A single-cell data relational sequencing clustering method based on generative adversarial networks

Abstract

The present invention discloses a single-cell data relational sequencing clustering method based on a generative adversarial network, the method comprising the following steps: step 1, data acquisition; step 2, data processing; step 3, graph construction; step 4, graph autoencoder training; step 5, point selection and deep model clustering; step 6, re-clustering. The method deeply mines the local structure and dynamic changes in the cell population by constructing a graph structure containing cell-to-cell + cell-to-gene, and uses an adversarial network to optimize the embedded representation to improve the accuracy and computational efficiency of clustering. The present invention not only enhances the ability of feature representation, but also better expresses the biological characteristics and relationships of cells in a low-dimensional space, and is suitable for fields such as cell classification, cancer research, and immunological analysis.

Description

Technical Field

[0001] The present invention belongs to the field of biomedical informatics, and relates to a single cell clustering method, and specifically to an improved cell clustering method combining a graph convolutional autoencoder (GAE) and a generative adversarial network (GAN). Background Art

[0002] Cell clustering analysis is of great significance in biomedical research, especially in single-cell RNA sequencing data analysis, cancer research and immunology research. Existing cell clustering methods usually adopt the "dimensionality reduction + clustering" strategy and rely on traditional statistical and machine learning algorithms. Dimensionality reduction technology can convert high-dimensional data into low-dimensional space while retaining the important features of the data as much as possible, which is crucial for subsequent clustering analysis. Traditional dimensionality reduction methods include some such as PCA, but there are certain defects, such as the inability to capture the nonlinear structure of the data. Therefore, autoencoder dimensionality reduction is introduced. Autoencoder is an unsupervised learning neural network that can learn effective representation or encoding of data. Compared with traditional linear dimensionality reduction methods, autoencoders can capture more complex features of data through nonlinear transformations. In order to more conveniently utilize graph structure relationships, graph autoencoders are further applied for dimensionality reduction.

[0003] As a model that combines a graph neural network (GNN) and an autoencoder, GAE can effectively capture the graph structure information of the data and provide a new method for clustering analysis of complex data. In the paper "GNN-based embedding for clustering scRNA-seq data", authors Madalina Ciortan and Matthieu Defrance proposed the Graph-sc method, which uses a graph autoencoder network to create embedded scRNA-seq cell data, and analyzed the performance of clustering these embeddings using various clustering algorithms. The Graph-sc method generates an embedded representation of scRNA-seq data through a graph autoencoder network, which can capture the graph structure information of the data, thereby better reflecting the similarities and differences between cells.

[0004] Existing cell clustering methods have many shortcomings when dealing with high-dimensional and noisy biological data. When using traditional graph autoencoder dimensionality reduction + K-means clustering, these problems are specifically:

[0005] (1) Complexity of constructing the adjacency matrix: When constructing the adjacency matrix, traditional graph autoencoders often only focus on the direct connections between cells and ignore the more complex interaction patterns in the data. This simplified approach limits the effect of dimensionality reduction and fails to fully utilize the intrinsic structural information of the data.

[0006] (2) Lack of optimization for adversarial training: Traditional graph autoencoders lack an optimization mechanism for adversarial training during dimensionality reduction and feature extraction, making it difficult to generate high-quality embedding representations, which affects the accuracy and stability of subsequent clustering analysis.

[0007] (3) Sensitive to initial centroid: The K-means clustering algorithm is highly dependent on the selection of the initial centroid. Different initial centroids may lead to different clustering results, affecting the stability and accuracy of clustering.

[0008] (4) Unable to handle complex nonlinear relationships: K-means assumes that the data distribution is spherical and the cluster spacing is equal. This is not flexible enough when dealing with biological data with complex nonlinear characteristics and cannot effectively capture the nonlinear relationships between cells and genes.

[0009] (5) Susceptible to noise and outliers: The K-means algorithm is sensitive to noise and outliers, which is particularly evident in high-dimensional biological data and can easily lead to deviations in clustering results. Summary of the invention

[0010] In order to solve the shortcomings of traditional K-means clustering in processing high-dimensional and noisy biological data, the present invention provides a single-cell data relationship sequencing clustering method based on generative adversarial networks. This method deeply mines the local structure and dynamic changes in the cell population by constructing a graph structure containing cell-to-cell + cell-to-gene, and uses adversarial networks to optimize the embedded representation to improve the accuracy and computational efficiency of clustering. The present invention not only enhances the ability of feature representation, but also better expresses the biological characteristics and relationships of cells in low-dimensional space, and is suitable for fields such as cell classification, cancer research and immunological analysis.

[0011] The objective of the present invention is achieved through the following technical solutions:

[0012] A single-cell data relational sequencing clustering method based on a generative adversarial network comprises the following steps:

[0013] Step 1: Data acquisition:

[0014] Download single-cell RNA sequencing data from public databases;

[0015] Step 2: Data processing:

[0016] Step 2-1, filter sparse genes and cells: delete genes with extremely low expression ratios in the entire dataset, as well as cells with extremely low expression ratios.

[0017] Step 2-2, select key genes: select a portion of genes with the most significant performance from the remaining genes.

[0018] Step 2-3, constructing a gene expression matrix: Screen all genes, remove genes whose expression ratio is less than the set value, and construct a new gene expression matrix DF;

[0019] Step 3: Graph construction:

[0020] Step 3-1, normalization processing: normalize the initial gene expression matrix DF to construct a normalized matrix B;

[0021] Step 3-2, PCA dimensionality reduction: PCA (Principal Component Analysis) is used to reduce the dimension of each row of the normalized matrix B into a gene feature expression matrix X2, and the gene feature expression matrix X2 is used to obtain the new cell feature expression matrix X1;

[0022] Step 3-3, inter-cell distance matrix: PCA is performed on the cell new feature expression matrix X1 to obtain the reduced-dimensional cell new feature expression matrix X3, and the inter-cell distance matrix P is obtained by calculating the Euclidean distance between each cell in the reduced-dimensional cell new feature expression matrix X3;

[0023] Step 3-4, inter-cell adjacency matrix: According to the KNN (K-Nearest Neighbors) algorithm, the inter-cell distance matrix P is used to construct the inter-cell adjacency matrix, and the rows are normalized to obtain a new inter-cell adjacency matrix A1;

[0024] Step 3-5, cell gene adjacency matrix: According to the normalized matrix B and formula , we get the adjacency matrix between cells and genes, and then normalize the rows to get the new cell-gene adjacency matrix W, where: B represents the data matrix, B[k,j] represents the expression level of the kth gene in the jth cell, Represents the weight matrix element in the graph neural network, m represents the total number of genes minus 1;

[0025] Step 3-6, construct a complete adjacency matrix: merge the inter-cell adjacency matrix A1, the inter-cell gene adjacency matrix W, the zero matrix and the identity matrix into the overall adjacency matrix A, and construct the corresponding cell-gene connection graph;

[0026] Step 4: Graph Autoencoder Training:

[0027] Construct a GCN encoder-decoder model containing multiple layers of graph convolutional layers and linear layers as a graph autoencoder, merge the cell new feature expression matrix X1 and the gene feature expression matrix X2 to form a feature matrix X, input the feature matrix X and the adjacency matrix A into the GCN encoder-decoder model for training, and generate preliminary cell clustering labels;

[0028] Step 5: Point selection and deep model clustering:

[0029] Step 5-1, select representative samples: After obtaining the initial cluster labels, use Kmeans to obtain the centroid coordinates of each cluster, and then use the Norm function to calculate the distance of each cell from the centroid. In each category, select the top 30-50% of cell samples closest to the centroid as representative samples;

[0030] Step 5-2, adversarial network training:

[0031] (1) Data preparation: Load gene expression data and cluster label data, and standardize representative samples;

[0032] (2) Define the generator and discriminator:

[0033] Generator: used to generate fake embedding representations similar to real cell embeddings. The structure includes multiple linear layers and LeakyReLU activation functions. The output layer uses the Tanh activation function to adapt to the feature value range.

[0034] Discriminator: used to distinguish real samples from fake samples. The structure includes multiple linear layers and LeakyReLU activation function. The output layer uses Softmax activation function for multi-classification.

[0035] (3) Training the discriminator: input real cell samples and calculate the loss of real samples; generate fake cell samples and calculate the loss of fake samples; the total loss of the discriminator is the sum of the loss of real samples and the loss of fake samples;

[0036] (4) Training the generator: Generate fake cell samples and calculate the output of the fake samples through the discriminator. The loss of the generator is to deceive the discriminator, that is, we hope that the fake samples will be considered as real samples by the discriminator. Through adversarial training, optimize the generator so that the generated embedding representation is closer to the distribution of real data.

[0037] Step 6: Re-clustering:

[0038] Step 6-1: After training, use the discriminator to classify all cell samples, calculate the probability that each sample belongs to each true category, and finally obtain the cluster label of each cell;

[0039] Step 6-2: Use the label consistency algorithm to ensure that the number of cluster labels of all cell samples is consistent with expectations, thereby completing re-clustering.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] The present invention significantly improves the accuracy and biological interpretability of cluster analysis by constructing a (cell-to-cell + cell-to-gene) adjacency matrix with a threshold. Specifically:

[0042] (1) Capturing complex relationships: Incorporating relationships between cells and between cell genes into the adjacency matrix and adjusting the relationship ratio to better capture the complex relationships in gene expression data. This method can more accurately reflect the deep interactions between cells and genes.

[0043] (2) Preliminary clustering optimization: In the preliminary clustering stage, some data points closest to the centroid are selected as representative samples. These samples concentrate the core features of clustering, effectively reduce the impact of noise and outliers on model training, ensure the representativeness and centrality of the training samples, and thus more accurately extract the features of gene expression data.

[0044] (3) Adversarial network optimization: Generate diverse samples through GAN, effectively avoiding the overfitting problem. The trained adversarial network model can capture the complex distribution of data. The generated new samples not only retain the key features of the original data, but also reveal the underutilized information in the data, thus enhancing the generalization ability of the model.

[0045] (4) Re-clustering improvement: Using the embedding representation optimized by the adversarial network, re-clustering analysis is performed to obtain more accurate and biologically meaningful clustering results. The combination of graph autoencoders and generative adversarial networks significantly improves the accuracy and computational efficiency of cell clustering, especially in the fields of single-cell RNA sequencing data, cancer cell heterogeneity research, and immune cell population analysis.

[0046] Through the above improvements, while improving the accuracy of clustering results, its biological interpretability and computational efficiency are also improved, providing powerful tools and technical support for research in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Some examples of matrix transformations involved in the experiment;

[0048] Figure 2 This is the overall flow chart of the single-cell data relational sequencing clustering method based on generative adversarial networks;

[0049] Figure 3This is the result of the preliminary clustering of the data GSE246147. The red cross points in the figure are the first 30% of the points closest to the centroid among all clusters;

[0050] Figure 4 This is the result diagram of the data GSE246147 after the final adversarial network model clustering, that is, the final clustering diagram of the experiment;

[0051] Figure 5 The results of the data GSE246147 measured by Seurat, SC3, Graph-sc, CIDR and GGC of the present invention are compared. The closer the ARI, FMI and ACC are to 1, the better the effect. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0053] The present invention provides a single-cell data relational sequencing clustering method based on a generative adversarial network. The method constructs a complex inter-cell + inter-cell gene structure based on a graph autoencoder, and further searches for more representative points to perform deep model training under the soft labels generated by the initial clustering after the encoder, so as to finally perform re-clustering. Figure 1 , Figure 2 As shown, the specific steps are as follows:

[0054] Step 1: Data acquisition:

[0055] Download single-cell RNA sequencing (scRNA-seq) data from public databases such as GEO or 10X Genomics. The data is usually stored in a matrix format, where rows represent genes, columns represent cells, and the value of each cell represents the expression level of a specific gene in a specific cell.

[0056] Step 2: Data processing:

[0057] After the data is read, data preprocessing is performed first.

[0058] Step 2-1, filter sparse genes and cells: remove genes whose expression ratio is lower than 1% of the entire dataset, and cells whose expression ratio is lower than 1% of the entire dataset. This step aims to reduce the noise and sparsity in the dataset, thereby improving the accuracy and credibility of subsequent analysis.

[0059] Step 2-2, select key genes: select the 2,000 most significant genes from the remaining genes. This step further simplifies the data set and improves the efficiency and interpretability of subsequent analysis by retaining the genes most relevant to the research object.

[0060] Step 2-3, construct a gene expression matrix: screen all genes, remove genes whose expression ratio is less than the set value, and construct a new gene expression matrix DF.

[0061] Step 3: Graph construction:

[0062] Step 3-1, normalization processing: normalize the initial gene expression matrix DF to construct a normalized matrix B.

[0063] Step 3-2, PCA dimensionality reduction: PCA is used to reduce the dimension of each row of the normalized matrix B into a gene feature expression matrix X2, and the gene feature expression matrix X2 is used to obtain the new cell feature expression matrix X1. The formula is: .

[0064] Step 3-3, inter-cell distance matrix: Perform PCA on the cell new feature expression matrix X1 to obtain the reduced-dimensional cell new feature expression matrix X3. By calculating the Euclidean distance between each cell in the reduced-dimensional cell new feature expression matrix X3, the inter-cell distance matrix P is obtained:

[0065]

[0066] In the formula, represents the Euclidean distance between cell i and cell j in the cell distance matrix P, Represents the value of cell i in the kth dimension in the new cell feature expression matrix X1 after dimensionality reduction, Represents the value of cell j in the kth dimension in the new feature expression matrix X1 after dimensionality reduction.

[0067] Step 3-4, inter-cell adjacency matrix: According to the KNN algorithm, the inter-cell distance matrix P is used to construct the inter-cell adjacency matrix, and the rows are normalized to obtain a new inter-cell adjacency matrix A1.

[0068] Step 3-5, cell gene adjacency matrix: According to the normalized matrix B and formula ,

[0069] The adjacency matrix between cells and genes is obtained, and then the rows are normalized to obtain a new cell-gene adjacency matrix W, where: B represents the data matrix (normalized matrix), B[k,j] represents the expression level of the kth gene in the jth cell, Represents the weight matrix element in the graph neural network, which determines the connection strength between cells and genes, and m represents the total number of genes minus 1 (because the index k starts from 0).

[0070] Step 3-6, construct a complete adjacency matrix: combine the inter-cell adjacency matrix A1, the inter-cell gene adjacency matrix W, the zero matrix and the identity matrix into the overall adjacency matrix A, the matrix form is , and construct the corresponding cell-gene connection map, n is the number of cells, p is the number of genes, , =1- Here we can use the threshold The matrix form is shown in Example 1:

[0071] Example 1

[0072] Step 4: Graph Autoencoder Training:

[0073] Construct a GCN encoder-decoder model containing multiple layers of graph convolutional layers and linear layers as a graph autoencoder, merge the cell new feature expression matrix X1 and the gene feature expression matrix X2 to form a feature matrix X, and input the feature matrix X and the adjacency matrix A into the GCN encoder-decoder model for training. The specific steps are as follows:

[0074] Step 4-1, encoding: Use multiple layers of graph convolutional layers to encode the input features. The specific steps are as follows: Each layer of graph convolutional layer propagates information through the adjacency matrix A to extract higher-order feature representations. LeakyReLU activation function and batch normalization are applied after each layer of graph convolutional layer to improve the expressiveness and stability of the model. The complete formula of the graph convolutional layer is as follows:

[0075]

[0076] Where A is the adjacency matrix, X is the node feature matrix, , is the node feature after propagation, , W is the learnable weight matrix, is a nonlinear activation function, , BatchNorm is a batch normalization operation used to accelerate training and improve model performance.

[0077] Step 4-2, Decoding: Use the linear layer to decode the encoded features and reconstruct the adjacency matrix. The decoder gradually restores the encoded information through multiple linear layers, and finally uses the Sigmoid function to output the reconstructed adjacency matrix.

[0078] Step 4-3, training: optimize the model parameters by minimizing the reconstruction error (MSE loss). During the training process, the model continuously adjusts the weights to reduce the difference between the actual adjacency matrix and the reconstructed adjacency matrix.

[0079] Step 4-4, latent variable generation: After training, the model outputs the reduced latent variable Z (embedded representation). Z contains the embedded representation of cells and genes, where the first n dimensions represent the characteristic expression of cells.

[0080] Step 4-5, preliminary clustering: Use the K-Means algorithm to cluster the feature representation of the cells (the first n dimensions of Z) to generate preliminary cell cluster labels.

[0081] Step 5: Point selection and deep model clustering:

[0082] Step 5-1, select representative samples: After obtaining the initial cluster labels, use Kmeans to obtain the centroid coordinates of each cluster, and then use the Norm function to calculate the distance of each cell from the centroid. In each category, select the first 30-50% of cell samples closest to the centroid as representative samples. These samples represent the center of each category, have more typical features and labels, and are less affected by noise and outliers.

[0083] Step 5-2, adversarial network training:

[0084] (1) Data preparation: Load gene expression data and cluster label data, and standardize representative samples.

[0085] (2) Define the generator and discriminator:

[0086] Generator: used to generate fake embedding representations similar to real cell embeddings. The structure includes multiple linear layers and LeakyReLU activation functions. The output layer uses the Tanh activation function to adapt to the feature value range. The propagation formula of the generator is as follows:

[0087]

[0088] Where G(z) is the output of the generator function G, the generated pseudo embedding representation; Z is the input noise vector of the generator, which is sampled from a Gaussian distribution; It is the i-th linear layer, which linearly transforms the input through the weight matrix and bias.

[0089] The first layer of linear transformation:

[0090] LeakyReLU activation function for layer 2:

[0091] Output layer Tanh activation function:

[0092] Discriminator: used to distinguish real samples from fake samples. The structure includes multiple linear layers and LeakyReLU activation function. The output layer uses Softmax activation function for multi-classification.

[0093] (3) Training the discriminator: Input real cell samples and calculate the loss of real samples, such as , Represents the distribution from real data The expected value of the real sample x sampled from represents the logarithmic probability value of the discriminator's prediction of the label y for the real sample x, Represents the probability distribution of the discriminator predicting that x belongs to each category, x is the real sample, y is the label of the real sample; generate fake cell samples and calculate the loss of fake samples; the total loss of the discriminator is the sum of the real sample loss and the fake sample loss.

[0094] (4) Train the generator: Generate fake cell samples and calculate the output of fake samples through the discriminator; the loss of the generator is to deceive the discriminator, that is, we hope that the fake samples will be considered as real samples by the discriminator; through adversarial training, optimize the generator so that the generated embedding representation is closer to the distribution of real data. The formula is as follows:

[0095]

[0096]

[0097] in, Represents the loss function of the generator. By minimizing this loss function, the generator G can generate more and more realistic fake samples. represents the expected value of the input noise z, G(z) is the real sample, and D(G(z)) is the output of the discriminator.

[0098] Step 6: Re-clustering:

[0099] Step 6-1: After training, use the discriminator to classify all cell samples, calculate the probability that each sample belongs to each true category, and finally obtain the cluster label of each cell;

[0100] Step 6-2: Use the label consistency algorithm to ensure that the number of cluster labels of all cell samples is consistent with expectations, thereby completing re-clustering.

[0101] Figure 3The result of the visualization using T-SNE technology after the preliminary clustering of the GSE246147 dataset is shown. Each point in the figure represents a cell, and different colors represent different cell clusters, with a total of 7 clusters. The red cross marks the top 30% of cells closest to the centroid in each cluster after preliminary clustering, which are mainly concentrated in the central area of ​​each cluster, which is consistent with the characteristic that representative samples should be closest to the centroid.

[0102] Figure 4 The final cell clustering results after GAN optimization are shown, visualized using t-SNE. The cluster boundaries in the final clustering diagram are clearer than those in the preliminary clustering diagram, and the cells in each cluster are more densely distributed. Figure 3 From the comparison, we can see the effectiveness of selecting representative cell samples + adversarial model training in optimizing clustering effects.

[0103] Figure 5 The performance of GGC and four comparative methods (Seurat, SC3, Graph-sc, CIDR) on three indicators (ARI, FMI, ACC) is shown. The closer the three indicators are to 1, the better the effect. The results show that the GGC method performs best on all three indicators, with scores of 0.83 (ARI), 0.88 (FMI), and 0.87 (ACC), respectively, showing its superior performance in clustering tasks. The CIDR method is second and also performs well, while the Seurat method is in the middle. In contrast, the SC3 and Graph-sc methods perform relatively poorly on all indicators. In summary, the GGC method has high accuracy and consistency when dealing with clustering tasks.

Claims

1. A single-cell data relational sequencing clustering method based on generative adversarial networks, characterized in that The method comprises the following steps: Step 1: Data acquisition: Download single-cell RNA sequencing data from public databases; Step 2: Data processing: Step 2-1, filter sparse genes and cells: delete genes whose expression ratio is lower than 1% in the entire dataset, and cells whose expression ratio is lower than 1% in the entire dataset; Step 2-2, select key genes: select the 2000 genes with the most significant performance from the remaining genes; Step 2-3, constructing a gene expression matrix: Screen all genes, remove genes whose expression ratio is less than the set value, and construct a new gene expression matrix DF; Step 3: Graph construction: Step 3-1, normalization processing: normalize the initial gene expression matrix DF to construct a normalized matrix B; Step 3-2, PCA dimensionality reduction: PCA is used to reduce the dimension of the genes in each row of the normalized matrix B into a gene feature expression matrix X2, and the gene feature expression matrix X2 is used to obtain the new cell feature expression matrix X1; Step 3-3, inter-cell distance matrix: PCA is performed on the cell new feature expression matrix X1 to obtain the reduced-dimensional cell new feature expression matrix X3, and the inter-cell distance matrix P is obtained by calculating the Euclidean distance between each cell in the reduced-dimensional cell new feature expression matrix X3; Step 3-4, inter-cell adjacency matrix: According to the KNN algorithm, the inter-cell distance matrix P is used to construct the inter-cell adjacency matrix, and the rows are normalized to obtain a new inter-cell adjacency matrix A1; Step 3-5, cell gene adjacency matrix: According to the normalized matrix B and formula , we get the adjacency matrix between cells and genes, and then normalize the rows to get the new cell-gene adjacency matrix W, where: B represents the data matrix, B[k,j] represents the expression level of the kth gene in the jth cell, Represents the weight matrix element in the graph neural network, m represents the total number of genes minus 1; Step 3-6, construct a complete adjacency matrix: merge the inter-cell adjacency matrix A1, the inter-cell gene adjacency matrix W, the zero matrix and the identity matrix into the overall adjacency matrix A, and construct the corresponding cell-gene connection graph; Step 4: Graph Autoencoder Training: Construct a GCN encoder-decoder model containing multiple layers of graph convolutional layers and linear layers as a graph autoencoder, merge the cell new feature expression matrix X1 and the gene feature expression matrix X2 to form a feature matrix X, input the feature matrix X and the adjacency matrix A into the GCN encoder-decoder model for training, and generate preliminary cell clustering labels; Step 5: Point selection and deep model clustering: Step 5-1, select representative samples: After obtaining the initial cluster labels, use Kmeans to obtain the centroid coordinates of each cluster, and then use the Norm function to calculate the distance of each cell from the centroid. In each category, select the top 30-50% of cell samples closest to the centroid as representative samples; Step 5-2, adversarial network training: (1) Data preparation: Load gene expression data and cluster label data, and standardize representative samples; (2) Define the generator and discriminator: Generator: used to generate fake embedding representations similar to real cell embeddings. The structure includes multiple linear layers and LeakyReLU activation functions. The output layer uses the Tanh activation function to adapt to the feature value range. Discriminator: used to distinguish real samples from fake samples. The structure includes multiple linear layers and LeakyReLU activation function. The output layer uses Softmax activation function for multi-classification. (3) Training the discriminator: input real cell samples and calculate the loss of real samples; generate fake cell samples and calculate the loss of fake samples; the total loss of the discriminator is the sum of the loss of real samples and the loss of fake samples; (4) Training the generator: Generate fake cell samples and calculate the output of the fake samples through the discriminator. The loss of the generator is to deceive the discriminator, that is, we hope that the fake samples will be considered as real samples by the discriminator. Through adversarial training, optimize the generator so that the generated embedding representation is closer to the distribution of real data. Step 6: Re-clustering: Step 6-1: After training, use the discriminator to classify all cell samples, calculate the probability that each sample belongs to each true category, and finally obtain the cluster label of each cell; Step 6-2: Use the label consistency algorithm to ensure that the number of cluster labels of all cell samples is consistent with expectations, thereby completing re-clustering.

2. The single-cell data relational sequencing clustering method based on generative adversarial network according to claim 1, characterized in that In step 3-3, the calculation formula of the cell-to-cell distance matrix P is as follows: In the formula, represents the Euclidean distance between cell i and cell j in the cell distance matrix P, Represents the value of cell i in the kth dimension in the new cell feature expression matrix X1 after dimensionality reduction, Represents the value of cell j in the kth dimension in the new feature expression matrix X1 after dimensionality reduction.

3. The single-cell data relational sequencing clustering method based on generative adversarial network according to claim 1, characterized in that The specific steps of step 4 are as follows: Step 4-1, encoding: use multi-layer graph convolutional layers to encode input features; Step 4-2, decoding: Use the linear layer to decode the encoded features and reconstruct the adjacency matrix. The decoder gradually restores the encoded information through multiple linear layers, and finally uses the Sigmoid function to output the reconstructed adjacency matrix. Step 4-3, training: optimize the model parameters by minimizing the reconstruction error. During the training process, the model continuously adjusts the weights to reduce the difference between the actual adjacency matrix and the reconstructed adjacency matrix; Step 4-4, latent variable generation: After training, the model outputs the reduced-dimensional latent variable Z, which contains the embedded representation of cells and genes, where the first n dimensions represent the characteristic expression of cells; Step 4-5, preliminary clustering: Use the K-Means algorithm to cluster the feature representation of cells and generate preliminary cell cluster labels.

4. The single-cell data relational sequencing clustering method based on generative adversarial network according to claim 3, characterized in that The specific steps of step 4-1 are as follows: each graph convolution layer propagates information through the adjacency matrix A to extract higher-order feature representations. LeakyReLU activation function and batch normalization are applied after each graph convolution layer to improve the expression ability and stability of the model. The complete formula of the graph convolution layer is as follows: Where A is the adjacency matrix, X is the node feature matrix, , is the node feature after propagation, , W is the learnable weight matrix, is a nonlinear activation function, , BatchNorm is a batch normalization operation used to accelerate training and improve model performance.

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