Single-cell Hi-C clustering method and system based on contact number weight smoothing and feature fusion

Abstract

The application relates to a single-cell Hi-C clustering method and system based on contact number weight smoothing and feature fusion, which comprises the following steps: (1) data preprocessing; (2) contact number weight-based smoothing; using a weight matrix to quantify the influence of different neighbor fragments on a target chromosome fragment; (3) restart random walk smoothing; using a restart random walk algorithm to perform smoothing processing on the chromosome contact matrix after the contact number weight-based smoothing processing; (4) contact binarization; (5) principal component extraction; using KPCA to perform dimension reduction and generate cell embedding; (6) feature fusion; (7) spectral clustering; using a spectral clustering algorithm to realize cell clustering. The single-cell Hi-C clustering method provided by the application is obviously superior to existing clustering methods, greatly improves the clustering effect when a large-scale single-cell Hi-C data set is processed, and can identify cell types with a small number of cells in the data set.

Description

Technical Field

[0001] This invention relates to a single-cell Hi-C clustering method and system based on contact number weight smoothing and feature fusion, belonging to the field of data clustering technology. Background Technology

[0002] Hi-C technology, through digesting and reconnecting spatially proximate chromosome segments and performing high-throughput sequencing, can determine spatial interactions between different sites on chromosomes. Single-cell Hi-C technology can capture the chromosome conformation of a single cell, enabling us to obtain chromosome interaction information at the single-cell level and further study the differences in genomic structure between different cell types, providing data and technical support for cell clustering. Existing high-performance clustering method for single-cell Hi-C data is scHiCluster, which uses convolutional smoothing and restarted random walk algorithms to process the chromosome contact matrix in single cells and uses principal component analysis (PCA) to generate cell embeddings. Finally, scHiCluster uses the K-means algorithm to cluster cells based on the cell embeddings. However, the scHiCluster algorithm still has the following problems: first, its clustering effect is poor when processing large-scale single-cell Hi-C datasets; second, it is difficult to identify cell types with a small number of cells in the dataset. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion;

[0004] This invention also provides a single-cell Hi-C clustering system based on contact number weight smoothing and feature fusion;

[0005] The proposed single-cell Hi-C clustering method significantly outperforms existing clustering methods, greatly improving the clustering effect when processing large-scale single-cell Hi-C datasets, and can identify cell types with a small number of cells in the dataset.

[0006] Terminology Explanation:

[0007] 1. Single-cell Hi-C data: This refers to data acquired through single-cell Hi-C technology, generally including two categories: cell characteristics and interaction information. Cell characteristic data contains specific cell information, such as cell type and the percentage of captured chromosome fragments mapped to the human genome sequence. Interaction information data contains specific information about chromosome fragment contacts within the cell, such as the start and end positions of the contacts. The processed data consists of three columns: the first and second columns are the chromosome fragment numbers after cutting, and the third column is the contact count between two chromosome fragments. For example, 47 60 5 indicates that there are 8 contacts between chromosome fragments 47 and 60.

[0008] 2. Chromosome interaction data, i.e., contact number, refers to the number of contact points between two chromosome segments in a three-dimensional spatial structure.

[0009] 3. KPCA, Kernel Principal Component Analysis, is a nonlinear data processing method. Its core idea is to project the data in the original space to a high-dimensional feature space through a nonlinear mapping, and then perform data processing based on principal component analysis (PCA) in the high-dimensional feature space.

[0010] The technical solution of this invention is as follows:

[0011] A single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion includes:

[0012] (1) Data preprocessing: Normalize chromosome interaction data in single-cell Hi-C data into chromosome contact matrices at a given resolution;

[0013] (2) Smoothing based on contact number weights; each row in the chromosome contact matrix represents the interaction information between the chromosome segment and all its neighbors; a weight matrix is ​​used to quantify the influence of different neighbor segments on the target chromosome segment;

[0014] (3) Restart random walk smoothing; use the restart random walk algorithm to smooth the chromosome contact matrix after the smoothing process based on contact number weight in step (2);

[0015] (4) Contact binarization; perform binarization on the matrix after the random walk smoothing process in step (3);

[0016] (5) Principal component extraction; KPCA was used for dimensionality reduction and cell embedding was generated;

[0017] (6) Feature fusion; Each row of the cell embedding generated by KPCA represents the chromosome structure information in a cell; Euclidean distance between cells is calculated through cell embedding, and a distance matrix is ​​constructed as a supplement to the cell embedding; The distance matrix and the matrix obtained after step (4) are merged by row merging to form a new feature matrix;

[0018] (7) Spectral clustering; Cell clustering is implemented using the spectral clustering algorithm.

[0019] According to a preferred embodiment of the present invention, step (1), standardizing the chromosome interaction data in the single-cell Hi-C data into a chromosome contact matrix at a given resolution, includes:

[0020] First, each chromosome is divided into n segments, where n = L / R, L represents the chromosome length, and R represents the resolution.

[0021] Secondly, the single-cell Hi-C data are represented as a chromosome contact matrix A. n*n A ij It is chromosome contact matrix A n*n The element in, A ij This represents the number of contacts between the i-th and j-th chromosome segments.

[0022] According to a preferred embodiment of the present invention, in step (2), a weight matrix P is used to quantify the influence of different neighboring segments on the target chromosome segment, including:

[0023] Based on the contact information of the target chromosome segments, the weight information of all neighbors of each target chromosome segment is generated and used as the row vector of the weight matrix P; two chromosome segments with a contact number not equal to 0 are neighbors, and the chromosome contact matrix A is... n*n The formula for calculating the corresponding weight matrix P is shown in equation (I):

[0024]

[0025] In equation (I), k represents the number of smoothing operations, and the range of k is: 1≤k≤6;

[0026] Chromosome contact matrix A n*n The smoothing process is shown in equations (II) and (III):

[0027] B (k) =A (k) ·P (k) (II)

[0028]

[0029] In equations (II) and (III), S represents the smoothed chromosome contact matrix, and A represents the chromosome contact matrix A. n*n Using the matrix S after the first smoothing 1 As input A for the second smoothing process 2 A (m+1) =S (m) It only smooths the upper triangular elements in A, and does not smooth the elements on the diagonal of A.

[0030] According to a preferred embodiment of the present invention, in step (3), the chromosome contact matrix after smoothing based on contact number weights in step (2) is smoothed using a restarted random walk algorithm; including:

[0031] Let S be an undirected weighted graph, where nodes represent chromosome segments. ij Represents the weight of the edge between chromosome segments i and j; the matrix S is smoothed using a restarted random walk algorithm, and matrix R is the normalized matrix of matrix S, defined as:

[0032] Each step of the restart random walk algorithm offers two choices: randomly walk to the next node or return to the starting node. This invention specifies the restart probability *r* as the probability of returning to the starting node, and 1-*r* as the probability of walking to an adjacent chromosome segment. The specific implementation process involves repeated calculations according to equation (IV):

[0033] U (t) =rU (t-1) R+(1-r)I (IV)

[0034] In equation (IV), t represents the number of iterations, and U (t) This represents the matrix smoothed by the random walk algorithm after t restarts. Restarting the random walk algorithm starts from U... (0) Start iteration, U (0) Both I and I are identity matrices. This represents the probability that chromosome segment i will migrate to chromosome segment j in the t-th iteration, when the condition ||U|| is satisfied. (t) -U (t-1) ||2≤10 -6 At that time, the restarted random walk process on matrix U converges, yielding the final matrix.

[0035] According to a preferred embodiment of the present invention, in step (4), the matrix after the random walk smoothing process in step (3) is subjected to contact binarization, including:

[0036] First, the matrix smoothed by the restarted random walk... Convert to a length of (n) (s) )2 A one-dimensional vector, where s represents the chromosome number and n... (s) This represents the number of chromosome segments divided from chromosome s;

[0037] Then, combine the vectors corresponding to chromosome s in all cells into a matrix. b represents the number of cells that need to be clustered;

[0038] For matrix Perform contact binarization to generate matrix

[0039] Finally, the matrices corresponding to the 23 chromosomes are merged by row merging. Combined into a single matrix F b*c ,in

[0040] Further preferred, contact binarization is achieved by setting a threshold thr i To filter matrix The elements in the selection process are shown in equation (V):

[0041]

[0042] In equation (V), thr i This represents the 80th percentile of the i-th row.

[0043] According to a preferred embodiment of the present invention, step (5), using KPCA for dimensionality reduction and generating cell embeddings, includes:

[0044] a. Calculate the average value of the original dataset, and then subtract the average value from all data in the original dataset;

[0045] b. Calculate the kernel matrix K using the kernel function of KPCA;

[0046] c. Calculate the eigenvalues ​​and eigenvectors of the kernel matrix;

[0047] d. Arrange the eigenvectors into a matrix by row according to the magnitude of their corresponding eigenvalues, and take the first k rows to form matrix P;

[0048] e, Y = PX, yields the dimensionality-reduced data Y.

[0049] Further preferred, the kernel function of KPCA is cosine.

[0050] According to a preferred embodiment of the present invention, in step (6), each row of the distance matrix Q is concatenated with the corresponding row of the cell embedding matrix F to obtain the final feature fusion matrix, i.e., the new feature matrix X.

[0051] According to a preferred embodiment of the present invention, in step (7), cell clustering is performed using a spectral clustering algorithm, including:

[0052] ① Input a new feature matrix X and construct a similarity matrix S using radial basis functions, where each row of the new feature matrix X contains the feature information of a cell;

[0053] ② Construct a similarity graph G based on the similarity matrix S, and obtain the adjacency matrix W from the similarity graph G;

[0054] ③ Calculate the degree matrix D and the Laplace matrix L = DW;

[0055] ④ Calculate the normalized Laplace matrix

[0056] ⑤ Calculate the n-dimensional eigenvectors corresponding to the k smallest eigenvalues ​​in the standardized Laplacian matrix L′;

[0057] ⑥ Combine the first k eigenvectors into an n x k matrix V n*k ;

[0058] ⑦ Apply equation (VI) to matrix V n*k Standardize:

[0059]

[0060] In formula (VI), Each row in matrix M represents a sample, which is the low-dimensional representation of each row in matrix X;

[0061] ⑧ Use the k-means algorithm to perform clustering to obtain a cluster partition containing k clusters.

[0062] A single-cell Hi-C clustering system based on contact number weight smoothing and feature fusion includes:

[0063] The data preprocessing module is configured to normalize chromosome interaction data in single-cell Hi-C data into a chromosome contact matrix at a given resolution.

[0064] The contact number-weighted smoothing module is configured such that each row in the chromosome contact matrix represents the interaction information between the chromosome segment and all its neighbors; a weight matrix is ​​used to quantify the influence of different neighbor segments on the target chromosome segment.

[0065] The restart random walk smoothing module is configured to use the restart random walk algorithm to smooth the chromosome contact matrix after smoothing based on contact number weights.

[0066] The contact binarization module is configured to perform binarization on the matrix after the restarted random walk smoothing process.

[0067] The principal component extraction module is configured to use KPCA for dimensionality reduction and generate cell embeddings.

[0068] The feature fusion module is configured to: each row of the cell embedding generated by KPCA represents the chromosome structure information of a cell; calculate the Euclidean distance between cells through the cell embedding and construct a distance matrix as a supplement to the cell embedding; merge the distance matrix and the matrix obtained after dimensionality reduction using KPCA and cell embedding processing by row merging to form a new feature matrix;

[0069] The spectral clustering module is configured to use a spectral clustering algorithm to perform cell clustering.

[0070] The beneficial effects of this invention are as follows:

[0071] 1. Due to the current immaturity of Hi-C data acquisition technology, a discrepancy exists between the number of contacts in Hi-C data and the actual number of contacts. Therefore, this invention proposes a novel method to reduce this discrepancy by minimizing the specificity of chromosome structures in different cell types. Existing clustering methods smooth the contact information of target chromosome segments using contact information from linearly adjacent chromosome segments or spatially adjacent chromosome segments. However, these methods ignore the weight differences between spatially adjacent chromosome segments during the smoothing process. The novel contact number-based weighted smoothing method proposed in this invention assigns different weights to neighbor segments with different contact numbers, using these weights to quantify the influence of neighbor segments with different contact numbers on the target chromosome segment, thereby generating cell embeddings with more accurate cellular characteristics.

[0072] 2. The feature fusion method proposed in this invention merges the cell embedding matrix generated by KPCA dimensionality reduction with the Euclidean distance matrix between different cells, thereby achieving the effect of fusing intracellular chromosome structure information with intercellular distance information, thus supplementing the cell's feature information.

[0073] 3. The spectral clustering algorithm used in this invention is an algorithm developed from graph theory and has been widely used for clustering various types of data. Compared with the traditional K-Means algorithm used by the scHiCluster clustering method, spectral clustering is more adaptable to data distribution and has excellent clustering results. Attached Figure Description

[0074] Figure 1 This is a flowchart of the single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion of the present invention;

[0075] Figure 2 This is a diagram comparing the clustering performance of five clustering methods on 626 human cell datasets in ML1 and ML3.

[0076] Figure 3 This diagram illustrates the comparison of clustering performance of five clustering methods on the Ramani dataset, which contains 2655 human cells.

[0077] Figure 4(a) is a schematic diagram comparing the performance of five clustering methods based on ARI evaluation metrics at cell counts of 800, 1000, 1200, 1400, and 1600.

[0078] Figure 4(b) is a schematic diagram comparing the performance of five clustering methods based on the AMI evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600.

[0079] Figure 4(c) is a schematic diagram comparing the performance of five clustering methods based on the HM evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600.

[0080] Figure 4(d) is a schematic diagram comparing the performance of five clustering methods based on the FM evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600. Detailed Implementation

[0081] The present invention will be further defined below with reference to the accompanying drawings and embodiments, but is not limited thereto.

[0082] Example 1

[0083] A single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion, such as Figure 1 As shown, it includes:

[0084] (1) Data preprocessing: Normalize chromosome interaction data in single-cell Hi-C data into chromosome contact matrices at a given resolution;

[0085] (2) Smoothing based on contact number weights: Existing smoothing methods in clustering smooth the contact information of target chromosome segments through the contact information of linearly adjacent chromosome segments or spatially adjacent chromosome segments. However, these methods ignore the weight differences between spatially adjacent chromosome segments during the smoothing process. Therefore, to obtain more accurate contact information, this invention proposes a new smoothing method based on contact number weights. Each row in the chromosome contact matrix represents the interaction information between a chromosome segment and all its neighbors; since different neighbor segments have different contact numbers with the target segment, the influence of different neighbor segments on the target segment is also different. Therefore, a weight matrix is ​​needed to quantify the influence of different neighbor segments on the target chromosome segment;

[0086] (3) Restart random walk smoothing; use the restart random walk algorithm to smooth the chromosome contact matrix after the smoothing process based on contact number weight in step (2);

[0087] (4) Contact binarization; perform binarization on the matrix after the random walk smoothing process in step (3);

[0088] (5) Principal component extraction; KPCA was used for dimensionality reduction and cell embedding was generated;

[0089] (6) Feature fusion; Each row of the cell embedding generated by KPCA represents the chromosome structure information in a cell; Euclidean distance between cells is calculated through cell embedding, and a distance matrix is ​​constructed as a supplement to the cell embedding; Since the cell embedding and its related Euclidean distance matrix have the same number of rows, the distance matrix and the matrix obtained after processing in step (4) are merged by row merging to form a new feature matrix; In this process, the feature information of the cell is further supplemented by fusing the chromosome structure information within the cell and the distance information between cells.

[0090] (7) Spectral clustering; Cell clustering is implemented using the spectral clustering algorithm.

[0091] Example 2

[0092] The difference between this single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion as described in Example 1 is that:

[0093] In step (1), the chromosome interaction data in the single-cell Hi-C data is normalized into a chromosome contact matrix at a given resolution, including:

[0094] First, each chromosome is divided into n segments, where n = L / R, L represents the chromosome length, and R represents the resolution.

[0095] Secondly, the single-cell Hi-C data are represented as a chromosome contact matrix A.n*n A ij It is chromosome contact matrix A n*n The element in, A ij This represents the number of contacts between the i-th and j-th chromosome segments.

[0096] In step (2), a weight matrix P is used to quantify the influence of different neighboring segments on the target chromosome segment, including:

[0097] Based on the contact information of the target chromosome segments, the weight information of all neighbors of each target chromosome segment is generated and used as the row vector of the weight matrix P; two chromosome segments with a contact number not equal to 0 are neighbors, and the chromosome contact matrix A is... n*n The formula for calculating the corresponding weight matrix P is shown in equation (I):

[0098]

[0099] In equation (I), k represents the number of smoothing operations, and the range of k is: 1≤k≤6;

[0100] Chromosome contact matrix A n*n The smoothing process is shown in equations (II) and (III):

[0101] B (k) =A (k) ·P (k) (II)

[0102]

[0103] In equations (II) and (III), S represents the smoothed chromosome contact matrix, and A represents the chromosome contact matrix A. n*n To reduce noise and enhance features, inspired by the concept of convolution, this invention uses the matrix S after the first smoothing. 1 As input A for the second smoothing process 2 A (m+1) =S (m) Considering that the chromosome contact matrix A is symmetric, this invention only smooths the upper triangular elements of A, and does not smooth the elements on the diagonal of A. Therefore, the number of columns is always greater than the number of rows during the smoothing process.

[0104] In step (3), the chromosome contact matrix after smoothing based on contact number weights in step (2) is smoothed using the restarted random walk algorithm; including:

[0105] Rebooting the random walk algorithm helps infer relationships between nodes from a global perspective. Therefore, this invention uses the rebooted random walk algorithm to capture multifaceted relationships between two nodes from the overall structural information of the graph. Matrix S describes the connections between chromosome segments; therefore, S is represented as an undirected weighted graph, where nodes represent chromosome segments. ij Represents the weight of the edge between chromosome segments i and j; a restarted random walk algorithm is used to smooth matrix S, mining the affinity between chromosome segments from a global perspective and improving the accuracy of contact information. Matrix R is the normalized matrix of matrix S, defined as:

[0106] Each step of the restart random walk algorithm offers two choices: randomly walk to the next node or return to the starting node. This invention specifies the restart probability *r* as the probability of returning to the starting node, and 1-*r* as the probability of walking to an adjacent chromosome segment. The specific implementation process involves repeated calculations according to equation (IV):

[0107] U (t) =rU (t-1) R+(1-r)I (IV)

[0108] In equation (IV), t represents the number of iterations, and U (t) This represents the matrix smoothed by the random walk algorithm after t restarts. Restarting the random walk algorithm starts from U... (0) Start iteration, U (0) Both I and I are identity matrices. This represents the probability that chromosome segment i will migrate to chromosome segment j in the t-th iteration, when the condition ||U|| is satisfied. (t) -U (t-1) ||2≤10 -6 At that time, the restarted random walk process on matrix U converges, yielding the final matrix.

[0109] In step (4), the matrix after the random walk smoothing process in step (3) is subjected to contact binarization, including:

[0110] First, in order to obtain overall information about the cells, the matrix smoothed by the restarted random walk is... Convert to a length of (n) (s) ) 2 A one-dimensional vector, where s represents the chromosome number and n... (s) This represents the number of chromosome segments divided from chromosome s;

[0111] Then, combine the vectors corresponding to chromosome s in all cells into a matrix. b represents the number of cells that need to be clustered;

[0112] To standardize the scale of chromosome contact number in different cells, the matrix... Perform contact binarization to generate matrix

[0113] Finally, the matrices corresponding to the 23 chromosomes are merged by row merging. Combined into a single matrix F b*c ,in

[0114] Contact binarization is achieved by setting a threshold thr i To filter matrix The elements in the selection process are shown in equation (V):

[0115]

[0116] In equation (V), thr i This represents the 80th percentile of the i-th row.

[0117] The contact binarized matrices D and F are binary matrices, where connections between chromosome segments are represented only by 0s and 1s. This standardizes the scale of chromosome contact numbers in the contact matrices of different cells. This process helps preserve the most important structural information on chromosomes.

[0118] In step (5), KPCA is used for dimensionality reduction and cell embedding generation, including:

[0119] a. Calculate the average value of the original dataset, and then subtract the average value from all data in the original dataset;

[0120] b. Calculate the kernel matrix K using the kernel function of KPCA;

[0121] c. Calculate the eigenvalues ​​and eigenvectors of the kernel matrix;

[0122] d. Arrange the eigenvectors into a matrix by row according to the magnitude of their corresponding eigenvalues, and take the first k rows to form matrix P;

[0123] e, Y = PX, yields the dimensionality-reduced data Y.

[0124] The feature dimension of the binary matrix F after contact binarization is The matrix F is too large. To avoid the curse of dimensionality and extract the principal components of chromosome structure information in cells, matrix F must be reduced in dimensionality. Since no studies have shown that chromosome structure data are linearly correlated, KPCA is used for dimensionality reduction and to generate cell embeddings.

[0125] The kernel function of KPCA is cosine.

[0126] In step (6), each row of the cell embedding matrix F generated by KPCA dimensionality reduction represents the chromosome structure information of a cell. We calculate the Euclidean distance between each cell according to the Euclidean distance calculation formula and then generate the distance matrix Q. Since the distance matrix Q and the cell embedding matrix F have the same number of rows, we concatenate each row of the distance matrix Q with the corresponding row of the cell embedding matrix F to obtain the final feature fusion matrix, i.e., the new feature matrix X. In this way, the feature fusion matrix X integrates the chromosome structure information within the cell and the distance information between cells, further supplementing the cell's feature information.

[0127] In step (7), cell clustering is performed using a spectral clustering algorithm, including:

[0128] ① Input a new feature matrix X and construct a similarity matrix S using radial basis functions (RBF), where each row of the new feature matrix X contains the feature information of a cell;

[0129] ② Construct a similarity graph G based on the similarity matrix S, and obtain the adjacency matrix W from the similarity graph G;

[0130] ③ Calculate the degree matrix D and the Laplace matrix L = DW;

[0131] ④ Calculate the normalized Laplace matrix

[0132] ⑤ Calculate the n-dimensional eigenvectors corresponding to the k smallest eigenvalues ​​in the standardized Laplacian matrix L′;

[0133] ⑥ Combine the first k eigenvectors into an n x k matrix V n*k ;

[0134] ⑦ Apply equation (VI) to matrix V n*k Standardize:

[0135]

[0136] In formula (VI), Each row in matrix M represents a sample, which is the low-dimensional representation of each row in matrix X;

[0137] ⑧ Use the k-means algorithm to perform clustering to obtain a cluster partition containing k clusters.

[0138] The proposed clustering method scHiCSC was compared with four existing clustering methods (scHiCluster, Raw PCA, HiCRep+MDS, and Decay) in terms of performance. During the comparison, five commonly used clustering evaluation metrics—Adjusted RandIndex (ARI), Adjusted Mutual Information (AMI), Homogeneity (HM), and Fowlkes Mallows (FM)—were used to evaluate the performance of the five methods. The dataset used was the Ramani dataset downloaded from the GEO database. The Ramani dataset is a typical Hi-C dataset, containing six parts: ML1, ML2, ML3, ML4, PL1, and PL2. These six parts contain information on four human cell lines: GM12878, HAP1, HeLa, and K562, totaling 2655 cells after filtering. Seven subsets of different sizes were extracted from the Ramani dataset and used as the datasets for comparative experiments. The number of different cell types contained in these subsets is shown in Table 1.

[0139] Table 1

[0140]

[0141] The ML1 and ML3 portions of the Ramani dataset were used by scHiCluster for clustering analysis of human cells. Therefore, the performance of five clustering methods was first compared using the human cell data contained in ML1 and ML3. After data preprocessing, 626 human cells were selected from ML1 and ML3. Figure 2 This diagram illustrates the comparison of the clustering performance of five clustering methods on 626 human cell datasets in ML1 and ML3. Figure 2 As can be seen, this invention outperforms the other four clustering methods in all four metrics: AMI, ARI, HM, and FM, demonstrating superior performance. Furthermore, scHiCSC achieves ARI, AMI, HM, and FM scores of 0.872, 0.878, 0.818, and 0.92, respectively, which are 5.4%, 6.7%, 6.6%, 2%, and 4.2% higher than the second-best clustering method, scHiCluster.

[0142] To compare the performance of five clustering methods on large-scale datasets, data from 2655 human cells were selected from six parts of the Ramani dataset, and the results were compared on this dataset. Figure 3 This diagram illustrates the performance comparison of five clustering methods on the Ramani dataset, which contains 2655 human cells.

[0143] To verify the generalization ability of scHiCSC on datasets of different scales, data of 800, 1000, 1200, 1400 and 1600 cells were randomly selected from the Ramani dataset, and the generalization ability of the five clustering methods was compared. Figure 4(a) shows a performance comparison of five clustering methods based on the ARI evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600; Figure 4(b) shows a performance comparison of five clustering methods based on the AMI evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600; Figure 4(c) shows a performance comparison of five clustering methods based on the HM evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600; Figure 4(d) shows a performance comparison of five clustering methods based on the FM evaluation index at cell counts of 800, 1000, 1200, 1400, and 1600. Figures 4(a) to 4(d) As can be seen from the above, compared with the other four clustering methods, the clustering method scHiCSC proposed in this invention has excellent generalization ability.

[0144] The number of cells varies across different cell types in practical clustering applications. Cell types with a larger number of cells have distinct characteristics and are easily identified, while cell types with a smaller number of cells are difficult to identify. Therefore, the clustering method scHiCSC proposed in this invention was compared with four other clustering methods in its ability to identify cell types with a smaller number of cells.

[0145] Table 2 shows the recognition performance of five clustering methods on datasets of different scales for GM12878 cells. As can be seen from Table 2, the four existing clustering methods—scHiCluster, Raw_PCA, HiCRep+MDS, and Decay—cannot effectively identify GM12878 from HAP1, K562, and HeLa. This is because the number of cells in GM12878 is much smaller than in the other three cell types, and when the total number of cells is large, GM12878 is easily confused with the other three cell types. However, the clustering method scHiCSC proposed in this invention can identify GM12878 to a certain extent. This indicates that scHiCSC also has a good recognition effect on cell types with a small number of cells.

[0146] Table 2

[0147]

[0148]

[0149] Example 3

[0150] A single-cell Hi-C clustering system based on contact number weight smoothing and feature fusion includes:

[0151] The data preprocessing module is configured to normalize chromosome interaction data in single-cell Hi-C data into a chromosome contact matrix at a given resolution.

[0152] The contact number-weighted smoothing module is configured such that each row in the chromosome contact matrix represents the interaction information between the chromosome segment and all its neighbors; a weight matrix is ​​used to quantify the influence of different neighbor segments on the target chromosome segment.

[0153] The restart random walk smoothing module is configured to use the restart random walk algorithm to smooth the chromosome contact matrix after smoothing based on contact number weights.

[0154] The contact binarization module is configured to perform binarization on the matrix after the restarted random walk smoothing process.

[0155] The principal component extraction module is configured to use KPCA for dimensionality reduction and generate cell embeddings.

[0156] The feature fusion module is configured to: each row of the cell embedding generated by KPCA represents the chromosome structure information of a cell; calculate the Euclidean distance between cells through the cell embedding and construct a distance matrix as a supplement to the cell embedding; merge the distance matrix and the matrix obtained after dimensionality reduction using KPCA and cell embedding processing by row merging to form a new feature matrix;

[0157] The spectral clustering module is configured to use a spectral clustering algorithm to perform cell clustering.

Claims

1. A single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion, characterized in that, include: (1) Data preprocessing; Normalize chromosome interaction data in single-cell Hi-C data to a chromosome contact matrix at a given resolution; (2) Smoothing based on contact number weights; each row in the chromosome contact matrix represents the interaction information between the chromosome segment and all its neighbors; a weight matrix is ​​used to quantify the influence of different neighbor segments on the target chromosome segment; (3) Restart random walk smoothing; use the restart random walk algorithm to smooth the chromosome contact matrix after the smoothing process based on contact number weight in step (2); (4) Contact binarization; perform binarization on the matrix after the random walk smoothing process in step (3); (5) Principal component extraction; KPCA was used for dimensionality reduction and cell embedding was generated; (6) Feature fusion; Each row of the cell embedding generated by KPCA represents the chromosome structure information of a cell; The Euclidean distance between cells is calculated through cell embedding, and a distance matrix is ​​constructed as a supplement to the cell embedding. The distance matrix and the matrix obtained after processing in step (4) are merged by row merging to form a new feature matrix. (7) Spectral clustering; Cell clustering is implemented using the spectral clustering algorithm; In step (3), the restart random walk algorithm is used to smooth the chromosome contact matrix after the smoothing process based on the contact number weight in step (2); include: Let S be an undirected weighted graph, where nodes represent chromosome segments. ij Represents the weight of the edge between chromosome segments i and j; the matrix S is smoothed using a restarted random walk algorithm, and matrix R is the normalized matrix of matrix S, defined as: Each step of the restart random walk algorithm offers two choices: randomly walk to the next node or return to the starting node. The restart probability *r* is specified as the probability of returning to the starting node, and 1-*r* is the probability of walking to an adjacent chromosome segment. The specific implementation process involves repeated calculations according to equation (IV): U (t) =rU (t-1) R+(1-r)I (IV) In equation (IV), t represents the number of iterations, and U (t) This represents the matrix smoothed by the random walk algorithm after t restarts. Restarting the random walk algorithm starts from U... (0) Start iteration, U (0) Both I and I are identity matrices. This represents the probability that chromosome segment i will migrate to chromosome segment j in the t-th iteration, when the condition ||U|| is satisfied. (t) -U (t-1) ||2≤10 -6 At that time, the restarted random walk process on matrix U converges, yielding the final matrix.

2. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 1, characterized in that, In step (1), the chromosome interaction data in the single-cell Hi-C data is normalized into a chromosome contact matrix at a given resolution, including: First, each chromosome is divided into n segments, where n = L / R, L represents the chromosome length, and R represents the resolution. Secondly, the single-cell Hi-C data are represented as a chromosome contact matrix A. n*n A ij It is chromosome contact matrix A n*n The element in, A ij This represents the number of contacts between the i-th and j-th chromosome segments.

3. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 1, characterized in that, In step (2), a weight matrix P is used to quantify the influence of different neighboring segments on the target chromosome segment, including: Based on the contact information of the target chromosome segments, the weight information of all neighbors of each target chromosome segment is generated and used as the row vector of the weight matrix P; two chromosome segments with a contact number not equal to 0 are neighbors, and the chromosome contact matrix A is... n*n The formula for calculating the corresponding weight matrix P is shown in equation (I): In equation (I), k represents the number of smoothing operations, and the range of k is: 1≤k≤6; Chromosome contact matrix A n*n The smoothing process is shown in equations (II) and (III): B (k) * A (k) ·P (k) (II) In equations (II) and (III), S represents the smoothed chromosome contact matrix, and A represents the chromosome contact matrix A. n*n Using the matrix S after the first smoothing 1 As input A to the second smoothing process 2 A (m+1) =S (m) It only smooths the upper triangular elements in A, and does not smooth the elements on the diagonal of A.

4. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 1, characterized in that, In step (4), the matrix after the random walk smoothing process in step (3) is subjected to contact binarization, including: First, the matrix smoothed by the restarted random walk... Convert to a length of (n) (s) ) 2 A one-dimensional vector, where s represents the chromosome number and n... (s) This represents the number of chromosome segments divided from chromosome s; Then, combine the vectors corresponding to chromosome s in all cells into a matrix. b represents the number of cells that need to be clustered; For matrix Perform contact binarization to generate the matrix Finally, the matrices corresponding to the 23 chromosomes are merged by row merging. Combined into a single matrix F b*c ,in 5. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 4, characterized in that, Contact binarization is achieved by setting a threshold thr i To filter the matrix The elements in the sample are filtered as shown in equation (V): In equation (V), thr i This represents the 80th percentile of the i-th row.

6. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 1, characterized in that, In step (5), KPCA is used for dimensionality reduction and cell embedding generation, including: a. Calculate the average value of the original dataset, and then subtract the average value from all data in the original dataset; b. Calculate the kernel matrix K using the kernel function of KPCA; c. Calculate the eigenvalues ​​and eigenvectors of the kernel matrix; d. Arrange the eigenvectors into a matrix by row according to the magnitude of their corresponding eigenvalues, and take the first k rows to form matrix P; e, Y = PX, to obtain the dimension-reduced data Y; The kernel function of KPCA is cosine.

7. The single-cell Hi-C clustering method based on contact number weight smoothing and feature fusion according to claim 1, characterized in that, In step (6), each row of the distance matrix Q is concatenated with the corresponding row of the cell embedding matrix F to obtain the final feature fusion matrix, which is the new feature matrix X.

8. A single-cell Hi-C clustering method based on contact number weighting smoothing and feature fusion according to any one of claims 1-7, characterized in that, In step (7), cell clustering is performed using a spectral clustering algorithm, including: ① Input a new feature matrix X and construct a similarity matrix S using radial basis functions, where each row of the new feature matrix X contains the feature information of a cell; ② Construct a similarity graph G based on the similarity matrix S, and obtain the adjacency matrix W from the similarity graph G; ③ Calculate the degree matrix D and the Laplace matrix L = DW; ④ Calculate the normalized Laplace matrix ⑤ Calculate the normalized Laplace matrix L ′ The n-dimensional eigenvectors corresponding to the k smallest eigenvalues ​​in the vector; ⑥ Combine the first k eigenvectors into an n x k matrix V n*k ; ⑦ Apply equation (VI) to matrix V n*k Standardize: In formula (VI), Each row in matrix M represents a sample, which is the low-dimensional representation of each row in matrix X; ⑧ Use the k-means algorithm to perform clustering to obtain a cluster partition containing k clusters.

9. A single-cell Hi-C clustering system based on contact number weight smoothing and feature fusion, characterized in that, include: The data preprocessing module is configured as follows: Normalize chromosome interaction data in single-cell Hi-C data to a chromosome contact matrix at a given resolution; The contact number-weighted smoothing module is configured such that each row in the chromosome contact matrix represents the interaction information between the chromosome segment and all its neighbors; a weight matrix is ​​used to quantify the influence of different neighbor segments on the target chromosome segment. The restart random walk smoothing module is configured to use the restart random walk algorithm to smooth the chromosome contact matrix after smoothing based on contact number weights. The contact binarization module is configured as follows: Binarize the matrix after the random walk restart smoothing process; The principal component extraction module is configured to use KPCA for dimensionality reduction and generate cell embeddings. The feature fusion module is configured such that each row of the cell embedding generated by KPCA represents the chromosome structure information of a cell. The Euclidean distance between cells is calculated through cell embedding, and a distance matrix is ​​constructed as a supplement to the cell embedding. The distance matrix and the matrix obtained after cell embedding are merged by row merging and dimensionality reduction using KPCA to generate a new feature matrix. The spectral clustering module is configured to use a spectral clustering algorithm to perform cell clustering. The chromosome contact matrix, which has been smoothed based on contact number weights, is smoothed using the restarted random walk algorithm. include: Let S be an undirected weighted graph, where nodes represent chromosome segments. ij Represents the weight of the edge between chromosome segments i and j; the matrix S is smoothed using a restarted random walk algorithm, and matrix R is the normalized matrix of matrix S, defined as: Each step of the restart random walk algorithm offers two choices: randomly walk to the next node or return to the starting node. The restart probability *r* is specified as the probability of returning to the starting node, and 1-*r* is the probability of walking to an adjacent chromosome segment. The specific implementation process involves repeated calculations according to equation (IV): U (t) =rU (t-1) R+(1-r)I(IV) In equation (IV), t represents the number of iterations, and U (t) This represents the matrix smoothed by the random walk algorithm after t restarts. Restarting the random walk algorithm starts from U... (0) Start iteration, U (0) Both I and I are identity matrices. This represents the probability that chromosome segment i will migrate to chromosome segment j in the t-th iteration, when the condition ||U|| is satisfied. (t) -U (t-1) ||2≤10 -6 At that time, the restarted random walk process on matrix U converges, yielding the final matrix.

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