Single-cell methylation data clustering method based on multi-distance spectrum embedding fusion

Abstract

The present invention discloses a single cell methylation data clustering method based on multi-distance spectrum embedding fusion, obtains the single cell methylation data of the cell to be clustered and performs binarization processing, calculates the cosine distance matrix, Hamming distance matrix and Pearson distance matrix between the cells according to the obtained single cell methylation data, obtains three low-dimensional spectrum embedding representation matrices of the cell according to the three distance matrices using a spectrum embedding method, merges the three low-dimensional spectrum embedding representation matrices by column to obtain a feature matrix, uses the row vectors in the feature matrix as the feature representation vector of the cell, calculates the Euclidean distance between the feature representation vectors between the cells in pairs, obtains a methylation distance matrix, performs hierarchical clustering based on the methylation distance matrix, and obtains a cell clustering result. The present invention improves the accuracy of single cell methylation data clustering by fusing the low-dimensional spectrum embedding components of multiple distance matrices.

Description

Technical Field

[0001] The present invention belongs to the technical field of bioinformatics data, and more specifically, relates to a single cell methylation data clustering method based on multi-distance spectrum embedding fusion. Background Art

[0002] At present, as one of the research hotspots of single-cell sequencing technology in epigenomics, clustering analysis of single-cell methylation data has been difficult due to its own sparsity and random measurement. However, understanding the mechanism of epigenomics in single cells is of great significance for understanding cell differentiation and variation, so it is necessary to develop new methods to achieve clustering of single-cell methylation data.

[0003] Traditional single-cell methylation data clustering is mainly based on two ideas. One is to first predict the methylation status value of the unmeasured site through information related to a single CpG site (cytosine-phosphate-guanine site, that is, the site immediately following guanine after cytosine in the DNA sequence) of the cell, and then perform cluster analysis based on the predicted results. This method requires certain prior knowledge and the clustering results are greatly affected by the prediction performance; the other is to calculate a methylation state distance matrix described by the common sites between any pair of cells, and then perform hierarchical clustering on the matrix to obtain the cell distance results. Although this method does not require the methylation level of the single site to be predicted in advance, a single distance matrix is ​​difficult to accurately reflect the epigenetic heterogeneity between cells, so the performance on complex data sets is poor. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a single-cell methylation data clustering method based on multi-distance spectrum embedding fusion, which obtains a methylation distance matrix by fusing the low-dimensional spectrum embedding components of multiple distance matrices, and implements hierarchical clustering on this basis to obtain the final cell clustering result, thereby improving the accuracy of single-cell methylation data clustering.

[0005] To achieve the above-mentioned object of the invention, the single cell methylation data clustering method based on multi-distance spectrum embedding fusion of the present invention comprises the following steps:

[0006] S1: Obtain the single-cell methylation data of N cells to be clustered, and record the methylation data corresponding to cell i as X′ i ,i=1,2,…,N; for each single cell methylation data X′ i Perform binarization preprocessing to obtain the binarized methylation data X i ;

[0007] S2: For the single-cell methylation data obtained in step S1, calculate any two single-cell methylation data Xi and X j The cosine distance DM1(X i ,X j ), Hamming distance DM2(X i ,X j ) and Pearson distance DM3(X i ,X j ), i, j = 1, 2, ..., N, forming the N-order cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3;

[0008] S3: Using the spectrum embedding method, obtain the low-dimensional spectrum embedding representation matrices corresponding to the three distance matrices obtained in step S2 respectively. The specific method is as follows:

[0009] First, the weighted graph G corresponding to each distance matrix is ​​generated according to the cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3 p , p = 1, 2, 3, the specific method is: all cells are taken as weighted graph G p According to the distance matrix DM p Get the K nearest neighbor set φ of each cell i i , the value of K is set according to the actual situation to determine the neighboring situation between cells: if cell i and cell j are not each other's nearest neighbors, that is, or Then it is considered that cells i and j are not adjacent if cells i and j are each other's nearest neighbors, that is, i∈φ j And j∈φ i , then cells i and j are considered to be adjacent; then the thermal kernel function is used to assign weights to each edge The calculation formula is as follows:

[0010]

[0011] Among them, e represents a natural constant;

[0012] According to the weighted graph G p Get the weighted adjacency matrix W p ;

[0013] Then, the three weighted adjacency matrices W p Perform spectral embedding to generate 3 distance matrices DM p The corresponding low-dimensional spectral embedding representation matrix

[0014]

[0015] Among them, y pi =(y pi1 ,y pi2 ,…,ypiR ) indicates Y p The embedding vector corresponding to the i-th cell in , y pir Denotes the embedding vector y pi The rth eigenvalue in , r = 1, 2, …, R, where R represents the embedding dimension;

[0016] S4: embed the three low-dimensional spectra obtained in step S3 into the representation matrix Y p Merge by columns to generate an N×3R feature matrix FM=[Y1 Y2 Y3], and then replace the i-th row vector FM in the feature matrix FM i As the feature representation vector f of cell i i , calculate the feature representation vector f between cells pairwise i The Euclidean distance of , and the N-order distance matrix is ​​obtained, which is used as the methylation distance matrix

[0017] S5: Based on the methylation distance matrix Perform hierarchical clustering to obtain cell clustering results.

[0018] The present invention is based on a single-cell methylation data clustering method based on multi-distance spectrum embedding fusion. The single-cell methylation data of N cells to be clustered are obtained and binarized. The cosine distance matrix, Hamming distance matrix and Pearson distance matrix between cells are calculated according to the obtained single-cell methylation data. A spectral embedding method is used to obtain three low-dimensional spectral embedding representation matrices of the cells according to the three distance matrices. The three low-dimensional spectral embedding representation matrices are merged column by column to obtain a feature matrix. The row vectors in the feature matrix are used as feature representation vectors of the cells. The Euclidean distances between the feature representation vectors between the cells are calculated pairwise to obtain a methylation distance matrix. Hierarchical clustering is performed based on the methylation distance matrix to obtain a cell clustering result.

[0019] The present invention considers the methylation distance relationship between cell pairs described by different distance metrics, embeds and fuses multiple distance spectra, and then clusters single-cell methylation data, thereby overcoming the lack of accuracy in clustering single-cell methylation data based on a single distance matrix, and effectively improving the accuracy of single-cell methylation data clustering. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flowchart of a specific implementation of the single-cell methylation data clustering method based on multi-distance spectrum embedding fusion of the present invention. DETAILED DESCRIPTION

[0021] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0022] Example

[0023] Figure 1 1 is a flow chart of a specific implementation of the single cell methylation data clustering method based on multi-distance spectrum embedding fusion of the present invention. Figure 1 As shown, the specific steps of the single cell methylation data clustering method based on multi-distance spectrum embedding fusion of the present invention include:

[0024] S101: Obtain single cell methylation data:

[0025] Get the single-cell methylation data of N cells to be clustered, and record the methylation data corresponding to cell i as X′ i , i=1,2,…,N.

[0026] In the present invention, considering the bimodal distribution characteristics of the original data, the methylation data X′ of each single cell is i Perform binarization preprocessing to obtain the binarized methylation data X i The specific method is: record the original methylation data X′ i The median site methyl state value is β′, and the binarization threshold is T. The calculation formula for the binarized site methyl state value β is as follows:

[0027]

[0028] In this embodiment, the binarization threshold T = 0.5. When β = 0, it means that the site is in an unmethylated state, and when β = 1, it means that the site is in a methylated state.

[0029] S102: Calculate the distance matrix:

[0030] For the single cell methylation data obtained in step S101, calculate any two single cell methylation data X i and X j The cosine distance DM1(X i ,X j ), Hamming distance DM2(X i ,X j ) and Pearson distance DM3(X i ,X j), i, j = 1, 2, ..., N, forming the N-order cosine distance matrix DM1, Hamming distance matrix DM2 and Pearson distance matrix DM3. The following introduces the calculation method of each distance:

[0031] 1) Cosine distance

[0032] The cosine distance reflects the directional difference in the high-dimensional space between the methylation data of any two single cells. i and X j The cosine distance DM1(X i ,X j ) is calculated as:

[0033]

[0034] Among them, M ij Represents single cell methylation data X i and X j The number of common sites between im , X jm Represents single cell methylation data X i , X j The methylation status value of the mth public site in .

[0035] 2) Hamming distance

[0036] The Hamming distance reflects the proportion of sites with inconsistent methylation status between any two single cells. The single cell methylation data X i and X j The Hamming distance DM2(X i ,X j ) is calculated as:

[0037]

[0038] Among them, I() represents the indicative function. When the single cell methylation data X i , X j The methylation status value X of the mth common site in im , X jm If they are the same, return 1, otherwise return 0.

[0039] 3) Pearson distance:

[0040] The Pearson distance reflects the linear difference in the methylation state vectors between any two single cells. The single cell methylation data X i and X j The Pearson distance DM3(X i ,X j ) is calculated as:

[0041]

[0042] Among them, E[] represents the calculation of covariance, Represents single cell methylation data X i , X j The mean methylation status value of the common sites in .

[0043] Through the above three different distance metrics, the distance relationship between samples described by the single-cell methylation data can be aggregated into three different distance matrices, namely the cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3.

[0044] S103: Obtain low-dimensional embedding representation of cells:

[0045] In order to more accurately characterize the methylation distance relationship between different cells, the present invention uses a spectral embedding method to obtain low-dimensional spectral embedding representation matrices corresponding to the three distance matrices obtained in step S2. The specific method is as follows:

[0046] First, the weighted graph G corresponding to each distance matrix is ​​generated according to the cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3 p , p = 1, 2, 3, the specific method is: all cells are taken as weighted graph G p According to the distance matrix DM p Get the K nearest neighbor set φ of each cell i i , the value of K is set according to the actual situation to determine the neighboring situation between cells: if cell i and cell j are not each other's nearest neighbors, that is, or Then it is considered that cells i and j are not adjacent if cells i and j are each other's nearest neighbors, that is, i∈φ j And j∈φ i , then cells i and j are considered to be adjacent. Then the heat kernel function is used to assign weights to each edge. The calculation formula is as follows:

[0047]

[0048] Among them, e represents a natural constant;

[0049] According to the weighted graph G p Get the weighted adjacency matrix W p .

[0050] Then, the three weighted adjacency matrices W p Perform spectral embedding to generate 3 distance matrices DM p The corresponding low-dimensional spectral embedding representation matrix Yp :

[0051]

[0052] Among them, y pi =(y pi1 ,y pi2 ,…,y piR ) indicates Y p The embedding vector corresponding to the i-th cell in , y pir Denotes the embedding vector y pi The r-th eigenvalue in , r = 1, 2, …, R, where R represents the embedding dimension.

[0053] In this embodiment, the low-dimensional spectrum embedding representation matrix Y is obtained. p The specific method is:

[0054] Set the optimization objective function:

[0055]

[0056] Y p T D p Y p =I

[0057] Among them, D p According to the weighted adjacency matrix W p The obtained degree matrix has the elements on the diagonal The remaining elements are 0. represents the normalized Laplacian operator and I represents the identity matrix.

[0058] Low-dimensional spectral embedding representation matrix Y p The solution can be converted into the spectral decomposition problem of the generalized characteristic matrix, that is, first according to the weighted adjacency matrix W p Get the degree matrix D p , and then calculate the normalized Laplacian For the normalized Laplace operator L p Perform matrix decomposition and filter out the first R smallest non-zero eigenvalues ​​λ r The corresponding N-dimensional feature vector z r , that is, L p z r =λ r D p z r , the R eigenvectors z r The matrix composed of column vectors is the low-dimensional spectral embedding representation matrix Y p .

[0059] S104: Get methylation distance matrix:

[0060] The low-dimensional spectral embedding of the above multiple distance matrices is integrated to obtain a new distance matrix describing the relationship between the methylation states of cells, namely the methylation distance matrix. In order to merge the low-dimensional spectral embedding representation to reconstruct a new distance matrix for clustering, the present invention combines the three low-dimensional spectral embedding representation matrices Y obtained in step S3 p Merge by columns to generate a high-dimensional feature matrix FM. It can be seen that the feature matrix brings together information from three distance matrices {DM1, DM2, DM3 to achieve more accurate inter-cell methylation distance measurement. Then the i-th row vector FM in the feature matrix FM i As the feature representation vector f of cell i i , calculate the feature representation vector f between cells pairwise i The Euclidean distance between them is used to obtain the N-order distance matrix, which is used as the methylation distance matrix Methylation distance matrix Elements in The calculation formula is as follows:

[0061]

[0062] Among them, f ir′ 、f jr′ Represents cell i and feature representation vector f of cell i respectively. i 、f j The value of the r′th characteristic element in .

[0063] S105: Cell clustering:

[0064] Methylation distance matrix Perform hierarchical clustering to obtain cell clustering results.

[0065] In order to better illustrate the technical effect of the present invention, three publicly available single-cell methylation sequencing data sets were used to experimentally verify the present invention. These three single-cell methylation sequencing data sets are based on different single-cell methylation sequencing technologies, showing different sparsity and complexity. These three data sets are mouse embryonic stem cell data sets, human liver cancer cell data sets, and human blood cell data sets, which can be downloaded from https: / / www.ncbi.nlm.nih.gov / gds / . The corresponding GEO accession numbers are: GSE56879, GSE65364, and GSE8719. Table 1 is a list of specific information of the three single-cell methylation data sets in this embodiment.

[0066] Dataset Sequencing technology Cell number Number of categories GSE56879 scBS-seq 32 2 GSE65364 scTrio-seq 31 3 GSE87197 scWGBS-seq 122 6

[0067] Table 1

[0068] In this embodiment, a single cell methylation data clustering method based on a single distance matrix for hierarchical clustering is used as a comparison method. Since the label information of the cell can be obtained from a public data set source, after completing the cluster analysis, this embodiment evaluates the clustering performance of the present invention and the three comparison methods by using normalized mutual information (NMI) and adjusted Rand index (ARI). Normalized mutual information and adjusted Rand index are commonly used indicators for evaluating clustering performance, and their specific calculation formulas are not repeated here.

[0069] Table 2 is a comparison table of clustering performance of the present invention and three comparison methods on three data sets.

[0070]

[0071] Table 2

[0072] As shown in Table 2, the present invention achieved the best clustering performance and achieved the highest NMI and ARI on the three data sets, which proved the effectiveness and practicality of the present invention in improving the accuracy of clustering results of single-cell methylation data by fusing multiple distances.

[0073] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A single cell methylation data clustering method based on multi-distance spectrum embedding fusion, characterized in that: The following steps are involved: S1: Obtain the single-cell methylation data of N cells to be clustered, and record the methylation data corresponding to cell i as X′ i ,i=1,2,…,N; for each single cell methylation data X′ i Perform binarization preprocessing to obtain the binarized methylation data X i ; S2: For the single-cell methylation data obtained in step S1, calculate any two single-cell methylation data X i and X j The cosine distance DM1(X i ,X j ), Hamming distance DM2(X i ,X j ) and Pearson distance DM3(X i ,X j ), i, j = 1, 2, ..., N, forming the N-order cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3; S3: Using the spectrum embedding method, obtain the low-dimensional spectrum embedding representation matrices corresponding to the three distance matrices obtained in step S2 respectively. The specific method is as follows: First, the weighted graph G corresponding to each distance matrix is ​​generated according to the cosine distance matrix DM1, the Hamming distance matrix DM2 and the Pearson distance matrix DM3 p , p = 1, 2, 3, the specific method is: all cells are taken as weighted graph G p According to the distance matrix DM p Get the K nearest neighbor set φ of each cell i i , the value of K is set according to the actual situation to determine the neighboring situation between cells: if cell i and cell j are not each other's nearest neighbors, that is, or Then it is considered that cells i and j are not adjacent if cells i and j are each other's nearest neighbors, that is, i∈φ j And j∈φ i , then cells i and j are considered to be adjacent; then the thermal kernel function is used to assign weights to each edge The calculation formula is as follows: Among them, e represents a natural constant; According to the weighted graph G p Get the weighted adjacency matrix W p ; Then, the three weighted adjacency matrices W p Perform spectral embedding to generate three basic distance matrices DM p The corresponding low-dimensional spectral embedding representation matrix: Among them, y pi =(y pi1 ,y pi2 ,…,y piR ) indicates Y p The embedding vector corresponding to the i-th cell in , y pir Denotes the embedding vector y pi The rth eigenvalue in , r = 1, 2, …, R, where R represents the embedding dimension; S4: embed the three low-dimensional spectra obtained in step S3 into the representation matrix Y p Merge by columns to generate an N×3R feature matrix FM=[Y1 Y2 Y3], and then replace the i-th row vector FM in the feature matrix FM i As the feature representation vector f of cell i i , calculate the feature representation vector f between cells pairwise i The Euclidean distance of , and the N-order distance matrix is ​​obtained, which is used as the methylation distance matrix S5: Based on the methylation distance matrix Perform hierarchical clustering to obtain cell clustering results.

2. The single cell methylation data clustering method according to claim 1, characterized in that: The specific method of binarization preprocessing in step S1 is: Let the original methylation data X′ i The median site methyl state value is β′, and the binarization threshold is T. The calculation formula for the binarized site methyl state value β is as follows:

3. The single cell methylation data clustering method according to claim 1, characterized in that: In step S2, the cosine distance DM1 (X i ,X j ) is calculated as: Among them, M ij Represents single cell methylation data X i and X j The number of common sites between im , X jm Represents single cell methylation data X i , X j The methylation status value of the mth public site in .

4. The single cell methylation data clustering method according to claim 1, characterized in that: In step S2, the Hamming distance DM2(X i ,X j ) is calculated as: Among them, I() represents the indicative function. When the single cell methylation data X i , X j The methylation status value X of the mth common site in im , X jm If they are the same, return 1, otherwise return 0.

5. The single cell methylation data clustering method according to claim 1, characterized in that: In step S2, the Pearson distance DM3 (X i ,X j ) is calculated as: Among them, E[] represents the calculation of covariance, Represents single cell methylation data X i , X j The mean methylation status value of the common sites in .

6. The single cell methylation data clustering method according to claim 1, characterized in that: In step S3, the low-dimensional spectral embedding representation matrix Y is obtained. p The specific method is: First, according to the weighted adjacency matrix W p Get the degree matrix D p , and then calculate the normalized Laplacian For the normalized Laplace operator L p Perform matrix decomposition and filter out the first R smallest non-zero eigenvalues ​​λ r The corresponding N-dimensional feature vector z r , that is, L p z r =λ r D p z r , the R eigenvectors z r The matrix composed of column vectors is the low-dimensional spectral embedding representation matrix Y p .

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