A single-cell RNA sequencing data clustering method and system based on multi-scale hypergraph

Abstract

The application provides a single-cell RNA sequencing data clustering method and system based on a multi-scale hypergraph, a multi-scale similarity matrix is constructed from a gene expression matrix; a cell hypergraph is generated from the multi-scale similarity matrix; cell hypergraph fusion is performed; SVD decomposition is performed on the hypergraph Laplacian matrix of the fused cell hypergraph; the feature vector corresponding to the first minimum eigenvalue is extracted, K-means is performed to obtain a clustering result, and the function of improving the clustering effect of single-cell RNA sequencing data is realized. The application proposes a novel hypergraph generation method, better captures the high-order correlation between multiple cells, and more accurately captures the correlation between cells using multiple scales. Compared with the existing single-cell RNA sequencing data clustering method, the application proposes a unified clustering framework, which comprehensively learns the topological information between cells on multiple scales, constructs a cell hypergraph for clustering, and can obtain a better clustering result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of single-cell RNA sequencing data clustering, and particularly relates to a single-cell RNA sequencing data clustering method and system based on a multi-scale hypergraph. BACKGROUND

[0002] Single-cell RNA sequencing (scRNA-seq) is a method that uses next-generation sequencing technology to analyze individual cells and understand cell function at the gene and cell level. Unlike traditional large-scale RNA sequencing techniques, scRNA-seq can provide a more comprehensive understanding of cell heterogeneity and diversity within cell populations. scRNA-seq provides information on the transcriptome of individual cells, which can be used to identify cell subtypes, track cell differentiation stages, and monitor the progression of individual cells. This approach provides a new perspective for studying gene expression patterns at the cellular level.

[0003] The focus of single-cell research is to accurately identify cell types, which is a key requirement for understanding the diversity of cell populations. However, scRNA-seq data can pose challenges such as missing events and dimensionality disasters, making subsequent analysis difficult. Even within the same group of cells, there are significant differences in gene expression levels, which pose challenges for downstream analysis and always fail to obtain reliable clustering results.

[0004] In recent years, hypergraphs have received increasing attention due to their ability to model high-order relationships between complex data. Yang et al. proposed the SAFE-clustering method, which is an ensemble clustering method that integrates the results of four clustering methods and employs three hypergraph partitioning algorithms. This method provides a flexible, accurate, and robust solution for single-cell RNA-seq data clustering. However, the method of constructing a hypergraph from the results of four clustering methods is too complex and needs further improvement. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a single-cell RNA sequencing data clustering method and system based on a multi-scale hypergraph to improve the clustering effect of scRNA-seq data.

[0006] The technical solution adopted by the present application to solve the above technical problem is: a single-cell RNA sequencing data clustering method based on a multi-scale hypergraph, comprising the following steps:

[0007] S1: converting a gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning;

[0008] S2: generating a cell hypergraph based on the multi-scale similarity matrix;

[0009] S3: obtaining a fused cell hypergraph by using a fusion algorithm according to the cell hypergraph;

[0010] S4: calculating a hypergraph Laplacian matrix through the fused cell hypergraph, and performing SVD decomposition to obtain an eigenvector;

[0011] S5: extracting an eigenvector corresponding to a smallest K eigenvalue, and performing K-means to obtain a clustering result.

[0012] According to the above scheme, in step S1, the specific steps are as follows:

[0013] S11: obtaining gene expression data and normalizing, and then representing as a gene expression matrix, each row of the matrix representing a gene expression vector of a cell, and each column representing a gene expression level of the same gene in different cells;

[0014] S12: constructing three similarity matrices with the same dimension for the gene expression data and converting into a multi-scale similarity matrix, and performing symmetrization on the multi-scale similarity matrix.

[0015] According to the above scheme, in step S2, the specific steps are as follows:

[0016] A multi-scale cell hypergraph described by a triple {vertex set, hyperedge set, hyperedge weight matrix} is generated through the multi-scale similarity matrix, and a corresponding association matrix.

[0017] Further, in step S2,

[0018] Each vertex of the vertex set is used to represent a cell;

[0019] The hyperedge set represents a hyperedge set composed of neighbors of the cell vertex in the similarity matrix;

[0020] The association matrix is used to represent the importance of the cell vertex in the hyperedge.

[0021] According to the above scheme, in step S3, the specific steps are as follows:

[0022] The multi-scale cell hypergraph is fused and constructed into a fused cell hypergraph by averaging the association matrix corresponding to the cell hypergraph to fuse the association matrix.

[0023] According to the above scheme, in step S4, the specific steps are as follows:

[0024] S41: constructing a hypergraph Laplacian matrix through the association matrix, hyperedge degree matrix, vertex degree matrix and hyperedge weight matrix of the fused cell hypergraph;

[0025] S42: performing SVD decomposition on the hypergraph Laplacian matrix to obtain an eigenvector.

[0026] Further, in the step S41,

[0027] Each element of the hyperedge degree matrix represents the weight of a hyperedge, which is equal to the sum of the weights of the vertices connected by the hyperedge.

[0028] Each element of the vertex degree matrix represents the weight of a vertex, which is equal to the weight of the vertex multiplied by the weight of the hyperedge in the hyperedge connected to the vertex.

[0029] According to the above scheme, in the step S5, the specific steps are as follows:

[0030] S51: Select the eigenvectors corresponding to the first K smallest eigenvalues of the hypergraph Laplacian matrix according to the number of cell categories:

[0031] S52: Perform row normalization on the eigenvectors selected in step S51 to obtain normalized eigenvectors;

[0032] S53: Cluster the normalized eigenvectors using the K-means method to obtain the clustering result.

[0033] A single-cell RNA sequencing data clustering system based on multi-scale hypergraph,

[0034] The matrix conversion submodule is configured to convert the gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning.

[0035] The hypergraph generation submodule is configured to generate a cell hypergraph based on the multi-scale similarity matrix.

[0036] The fusion submodule is configured to obtain a fused cell hypergraph by using a fusion algorithm according to the cell hypergraph.

[0037] The decomposition submodule is configured to calculate a hypergraph Laplacian matrix through the fused cell hypergraph, and perform SVD decomposition to obtain eigenvectors.

[0038] The clustering submodule is configured to extract eigenvectors corresponding to the first K smallest eigenvalues, and perform K-means to obtain a clustering result.

[0039] A computer memory having stored therein a computer program executable by a computer processor, the computer program performing a single-cell RNA sequencing data clustering method based on a multi-scale hypergraph.

[0040] The beneficial effects of the present application are:

[0041] 1.A method and system for clustering single-cell RNA sequencing (scRNA-seq) data based on multi-scale hypergraph, comprising the following steps: constructing a multi-scale similarity matrix from a gene expression matrix; generating a cell hypergraph from the multi-scale similarity matrix; fusing the cell hypergraph; performing SVD decomposition on a hypergraph Laplacian matrix of the fused cell hypergraph; extracting eigenvectors corresponding to the first K smallest eigenvalues, and performing K-means to obtain a clustering result, thereby improving the clustering effect of scRNA-seq data.

[0042] 2.The method for generating a hypergraph is novel, better capturing the high-order correlation between multiple cells, and more accurately capturing the correlation between cells using multiple scales.

[0043] 3.Compared with the existing method for clustering scRNA-seq data, the present application proposes a unified clustering framework that comprehensively learns the topological information between cells at multiple scales and constructs a cell hypergraph for clustering, thereby obtaining a better clustering result.

[0044] Of course, implementing any product of the present application does not necessarily require all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0046] Figure 1 is a flowchart of an embodiment of the present application.

[0047] Figure 2 is a comparison bar chart of clustering performance indicators of the embodiment of the present application and the classical method on the Treutlein data set.

[0048] Figure 3 is a comparison chart of clustering effects of the embodiment of the present application and the classical method on the Treutlein data set. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solutions and advantages of the present application clearer, the following will further describe the present application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0050] Embodiment 1

[0051] Referring to​Figure 1 The specific steps of a single-cell RNA sequencing data clustering method based on a multi-scale hypergraph are as follows:

[0052] S1: converting a gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning;

[0053] S2: generating a cell hypergraph based on the multi-scale similarity matrix;

[0054] S3: obtaining a fused cell hypergraph through a fusion algorithm according to the cell hypergraph;

[0055] S4: calculating a hypergraph Laplacian matrix through the fused cell hypergraph, and performing SVD decomposition to obtain an eigenvector;

[0056] S5: extracting an eigenvector corresponding to the first K smallest eigenvalues, and performing K-means to obtain a clustering result.

[0057] Further, in step S1, the specific steps are as follows:

[0058] S11: obtaining gene expression data and normalizing, and then representing as a gene expression matrix, each row of the matrix representing a gene expression vector of a cell, and each column representing a gene expression level of a same gene in different cells;

[0059] S12: constructing three similarity matrices with the same dimensions from the gene expression data and converting into a multi-scale similarity matrix, and symmetrizing the multi-scale similarity matrix.

[0060] In step S2, the specific steps are as follows:

[0061] A multi-scale cell hypergraph described by a triple {vertex set, hyperedge set, hyperedge weight matrix} is generated through the multi-scale similarity matrix, and a corresponding correlation matrix.

[0062] Further, in step S2,

[0063] Each vertex of the vertex set is used to represent a cell;

[0064] The hyperedge set represents a hyperedge set composed of neighbors of the cell vertices in the similarity matrix;

[0065] The correlation matrix is used to represent the importance of the cell vertices in the hyperedge.

[0066] In step S3, the specific steps are as follows:

[0067] The multi-scale cell hypergraph is fused and constructed into a fused cell hypergraph by averaging the correlation matrix corresponding to the cell hypergraph to fuse the correlation matrix.

[0068] In step S4, the specific steps are as follows:

[0069] S41: constructing a hypergraph Laplacian matrix by fusing the association matrix, the hyperedge degree matrix, the vertex degree matrix and the hyperedge weight matrix of the hypergraph;

[0070] S42: obtaining an eigenvector by performing SVD decomposition on the hypergraph Laplacian matrix.

[0071] Further, in step S41,

[0072] Each element of the hyperedge degree matrix represents the weight of a hyperedge, which is equal to the sum of the weights of the vertices connected by the hyperedge.

[0073] Each element of the vertex degree matrix represents the weight of a vertex, which is equal to the weight of the vertex in the hyperedge connected to the vertex multiplied by the weight of the hyperedge.

[0074] In step S5, the specific steps are as follows:

[0075] S51: selecting the eigenvectors corresponding to the first K smallest eigenvalues of the hypergraph Laplacian matrix according to the number of cell categories:

[0076] S52: performing row normalization on the eigenvectors selected in step S51 to obtain normalized eigenvectors;

[0077] S53: clustering the normalized eigenvectors by using the K-means method to obtain a clustering result.

[0078] In this embodiment, a multi-scale similarity matrix is constructed from a gene expression matrix; a cell hypergraph is generated from the multi-scale similarity matrix; the cell hypergraphs are fused; the hypergraph Laplacian matrix of the fused cell hypergraph is decomposed by SVD; the eigenvectors corresponding to the first K smallest eigenvalues are extracted, and K-means is used to obtain a clustering result, thereby improving the clustering effect of scRNA-seq data.

[0079] Embodiment 2

[0080] The steps of this embodiment are the same as those of Embodiment 1, except that each step is applied to a specific example. Specifically, the steps include the following steps:

[0081] S1: converting a gene expression matrix into a multi-scale similarity matrix by multi-scale similarity learning; the specific steps are as follows:

[0082] S11: taking the Treutlein (GSE52583) dataset as an example, the normalized gene expression data is represented as , where each row represents a gene expression vector of a cell, i.e. , each column represents the gene expression level of the same gene in different cells, where ​=80 represents the number of cells, =959 represents the number of genes, i.e. , .

[0083] S12: Similarity matrixes are constructed for gene expression data Three similarity matrixes with size , , and are constructed, where represents the similarity between cell under the corresponding similarity calculation method, =4 represents the number of nearest neighbors, and the value of the nearest neighbor is selected as The value of is determined by the number of cells and the proportion of the selected nearest neighbor, and the similarity between cells and cells in the gene expression data is calculated by multi-scale similarity learning:

[0084] (1)

[0085] (2)

[0086] In formula (1)~formula (2):

[0087] represents the similarity matrix calculated by the Euclidean distance,

[0088] represents the Euclidean distance between cell and cell ,

[0089] is a scaling index for controlling the overall similarity;

[0090] (3)

[0091] (4)

[0092] (5)

[0093] In formula (3)~formula (5):

[0094] represents the similarity matrix calculated by the Pearson correlation coefficient,

[0095] represents the Pearson correlation coefficient between cell and cell ,

[0096] Indicates the The first The expression level of genes,

[0097] Indicates all The average value of M=959,

[0098] A scaling metric to control the overall similarity;

[0099] (6)

[0100] (7)

[0101] (8)

[0102] In formulas (6) to (8):

[0103] Represents the similarity matrix calculated by the Spearman correlation coefficient,

[0104] Represents cells and cells The Spearman correlation coefficient between

[0105] Indicates the The gene in The expression ranking of cells

[0106] A scaling indicator to control the overall similarity.

[0107] Multi-scale similarity matrix 、 and Symmetrize:

[0108] (9)

[0109] (10)

[0110] (11)

[0111] S2: Generate a cell hypergraph based on the multi-scale similarity matrix; the specific steps are:

[0112] Through the multi-scale similarity matrix 、 and Generating multi-scale cell hypergraphs 、 and and their corresponding association matrix 、 and ; denote the vertex set of each vertex as a cell;

[0113] (12)

[0114] (13)

[0115] (14)

[0116] (15)

[0117] (16)

[0118] (17)

[0119] In formula (12) to formula (17):

[0120] denote the hyperedge set corresponding to the hypergraph generated by the th similarity matrix,

[0121] denote the hyperedge set composed of the =4 neighbors of the cell vertex in the th similarity matrix,

[0122] 、 and denote the hyperedge weight matrix corresponding to the generated cell hypergraph, which are unit matrices with a dimension of =80×80,

[0123] 、 and denote the association matrix corresponding to the generated cell hypergraph with a dimension of =80×80, which represents the importance of the cell vertex in the hyperedge .

[0124] S3: fuse the cell hypergraph by a fusion algorithm; the specific steps are as follows:

[0125] fuse the multi-scale cell hypergraphs 、 and to construct a fused cell hypergraph , achieved by averaging the fusion correlation matrix:

[0126] (18)

[0127] (19)

[0128] (20)

[0129] In formula (18)-formula (20):

[0130] represents the hyperedge set of the fused cell hypergraph,

[0131] Indicates the first A super edge,

[0132] is the first cell in the 3-cell hypergraph The sum of the superedges,

[0133] Represents the association matrix of the fused cell hypergraph, with dimension =80×80,

[0134] Represents the hyperedge weight matrix of the fused cell hypergraph, which is a unit matrix with dimension =80×80.

[0135] S4: Calculate the hypergraph Laplacian matrix by calculating the fused cell hypergraph obtained in step S3, and perform SVD decomposition to obtain the eigenvectors; the specific steps are:

[0136] S41: By fusing the cell hypergraph association matrix Constructing the hypergraph Laplacian matrix :

[0137] (twenty one)

[0138] In formula (21):

[0139] The hyperedge degree matrix of the fused cell hypergraph is a diagonal matrix with dimension =80×80,

[0140] Indicates the The weight of a hyperedge is equal to the sum of the weights of the vertices connected by the hyperedge.

[0141] Represents the vertex degree matrix of the fused cell hypergraph, which is a diagonal matrix with dimension =80×80,

[0142] Indicates the The weight of a vertex is equal to the weight of the vertex in the hyperedge connected to the vertex multiplied by the hyperedge weight.

[0143] Represents the identity matrix, with dimensions =80×80.

[0144] S42: Laplacian Matrix of Hypergraph Perform SVD decomposition:

[0145] (twenty two)

[0146] In formula (22):

[0147] represents a left singular matrix,

[0148] represents the singular value matrix,

[0149] represents a right singular matrix.

[0150] S5: Extract the first K=5 smallest eigenvalue eigenvectors from the eigenvectors obtained in step S4, and perform K-means to obtain the clustering results; the specific steps are as follows:

[0151] S51: Select the hypergraph Laplacian matrix forward = The eigenvectors corresponding to the 5 smallest eigenvalues ​​are of size :

[0152] ,Pick (twenty three)

[0153] In formula (23):

[0154] Indicates the The eigenvector corresponding to the minimum eigenvalue is taken represents the eigenvector corresponding to the fifth smallest eigenvalue,

[0155] =5 means the number of cell types is 5,

[0156] Pick The row vector represents the embedding representation of the cell.

[0157] S52: Perform row normalization on the feature vector selected in step S51 to obtain a normalized feature vector :

[0158] ,Pick (twenty four)

[0159] In formula (24):

[0160] Representation matrix No. OK, Representation matrix No. OK,

[0161] Representation matrix No. OK norm, Representation matrix No. OK norm,

[0162] Represents a very small constant used to avoid division by 0.

[0163] The K-means method is used to normalize the feature vector Perform clustering and obtain clustering results .

[0164] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0165] Four performance evaluation indicators, such as Adjusted Rand Index (ARI), Accuracy (ACC), Normalized Mutual Information (NMI), and Purity, were used to compare the clustering results of the clustering method proposed in the present invention with those of three classic methods, MTGDC, MPSSC, and SIMLR, to verify the effectiveness of the method of the present invention in clustering single-cell RNA sequencing data.

[0166] Performance comparison results are as follows Figure 2 As shown in the figure, the method of the present invention shows a significant advantage in the comparison of the four evaluation indicators, with the highest values ​​in all of them. This shows that the method of the present invention is effective in clustering single-cell RNA sequencing data and has high accuracy.

[0167] Figure 3For the comparison chart of the clustering effect of the t-SNE-based classical method of the method and the comparison method, the distance between the cell clusters of the method is large, and the visualization effect is good, indicating that the method can effectively distinguish different types of cells. The above results show that, compared with the existing single-cell RNA sequencing data clustering method, the method can obtain better clustering results.

[0168] Embodiment 3

[0169] This embodiment is used to realize the principle of the above method embodiment and constructs a single-cell RNA sequencing data clustering system based on a multi-scale hypergraph, which includes a matrix conversion submodule, a hypergraph generation submodule, a fusion submodule, a decomposition submodule and a clustering submodule.

[0170] The matrix conversion submodule is used to convert the gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning.

[0171] The hypergraph generation submodule is used to generate a cell hypergraph based on the multi-scale similarity matrix.

[0172] The fusion submodule is used to obtain a fused cell hypergraph by using a fusion algorithm according to the cell hypergraph.

[0173] The decomposition submodule is used to calculate a hypergraph Laplacian matrix through the fused cell hypergraph, and perform SVD decomposition to obtain a feature vector.

[0174] The clustering submodule is used to extract the feature vector corresponding to the first K smallest eigenvalues, and perform K-means to obtain a clustering result.

[0175] Each submodule is mainly used to realize each step of the method embodiment, and will not be described here.

[0176] It should be noted that, according to the needs of implementation, each step / component described in the present application can be split into more steps / components, or two or more steps / components or part of the operation of the steps / components can be combined into a new step / component to achieve the purpose of the present application.

[0177] The embodiment also includes a processor, a communication interface, a memory and a communication bus; the processor, the communication interface and the memory complete the communication among each other through the communication bus; the memory stores a computer program, and when the program is executed by the processor, the processor executes the steps of a method for quickly verifying an offline vehicle AEB system.

[0178] The embodiment also provides a computer readable storage medium, which stores executable instructions, and the instructions are executed by a processor to make the processor realize a method for quickly verifying an offline vehicle AEB system.

[0179] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects.

[0180] Furthermore, the present application can take the form of a computer program product on one or more computer readable storage media (including, but not limited to, disk memory, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0181] The present application is described in reference to the block diagrams of devices (systems) according to embodiments 1 of the present application and flowcharts of methods and computer program products according to embodiment 2 of the present application. It will be understood that each flow or block in the flowcharts or block diagrams, and combinations of flows or blocks in the flowcharts or block diagrams, can be implemented by computer program instructions.

[0182] These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart or block diagram block or blocks. Figure 1 Figure 1 A system for implementing each flow or a combination of flows or blocks specified in the flowchart or block diagram block or blocks.

[0183] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flowchart or block diagram block or blocks. Figure 1 Figure 1 A method for implementing each flow or a combination of flows or blocks specified in the flowchart or block diagram block or blocks.

[0184] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flowchart or block diagram block or blocks. Figure 1 Figure 1 A method for implementing each flow or a combination of flows or blocks specified in the flowchart or block diagram block or blocks.

[0185] The above embodiments are only used to illustrate the design ideas and characteristics of the present application, and the purpose is to make those skilled in the art understand the present application and implement it, and the protection scope of the present application is not limited to the above embodiments. Therefore, any equivalent changes or modifications made according to the principles and design ideas disclosed in the present application are within the protection scope of the present application.​​​

Claims

1. A multi-scale hypergraph-based clustering method for single-cell RNA sequencing data, characterized by: The following steps are involved: S1: Convert the gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning; the specific steps are: S11: Gene expression data are obtained and normalized, and then represented as a gene expression matrix, where each row of the matrix represents the gene expression vector of a cell, and each column represents the gene expression level of the same gene in different cells; S12: construct a similarity matrix with the same three dimensions for the gene expression data and convert it into a multi-scale similarity matrix, and symmetrize the multi-scale similarity matrix; S2: Generate a cell hypergraph based on the multi-scale similarity matrix; the specific steps are: Generate a multi-scale cell hypergraph described by a triple {vertex set, hyperedge set, hyperedge weight matrix} and the corresponding association matrix through a multi-scale similarity matrix; S3: A fusion algorithm is used to obtain a fused cell hypergraph based on the cell hypergraph; the specific steps are: The correlation matrices corresponding to the cell hypergraphs are averaged to fuse the correlation matrices, and the multi-scale cell hypergraphs are fused to form a fused cell hypergraph. S4: Calculate the hypergraph Laplacian matrix by fusing the cell hypergraph and perform SVD decomposition to obtain the eigenvectors; S5: Extract the eigenvectors corresponding to the first K smallest eigenvalues ​​and perform K-means to obtain the clustering results.

2. The method for clustering single-cell RNA sequencing data based on a multi-scale hypergraph according to claim 1, characterized in that: In the step S2, Each vertex in the vertex set is used to represent a cell; The hyperedge set represents the hyperedge set consisting of the neighbors of the cell vertices in the similarity matrix; The incidence matrix is ​​used to represent the importance of cell vertices in the hyperedge.

3. The method for clustering single-cell RNA sequencing data based on a multi-scale hypergraph according to claim 1, characterized in that: In the step S4, the specific steps are: S41: Construct the hypergraph Laplacian matrix by fusing the incidence matrix, hyperedge degree matrix, vertex degree matrix and hyperedge weight matrix of the cell hypergraph; S42: Perform SVD decomposition on the hypergraph Laplacian matrix to obtain eigenvectors.

4. The method for clustering single-cell RNA sequencing data based on a multi-scale hypergraph according to claim 3, characterized in that: In the step S41, Each element of the hyperedge degree matrix represents the weight of a hyperedge, which is equal to the sum of the weights of the vertices connected by the hyperedge; Each element of the vertex degree matrix represents the weight of a vertex, which is equal to the weight of the vertex in the hyperedge connected to the vertex multiplied by the hyperedge weight.

5. The method for clustering single-cell RNA sequencing data based on a multi-scale hypergraph according to claim 1, characterized in that: In the step S5, the specific steps are: S51: Select the eigenvectors corresponding to the first K smallest eigenvalues ​​of the hypergraph Laplacian matrix according to the number of cell categories: S52: performing row normalization on the feature vector selected in step S51 to obtain a normalized feature vector; S53: Use the K-means method to cluster the normalized feature vectors to obtain clustering results.

6. A multi-scale hypergraph-based single-cell RNA sequencing data clustering system, characterized by: The matrix conversion submodule is used to convert the gene expression matrix into a multi-scale similarity matrix through multi-scale similarity learning; specifically: Gene expression data are obtained and normalized, and then represented as a gene expression matrix, where each row of the matrix represents the gene expression vector of a cell, and each column represents the gene expression level of the same gene in different cells; Construct a similarity matrix with the same three dimensions for gene expression data and convert it into a multi-scale similarity matrix, and then symmetrize the multi-scale similarity matrix; The hypergraph generation submodule is used to generate a cell hypergraph based on a multi-scale similarity matrix; specifically: Generate a multi-scale cell hypergraph described by a triple {vertex set, hyperedge set, hyperedge weight matrix} and the corresponding association matrix through a multi-scale similarity matrix; The fusion submodule is used to obtain a fused cell hypergraph using a fusion algorithm based on the cell hypergraph; specifically: The correlation matrices corresponding to the cell hypergraphs are averaged to fuse the correlation matrices, and the multi-scale cell hypergraphs are fused to form a fused cell hypergraph. The decomposition submodule is used to calculate the hypergraph Laplacian matrix by fusing the cell hypergraph and perform SVD decomposition to obtain the eigenvectors; The clustering submodule is used to extract the eigenvectors corresponding to the first K smallest eigenvalues ​​and perform K-means to obtain the clustering results.

7. A computer memory, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes a single-cell RNA sequencing data clustering method based on a multi-scale hypergraph as described in any one of claims 1 to 5.

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