation matrix Q v The matching target gets the target assignment To enhance the confidence of cluster assignment, the specific definition is 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 P v 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. The soft-assigned labels of the two omics are averaged to obtain the final clustering result, which is defined as follows: Among them, c i Represents the predicted cluster label of the i-th cell; The overall loss can be defined as follows: Among them, α1 and α2 are two hyperparameters used to control the losses of different parts, L cl is the feature interaction contrast loss, Feature reconstruction and graph reconstruction losses of graph autoencoders under different omics.

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