Association map embedded cell class group division method for single-cell RNA sequencing data

Abstract

The invention relates to an association graph embedded cell class group division method for single-cell RNA sequencing data, and belongs to the field of cell class group division in single-cell RNA sequencing data analys.The method comprises the steps that firstly, the single-cell RNA sequencing data is preprocessed, then a cell-cell multi-view association graph space is constructed through three feature extraction methods, and the association graph space is used for extracting the single-cell RNA sequencing data; therefore, view angle consistency and view angle specificity information can be better utilized. And optimizing a cell-cell multi-view association graph space by using a self-adaptive neighborhood graph learning method. Then, respectively carrying out spectrum embedding decomposition 1 and spectrum embedding decomposition 2 on the cell-cell consensus association graph and the cell-cell multi-view association graph with the inconsistent parts removed to obtain a corresponding consistent embedding matrix, a view consistent embedding matrix and a view specific embedding matrix; and finally, combining the consistent embedding matrix and the view consistent embedding matrix to obtain a biconsistent embedding matrix, and obtaining a division result of a cell class group by using a k-means method. Compared with other methods, the cell group division accuracy is higher, and the performance is more stable.

Description

Technical Field

[0001] The present invention belongs to the field of single-cell RNA sequencing data analysis, and in particular relates to a method for embedding cell grouping into an association graph for single-cell RNA sequencing data. Background Art

[0002] Single-cell RNA sequencing technology combined with high-throughput sequencing technology can measure gene expression levels in cells at the single-cell level, thereby revealing cell transcriptional heterogeneity, which lays a good foundation for biologists to decipher cell functions from gene expression profiles and explore the diversity of the molecular basis of heterogeneity. A key step in downstream analysis of single-cell RNA sequencing data is to divide cells with the same gene expression pattern into the same group in order to analyze the biological mechanism of cells and the regulatory pattern of cell groups. However, the high dimensionality, high sparsity and complex noise interference of single-cell RNA sequencing data itself will seriously affect the judgment of single-cell gene expression patterns, which makes some different types of cells be misclassified into the same group, which brings great challenges to the effective division of cell groups. The traditional method is to use a single-view method to process single-cell RNA sequencing data, which cannot achieve the ideal cell group division effect. Therefore, a novel method that can overcome these difficulties is needed to solve the application of cell group division for single-cell RNA sequencing data. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a method for embedding cell populations into association graphs for single-cell RNA sequencing data, the method comprising the steps of:

[0004] Obtain a single-cell RNA sequencing dataset, remove genes with low expression values ​​from the dataset, and obtain a single-cell RNA gene expression matrix X. Based on X, three feature extraction methods are used to construct a cell-cell multi-view association graph space {S (1) , S (2) , S (3)};

[0005] The adaptive neighborhood graph learning method is used to optimize the cell-cell multi-view association graph space for the single-cell RNA gene expression matrix X;

[0006] The cell-cell consensus association graph is obtained by spatially separating the inconsistent parts of the cell-cell multi-view association graph and performing spectral embedding decomposition 1 on it to obtain a consistent embedding matrix;

[0007] The view-consistent embedding matrix and the view-specific embedding matrix are obtained by performing spectral embedding decomposition 2 on the cell-cell multi-view association graph space;

[0008] Constructing a view-specific embedding tensor using the view-specific embedding matrix and applying a weighted tensor low-rank constraint to it;

[0009] The consistent embedding matrix and the view consistent embedding matrix are combined into a cell double consistent embedding matrix, and the k-means method is applied to obtain the cell group division result. The accuracy of group division is obtained by combining the real labels of the cells in the data set.

[0010] Furthermore, the single-cell RNA sequencing dataset is stripped of genes with low expression values ​​to obtain the single-cell RNA gene expression matrix X, and a cell-cell multi-view association graph space {S (1) , S (2) , S (3) The three feature extraction methods of} are as follows: PCA method is used to reduce the dimension of X, and the PCC method is used to calculate the correlation between cells in the gene expression matrix after dimension reduction to construct the cell-cell association map S (1) ; Obtain a low-rank factor U from X by the NNDSVD method, perform matrix multiplication on the transposed U and X to obtain another low-rank factor V, then perform the inner product on V to obtain the self-representation matrix Z, and symmetrize Z as the cell-cell association map S (2) ; Use Gaussian, polynomial, and linear kernel functions to calculate three kernel matrices for X, and take the average of the three kernel matrices to get the comprehensive kernel matrix K G , for K G Perform eigendecomposition to obtain a low-redundancy representation N, use N as the inner product and symmetrize it as the cell-cell association graph S (3) ; S (1) , S (2) and S (3) Composing the cell-cell multi-view association graph space.

[0011] Furthermore, the adaptive neighborhood graph learning method is expressed as:

[0012]

[0013] in, is the cell-cell association diagram at view v, represents the correlation between the i-th cell and the j-th cell in the perspective v, n is the number of cells, x i represents the gene expression of the ith cell in X.

[0014] Furthermore, the expression formula of the spectral embedding decomposition 1 is:

[0015]

[0016] in, is the cell-cell consensus association graph, which is the cell-cell multi-view association graph space {S (1) , S (2) , S(3)}The common part after removing the inconsistent parts, is the consistent embedding matrix, n is the number of cells, k is the rank, H T is the transpose of H.

[0017] Furthermore, the expression formula of the spectral embedding decomposition 2 is:

[0018]

[0019] in, represents the view-consistent embedding matrix, represents the specific embedding matrix of the view v, n is the number of cells, k is the rank, Q (v) The transpose of .

[0020] Furthermore, the expression formula of the weighted tensor low-rank constraint is:

[0021]

[0022] in, is the view-specific embedding matrix Q (1) , Q (2) and Q (3) The third-order tensor formed by represents the low-rank constraint, ω j is the jth element of the weight vector ω, Represents a tensor Perform a fast Fourier transform on the i-th slice along the third dimension, for The j-th largest singular value of .

[0023] Furthermore, the consistent embedding matrix H and the perspective consistent embedding matrix F are concatenated to obtain the cell double consistent embedding matrix P, and then the k-means method is used on P to obtain the division result of the cell groups, and the accuracy of the division is obtained by combining the true labels of the cells in the data set.

[0024] The present invention provides a method for embedding cell grouping into association graphs for single-cell RNA sequencing data, which has the following advantages:

[0025] (1) The method constructs a cell-cell multi-view association graph space for a single-modal single-cell RNA sequencing dataset using three different feature extraction methods, fully exploring the associations between cells from different perspectives.

[0026] (2) The method performs spectral embedding decomposition 1 and spectral embedding decomposition 2 on the cell-cell consensus association graph and the cell-cell multi-view association graph space, respectively, thereby filtering out noise while retaining the key associations between cells and comprehensively utilizing the valuable consistency information and complementary information between perspectives.

[0027] (3) The method imposes a weighted tensor low-rank constraint on the view-specific embedding tensor, and uses the tensor structure to flexibly explore the high-order correlation of the view association graph, thereby obtaining potential cross-view associations between cells and improving the accuracy of dividing cell clusters. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] 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.

[0029] Figure 1 It is a flow chart of a method for embedding a correlation graph into cell grouping for single-cell RNA sequencing data provided by the present invention;

[0030] Figure 2 This is a diagram showing the visualization of the partitioning results using the t-SNE tool on the Pollen dataset using the present invention and the other three mainstream methods.

[0031] The methods represented by the sub-graphs in the figure are, from left to right: the present invention (Ours), JLONMFSC, SSNMDI, and MTGDC. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0033] Exemplary Methods

[0034] like Figure 1 The present invention provides a method for embedding cell populations into association graphs for single-cell RNA sequencing data, the method steps are as follows:

[0035] Step S110: Remove genes with low expression values ​​from the acquired single-cell RNA sequencing data set to obtain a single-cell RNA gene expression matrix X, and use three feature extraction methods to construct a cell-cell multi-view association graph space {S (1) , S (2) , S (3)}: Use PCA method to reduce the dimension of X, and use PCC method to calculate the correlation between cells and construct cell-cell association map S for the gene expression matrix after dimension reduction (1) ; The low-rank factor U is obtained by using the NNDSVD method on X, U is transposed and then matrix multiplied with X to obtain another low-rank factor V, and then V is inner-producted to obtain the self-representation matrix Z, which is symmetric as the cell-cell association map S (2) ; Use Gaussian, polynomial, and linear kernel functions to obtain three kernel matrices respectively, and take the average of the three kernel matrices to obtain the comprehensive kernel matrix K G , for K G Perform eigendecomposition to obtain a low-redundancy representation N, use N as the inner product and symmetrize it as the cell-cell association graph S (3) ; S (1) , S (2) and S (3) Composing the cell-cell multi-view association graph space.

[0036] Step S120: Optimize the cell-cell multi-view association graph space by learning the associations between cells in the single-cell RNA gene expression matrix X using an adaptive neighborhood graph learning method, and the expression formula is as follows:

[0037]

[0038] in, A cell-cell association graph representing a visual angle v, represents the correlation between the ith cell and the jth cell, n is the number of cells, x i represents the gene expression of the i-th cell in X.

[0039] Step S130: Divide the cell-cell multi-view association graph space into consistent parts and inconsistent parts, and perform spectral embedding decomposition 1 on the cell-cell consensus association graph C with the inconsistent parts removed to obtain a consistent embedding matrix, which is expressed as:

[0040]

[0041] in, is the cell-cell consensus association graph, C contains the consensus associations between cells, is a consistent embedding matrix, k is the rank, H represents the embedded information of gene expression in cells, H Tis the transpose of H.

[0042] Step S140: By analyzing the cell-cell multi-view association graph space {S (1) , S (2) , S (3)} Perform spectral embedding decomposition 2 to obtain visual Figure 1 The consistent embedding representation and view-specific embedding representation are expressed as follows:

[0043]

[0044] in, is a view-consistent embedding matrix, F contains the embedding information of gene expression that is consistent across views, is the specific embedding matrix belonging to the view v, Q (v) contains embedded information about gene expression specific to view v, Q (v) The transpose of .

[0045] Step S150: Tensor Apply the low-rank constraint on the weighted tensor, which is expressed as:

[0046]

[0047] in, is the view-specific embedding matrix Q (1) , Q (2) and Q (3) The third-order tensor formed by represents the low-rank constraint, ω j is the jth element of the weight vector ω, Represents a tensor Perform a fast Fourier transform on the i-th slice along the third dimension, for The j-th largest singular value of .

[0048] Step S160: The consistent embedding matrix H and the perspective consistent embedding matrix F are concatenated to obtain a cell bi-consistent embedding matrix P, which contains the embedding information of gene expression in the bi-consistent cells. The k-means method is applied to P to obtain the results of cell clustering, and the accuracy of clustering is obtained by combining the true labels of the cells in the data set.

[0049] According to the present embodiment, the single-cell RNA sequencing data is first preprocessed to obtain a single-cell RNA gene expression matrix, and three different feature extraction methods are used to construct a cell-cell multi-view association graph space for the gene expression matrix. Then, the association graph space is optimized using an adaptive neighborhood graph learning method. Then, the cell-cell consensus association graph and the cell-cell multi-view association graph space are subjected to spectral embedding decomposition 1 and spectral embedding decomposition 2, respectively, to obtain a consistent embedding matrix, a visual matrix, and a spatial correlation matrix. Figure 1 The consistent embedding matrix and the view-specific embedding matrix are then Figure 1 The double consistent embedding matrix is ​​combined to obtain the double consistent embedding matrix, and finally the k-means method is used to obtain the cell cluster division result, and the accuracy of the division is obtained by combining the real cluster labels of the cells in the dataset.

[0050] To further illustrate, assuming that a single-cell RNA sequencing data set is divided into cell groups according to the present implementation method, a grouping result with higher accuracy than most mainstream methods can be obtained.

[0051] Detailed description of the invention Results

[0052] This embodiment uses a publicly available single-cell RNA sequencing dataset. The details of the dataset are described as follows:

[0053] The Pollen dataset is from the National Center for Biotechnology Information (https: / / www.ncbi.nlm.nih.gov / ). The dataset consists of single cells from the developing human cortex, including 301 cells, 23,730 genes, and 11 cell populations.

[0054] In order to verify the superiority of this implementation (Ours), this implementation is compared with four other baseline methods for cell clustering of single-cell RNA sequencing data, including SMSC, SIMLR, SNN-cliq, SCEA and other methods. The clustering accuracy (ACC) of these methods on the above public datasets will be compared. The specific data comparison is shown in Table 1.

[0055] Table 1 Pollen dataset cell group classification accuracy (%)

[0056] SMSC SIMLR SNN-cliq SCEA Ours 76.1 83.9 63.9 92.4 96.8

[0057] By comparing the data in the above table, we can clearly see that Ours achieves the best performance and significantly improves the accuracy of cell clustering for single-cell RNA sequencing data. The quantitative results fully demonstrate the superiority of Ours, because Ours uses multi-view learning methods to fully utilize the consistency information and complementary information in multiple perspectives, better capture the gene expression patterns of cells in single-cell RNA sequencing data, and thus classify cells with the same gene expression pattern into the same group, thereby improving the accuracy of cell clustering.

[0058] This embodiment proposes a method for embedding cell clustering based on association graphs of single-cell RNA sequencing data, which is used to perform cell clustering on single-cell RNA sequencing data. A cell-cell multi-view association graph space is constructed by using three feature extraction methods on the preprocessed single-cell RNA sequencing data. Then, the cell-cell multi-view association graph space is further optimized using an adaptive neighborhood graph learning method based on the single-cell RNA gene expression matrix. Then, spectral embedding decomposition 1 and spectral embedding decomposition 2 are performed on the cell-cell consensus association graph and the cell-cell multi-view association graph space after removing inconsistent parts, respectively, to obtain a consistent embedding matrix, a visual matrix, and a spatial matrix. Figure 1 The consistent embedding matrix and the view-specific embedding matrix are then combined with the consistent embedding matrix and the view-specific embedding matrix. Figure 1 The consistent embedding matrix is ​​combined to obtain a double consistent embedding matrix, and finally the cell group division result is obtained by the k-means method. The experimental results on the public single-cell RNA sequencing dataset Pollen show that this implementation method has higher accuracy and better superiority in cell group division than other methods.

[0059] It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principles of the present invention, and do not constitute a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modifications that fall within the scope and boundaries of the appended claims, or the equivalent forms of such scope and boundaries.

Claims

1. A method for embedding cell populations into association graphs for single-cell RNA sequencing data, characterized in that: The method comprises the steps of: Obtain a single-cell RNA sequencing dataset, remove genes with low expression values ​​from the dataset, and obtain a single-cell RNA gene expression matrix X. Based on X, three feature extraction methods are used to construct a cell-cell association map S. (1) , S (2) , S (3) , and constitute the cell-cell multi-view association graph space {S (1) , S (2) , S (3) }; The adaptive neighborhood graph learning method is used to optimize the cell-cell multi-view association graph space for the single-cell RNA gene expression matrix X; By spatially separating the inconsistent parts of the cell-cell multi-view association graph, we obtain the cell-cell consensus association graph C, and perform spectral embedding decomposition 1 on C to obtain the consistent embedding matrix H; By performing spectral embedding decomposition 2 on the cell-cell multi-view association graph space, we obtain the view-consistent embedding matrix F and the view-specific embedding matrix Q (1) , Q (2) and Q (3) ; Use the view-specific embedding matrix Q (1) , Q (2) and Q (3) Constructing view-specific embedding tensors right Imposing low-rank constraints on weighted tensors; The consistent embedding matrix H and the view consistent embedding matrix F are combined into the cell double consistent embedding matrix P. The k-means method is applied to P to obtain the cell cluster division results. The accuracy of cluster division is obtained by combining the true labels of the cells in the dataset.

2. The method for embedding cell populations into association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The three feature extraction methods for constructing the cell-cell multi-view association graph space are as follows: The single-cell RNA gene expression matrix X is reduced in dimension by the PCA method, and then the correlation between cells is calculated using the PCC method on the low-dimensional gene expression matrix to obtain the cell-cell association map S (1) ; The low-rank factor U is obtained from the single-cell RNA gene expression matrix X by the NNDSVD method. U is transposed and multiplied with X to obtain another low-rank factor V. The self-expression matrix Z of X is obtained by doing the inner product with V. Z is then symmetric as the cell-cell association map S. (2) ; The single-cell RNA gene expression matrix X is calculated using three kernel functions: Gaussian, polynomial, and linear to obtain three kernel matrices. The three kernel matrices are averaged to obtain the comprehensive kernel matrix K. G , for K G Perform eigendecomposition to obtain a low-redundancy representation N of X, use N to do the inner product and symmetrize it as the cell-cell association graph S (3) ; The above cell-cell association graphs are combined into a cell-cell multi-view association graph space {S (1) , S (2) , S (3) }.

3. The method for classifying cell groups in association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The adaptive neighborhood graph learning method is expressed as: in, A cell-cell association graph representing a visual angle v, represents the correlation between the i-th cell and the j-th cell in the perspective v, n is the number of cells, x i represents the gene expression of the i-th cell in X.

4. The method for embedding cell populations into association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The expression formula of the spectral embedding decomposition 1 is: s.t.H T H=I in, represents the consistent embedding matrix, k is the rank, H T is the transpose of H.

5. The method for embedding cell populations into association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The expression formula of the spectral embedding decomposition 2 is: s.t.FF T =I in, represents the view-consistent embedding matrix, represents the specific embedding matrix of the view v, Q (v) The transpose of .

6. The method for embedding cell populations into association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The expression formula of the weighted tensor low rank constraint is: in, is the view-specific embedding matrix Q (1) , Q (2) and Q (3) The third-order tensor formed by represents the low-rank constraint, ω j is the jth element of the weight vector ω, Represents a tensor Perform a fast Fourier transform on the i-th slice along the third dimension, for The j-th largest singular value of .

7. The method for embedding cell populations into association graphs for single-cell RNA sequencing data according to claim 1, characterized in that: The consistent embedding matrix H and the view consistent embedding matrix F are combined into the cell double consistent embedding matrix P. The k-means method is applied to P to obtain the cell cluster division results. The accuracy of cluster division is obtained by combining the true labels of the cells in the dataset.

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