A method for imputing scRNA-seq data based on nonnegative matrix factorization

Abstract

This invention discloses a method for imputing missing values ​​in scRNA-seq data based on nonnegative matrix factorization, belonging to the technical field of deep learning and data imputation methods. This invention solves the problem of low accuracy in imputing missing values ​​in single-cell RNA sequencing data using existing methods. The main technical solution of this invention is as follows: Step 1: Filter cells based on gene data to obtain RNA sequencing data of the remaining cells after filtering; normalize, screen genes, and perform logarithmic transformation on the RNA sequencing data of the remaining cells after filtering to generate matrix X; Step 2: Decompose matrix X to obtain a feature matrix and a coefficient matrix; Step 3: Construct an input matrix for an autoencoder based on the feature matrix, use the input matrix as the input of the autoencoder, and output the imputed feature matrix through the autoencoder; Step 4: Perform decomposition, logarithmic reduction, and inverse normalization on the imputed feature matrix in sequence to obtain the imputed result. This invention can be applied to RNA sequencing data imputation.

Description

Technical Field

[0001] This invention belongs to the technical field of deep learning and data imputation methods, specifically relating to a scRNA-seq data imputation method based on nonnegative matrix factorization. Background Technology

[0002] Sequencing technology is used to determine the sequences of biomolecules, such as deoxyribonucleic acid (DNA) and amino acids. Through sequencing, humans can read and understand the code of life. Over time, sequencing technology has undergone multiple iterations, resulting in technologies including Sanger sequencing, high-throughput sequencing, and third-generation sequencing based on nanopore technology. With advancements in sequencing technology and deeper research into genomes, it has become an important tool in the fields of medicine and life sciences. Currently, single-cell RNA sequencing (scRNA-seq) technology has become the primary method for studying single-cell transcriptomics, capable of detecting gene expression levels in individual cells. However, due to technical limitations and biological noise, single-cell RNA sequencing measurements often contain missing values, affecting the accuracy and interpretability of the data. Therefore, effectively filling in missing values ​​has become a hot research topic in this field.

[0003] In single-cell RNA sequencing data, dropout events refer to the phenomenon where certain gene expression is not detected in some cells. This is due to the limitations of single-cell RNA sequencing technology. The presence of dropout events leads to severe data sparsity and missing values. Therefore, imputing these missing values ​​is a necessary step for better subsequent analysis.

[0004] Currently, deep learning, as an artificial intelligence technology, has achieved remarkable results in fields such as image classification and speech recognition. In bioinformatics, it is also widely applied to genomics. Deep learning can classify, cluster, and perform dimensionality reduction analysis on gene expression data through multi-layer neural network models. It can also be used for modeling and predicting gene regulatory networks, as well as optimizing and designing gene editing technologies. Although some researchers have transferred the most widely used convolutional neural network and recurrent neural network frameworks to the biomedical field, the application of deep learning in biomedicine remains limited. This is mainly due to two reasons: first, traditional RNN / CNN models are generally not suitable for modeling genomic data because these models struggle to handle the special properties of sequence data, such as long-term dependencies; second, there is a lack of user-friendly automated machine learning frameworks for those unfamiliar with deep learning, which presents a certain technical hurdle for its application.

[0005] In summary, imputing missing values ​​in single-cell RNA sequencing data is an urgent problem to be solved. However, the accuracy of imputing missing values ​​using existing methods is still low, and the effect of imputing missing values ​​in single-cell RNA sequencing data is not good. Summary of the Invention

[0006] The purpose of this invention is to address the problem of low accuracy in imputing missing values ​​in single-cell RNA sequencing data using existing methods, and to propose a non-negative matrix factorization-based scRNA-seq data imputation method.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] A method for imputing scRNA-seq data based on nonnegative matrix factorization, the method specifically includes the following steps:

[0009] Step 1: Filter the cells based on the gene data in the original single-cell RNA sequencing data to obtain the RNA sequencing data of the remaining cells after filtering.

[0010] The RNA sequencing data of the remaining cells after filtering were normalized, and gene screening was performed based on the normalized data. Specifically, I gene data were screened out for each remaining cell after filtering.

[0011] The matrix composed of the gene data of each selected cell is denoted as matrix X. N Then for matrix X N Perform a logarithmic transformation to generate matrix X;

[0012] Step 2: Decompose matrix X:

[0013] X≈WH

[0014] Where W is the feature matrix with dimension I×r, and H is the coefficient matrix with dimension r×J;

[0015] Step 3: Construct the input matrix of the autoencoder based on the feature matrix W, use the input matrix as the input of the autoencoder, and output the filled feature matrix through the autoencoder.

[0016] Step 4: Perform decomposition, logarithmic restoration, and inverse normalization on the filled feature matrix in sequence to obtain the complement value result.

[0017] Furthermore, the pair of matrix X N The logarithmic transformation is performed to generate matrix X, specifically as follows:

[0018]

[0019] Where i represents the i-th gene, i = 1, 2, ..., I, I is the total number of genes in each cell of the matrix, and j represents the j-th cell, j = 1, 2, ..., J, J is the total number of cells. Let X be a matrix N The element in the i-th row and j-th column, X ij Let X be the element in the i-th row and j-th column of the generated matrix X.

[0020] Furthermore, r is less than I, and (I+J)r <IJ。

[0021] Furthermore, the calculation methods for W and H are as follows:

[0022] Step 2: 1. Initialize the iteration count l = 0, and randomly initialize the feature matrix W0 and coefficient matrix H0;

[0023] Step 22: Update the feature matrix:

[0024] W′ l+1 =W l ×(W l H l ×H l T ) / (W l ×H l ×H l T )

[0025] Among them, H l T For the coefficient matrix H l The transpose of W′ l+1 This is the initially updated feature matrix;

[0026] Steps two and three: If the initially updated feature matrix W′ l+1 If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated feature matrix W. l+1 If the initially updated feature matrix W′ l+1 If no negative values ​​exist in the array, then W′ is directly set to... l+1 The updated feature matrix W l+1 ;

[0027] Using the updated feature matrix W l+1 Perform steps two and four;

[0028] Step 24: Update the coefficient matrix:

[0029] H′ l+1 =H l ×(W l+1 T ×W l H l) / (W l+1 T ×W l+1 ×H l )

[0030] Among them, W l+1 T For W l+1 The transpose of H′ l+1 This is the initially updated coefficient matrix;

[0031] Step 25: If the coefficient matrix H′ is initially updated... l+1 If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated coefficient matrix H. l+1 If the coefficient matrix H′ is initially updated l+1 If no elements in H′ contain negative values, then H′ can be directly set to H′. l+1 The updated coefficient matrix H l+1 ;

[0032] Using the updated coefficient matrix H l+1 Perform step two six;

[0033] Step 26: Determine whether the set iteration stop condition has been met;

[0034] If the iteration stopping condition is met, the feature matrix updated in the last iteration is taken as W, and the coefficient matrix updated in the last iteration is taken as H.

[0035] If the iteration stopping condition is not met, let l = l + 1 and return to step two.

[0036] Furthermore, the iteration stopping condition is that at least one of condition (1) and condition (2) is satisfied, wherein:

[0037] Condition (1) The maximum number of iterations set has been reached;

[0038] Condition (2): The change in the feature matrix obtained in two adjacent iterations is less than the threshold and the change in the coefficient matrix obtained in two adjacent iterations is less than the threshold.

[0039] Furthermore, the change is the Euclidean distance or KL divergence.

[0040] Furthermore, the construction of the input matrix of the autoencoder based on the feature matrix W specifically involves:

[0041]

[0042] in, It is the Hadamard product, M is a binary mask containing 1s, and R is the input matrix of the autoencoder.

[0043] Furthermore, the autoencoder includes an encoder and a decoder, and the loss function used to train the autoencoder is:

[0044]

[0045] Where E is the encoder matrix, D is the decoder matrix, σ is the sigmoid activation function, and ||·|| O This indicates that the loss is calculated only for non-zero counts existing in R, where λ is the regularization coefficient, ||·|| F It is the F-norm.

[0046] Furthermore, the filled feature matrix is ​​as follows:

[0047]

[0048] Where ψ is the ReLU activation function of the decoder. This is the feature matrix after filling in the missing parts.

[0049] Furthermore, the decomposition and restoration of the filled feature matrix specifically involves:

[0050]

[0051] in, This is the result of decomposition and reduction.

[0052] The beneficial effects of this invention are:

[0053] Compared to traditional interpolation algorithms, this invention exhibits stronger learning capabilities and adaptability. By introducing matrix factorization, key features can be extracted from the original data, avoiding excessive noise interference. Furthermore, the autoencoder effectively captures the nonlinear relationships within the data by learning its latent representation, further improving the accuracy of data interpolation.

[0054] Meanwhile, the method of this invention has high computational efficiency. The matrix factorization method has a fast computation speed and can complete the processing of large-scale data in a short time, thus improving work efficiency. Attached Figure Description

[0055] Figure 1 This is a flowchart of a scRNA-seq data imputation method based on nonnegative matrix factorization according to the present invention;

[0056] Figure 2 This is a cluster analysis evaluation index of the complementation effect of the present invention and several traditional methods on the Trapnell dataset;

[0057] In the figure, the bars corresponding to each clustering evaluation index, from left to right, represent AnImpute, AutoImpute, DrImpute, Raw, and ScImpute, respectively.

[0058] Figure 3 This is a cluster analysis evaluation index of the complementation effect of the present invention and several traditional methods on the Usoskin dataset;

[0059] Figure 4 This is a cluster analysis evaluation index diagram showing the effect of the present invention and several traditional methods on the hPSC dataset in terms of the complementation effect. Detailed Implementation

[0060] The present application will now be described in further detail with reference to specific embodiments and accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are all within the scope of protection of the present invention.

[0061] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a method for imputing scRNA-seq data based on nonnegative matrix factorization. The method specifically includes the following steps:

[0062] Step 1: Filter the cells based on the gene data in the original single-cell RNA sequencing data to obtain the RNA sequencing data of the remaining cells after filtering.

[0063] If a cell's RNA sequencing data contains a large number of genes with a value of 0, then that cell will be filtered out.

[0064] The RNA sequencing data of the remaining cells after filtering were normalized according to the library size of each sample (cell), and gene screening was performed based on the normalized data. For each remaining cell after filtering, I gene data were screened out so that all samples have one million readings.

[0065] The specific process of gene selection is as follows:

[0066] For a single cell, calculate the expression variability of each gene in the cell (for a single gene, the expression variability is defined as the standard deviation of gene expression divided by the mean), sort the expression variability of each gene in the cell in descending order, and select the gene data with the highest expression variability.

[0067] Similarly, gene selection is performed for each cell individually. The matrix composed of the gene data of each selected cell is denoted as matrix X. N(The gene data of each cell is used as a column of the matrix), and then the matrix X is... N Perform a logarithmic transformation to generate matrix X;

[0068] Step 2: Decompose matrix X:

[0069] X≈WH

[0070] Where W is the feature matrix with dimension I×r, and H is the coefficient matrix with dimension r×J;

[0071] Step 3: Construct the input matrix of the autoencoder based on the feature matrix W, use the input matrix as the input of the autoencoder, and output the filled feature matrix through the autoencoder.

[0072] Step 4: Perform decomposition, logarithmic restoration, and inverse normalization on the filled feature matrix in sequence to obtain the complement value result.

[0073] This invention proposes a nonnegative matrix factorization-based method for imputing missing values ​​in scRNA-seq data. This method can effectively fill in missing values ​​in single-cell RNA sequencing data while maintaining data accuracy and interpretability. Based on the traditional autoencoder model, matrix factorization is introduced for dimensionality reduction and feature extraction. It decomposes a nonnegative matrix into the product of two nonnegative matrices, where one matrix represents the latent features of the data, and the other matrix represents the weight of each sample on these features. This achieves dimensionality reduction (non-linear dimensionality reduction) of the original data. The dimension of the decomposed matrix is ​​much smaller than the initial data matrix, thus saving storage space and reducing the use of computational resources.

[0074] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the matrix x... N The logarithmic transformation is performed to generate matrix X, specifically as follows:

[0075]

[0076] Where i represents the i-th gene, i = 1, 2, ..., I, I is the total number of genes in each cell of the matrix, and j represents the j-th cell, j = 1, 2, ..., J, J is the total number of cells. Let X be a matrix N The element in the i-th row and j-th column, X ij Let X be the element in the i-th row and j-th column of the generated matrix X.

[0077] Adding a pseudo-count of 1.01 avoids infinite values ​​in parameter estimation in subsequent steps. The advantage of logarithmic transformation is that it prevents a few large observations from having a significant impact, makes the transformed values ​​continuous, and thus provides greater flexibility in modeling.

[0078] The other steps and parameters are the same as in Specific Implementation Method 1.

[0079] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that: r is less than I, and (I+J)r <IJ。

[0080] Decomposing matrix X can reduce the dimensionality of the original data (non-linear dimensionality reduction) and extract features, thereby saving storage space and reducing the use of computing resources. Here, matrix W represents the spatial representation of the features, and matrix H represents the representation of each sample in the feature space.

[0081] Other steps and parameters are the same as in specific implementation method one or two.

[0082] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the calculation methods for W and H are as follows:

[0083] Step 2: 1. Initialize the iteration count l = 0, and randomly initialize the feature matrix W0 and coefficient matrix H0;

[0084] Step 22: Update the feature matrix:

[0085] W′ l+1 =W l ×(W l H l ×H l T ) / (W l ×H l ×H l T )

[0086] Among them, H l T For the coefficient matrix H l The transpose of W′ l+1 This is the initially updated feature matrix;

[0087] Steps two and three: If the initially updated feature matrix W′ l+1 If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated feature matrix W. l+1 If the initially updated feature matrix W′ l+1 If no negative values ​​exist in the array, then W′ is directly set to... l+1 The updated feature matrix W l+1 ;

[0088] Using the updated feature matrix W l+1 Perform steps two and four;

[0089] Step 24: Update the coefficient matrix:

[0090] H′l+1 =H l ×(W l+1 T ×W l H l ) / (W l+1 T ×W l+1 ×H l )

[0091] Among them, W l+1 T For W l+1 The transpose of H′ l+1 This is the initially updated coefficient matrix;

[0092] Step 25: If the coefficient matrix H′ is initially updated... l+1 If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated coefficient matrix H. l+1 If the coefficient matrix H′ is initially updated l+1 If no elements in H′ contain negative values, then H′ can be directly set to H′. l+1 The updated coefficient matrix H l+1 ;

[0093] Using the updated coefficient matrix H l+1 Perform step two six;

[0094] Step 26: Determine whether the set iteration stop condition has been met;

[0095] If the iteration stopping condition is met, the feature matrix updated in the last iteration is taken as W, and the coefficient matrix updated in the last iteration is taken as H.

[0096] If the iteration stopping condition is not met, let l = l + 1 and return to step two.

[0097] The matrix obtained in this way gradually approximates the original data matrix.

[0098] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0099] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the iteration stopping condition is at least one of condition (1) and condition (2), wherein:

[0100] Condition (1) The maximum number of iterations set has been reached;

[0101] Condition (2): The change in the feature matrix obtained in two adjacent iterations is less than the threshold and the change in the coefficient matrix obtained in two adjacent iterations is less than the threshold.

[0102] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0103] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the variable is Euclidean distance or KL divergence.

[0104] It should be noted that the variables in this invention can be Euclidean distance or KL divergence, but are not limited to Euclidean distance or KL divergence.

[0105] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0106] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: the construction of the input matrix of the autoencoder based on the feature matrix W is specifically as follows:

[0107]

[0108] in, It is the Hadamard product, M is a binary mask containing 1s, R is the input matrix of the autoencoder, R contains non-zero terms and is 0 elsewhere, and W represents the count matrix to be estimated.

[0109] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0110] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the autoencoder includes an encoder and a decoder, and the loss function used to train the autoencoder is:

[0111]

[0112] Where E is the encoder matrix, D is the decoder matrix, σ is the sigmoid activation function, and ||·|| O This indicates that the loss is calculated only for non-zero counts in R, where λ is the regularization coefficient. Regularization aims to prevent overfitting to non-zero values ​​in the count matrix. F It is the F-norm.

[0113] The autoencoder is trained using gradient descent, where gradients are computed via backpropagation to minimize the loss function. An RMSProp optimizer is used to adjust the learning rate, thus avoiding getting trapped in local minima and reaching the minimum of the loss function faster, achieving perfect interpolation. Both the encoder and decoder matrices are initialized with random normal distributions, and the decoder output uses the ReLU activation function.

[0114] The hyperparameters of the autoencoder are selected as follows:

[0115] (1) The regularization coefficient λ is used to control the contribution of the regularization term to the loss function.

[0116] (2) Size of the hidden layer (dimensionality of the latent space).

[0117] (3) Initial value of learning rate.

[0118] (4) Threshold: When the change in the loss function value is less than the threshold, gradient descent stops, indicating convergence.

[0119] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0120] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the filled feature matrix is:

[0121]

[0122] Where ψ is the ReLU activation function of the decoder. This is the feature matrix after filling in the missing parts.

[0123] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0124] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the decomposition and restoration of the filled feature matrix is ​​specifically as follows:

[0125]

[0126] in, This is the result of decomposition and reduction.

[0127] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0128] Experimental Section

[0129] To evaluate the effectiveness of the missing value imputation method of this invention, the clustering results obtained are compared with those obtained by directly normalizing the original data. Simultaneously, the differences in clustering evaluation metrics between the processed and original data are calculated to analyze the impact of the imputation process on the data clustering results. By analyzing each group of data and combining it with the clustering evaluation metrics, charts can be generated and auxiliary analyses can be performed, thereby drawing conclusions about the clustering effectiveness of different missing value imputation methods. Compared with traditional missing value imputation methods, the missing value imputation method of this invention exhibits stronger ability to identify true zero values, demonstrating excellent performance and strong robustness.

[0130] After supplementing the sequencing data of single-cell RNA, the performance differences between the method of this invention and the method without improvements to the input of the autoencoder and several current mainstream methods are compared. The algorithm is evaluated by its practical application and effect on different datasets.

[0131] Data was downloaded from the Gene Expression Omnibus (GEO) website, and the cluster labels for each data point were recorded. Due to the inconsistent data types in the original data files, the read count data were first converted to gene expression levels. Then, TPM normalization was performed on the processed raw data. Four different missing value imputation methods were used, including ScImpute, DrImpute, AutoImpute, and AnImpute (the method proposed in this invention). T-SNE dimensionality reduction and visualization were performed on the imputed data to reveal the clustering patterns in a low-dimensional space. To further explore the clustering structure of the data, the K-means algorithm was used for cluster analysis on the processed data.

[0132] To evaluate the effectiveness of the four missing value imputation algorithms, the clustering results obtained were compared with the clustering results obtained by directly normalizing the original data.

[0133] Figure 2 , Figure 3 and Figure 4 This diagram illustrates the comparison of cluster analysis evaluation metrics between this invention and three other methods on three datasets, using four common external clustering evaluation metrics.

[0134] (1) RAND Index: The RAND index calculates the similarity between the predicted and actual values ​​of a sample. The value ranges from [0,1]. The closer the value is to 1, the higher the consistency between the clustering result and the actual situation. The specific calculation process is as follows:

[0135]

[0136] (2) Adjusted Rand Index: For random results, the Rand index cannot guarantee that the score is close to zero. Therefore, the adjusted Rand index with higher discrimination is proposed. The value range is [-1,1]. The ARI measures the degree of agreement between two data distributions. The closer the value is to 1, the higher the consistency between the clustering result and the real situation.

[0137]

[0138] (3) Jaccard coefficient: The Jaccard coefficient characterizes all pairs of samples belonging to the same class (either belonging to the same class in C, or belonging to the same class in C). * (They belong to the same category), and are both in C and C. *The ratio of the number of samples belonging to the same class, with a value range of [0,1].

[0139]

[0140] (4) FM index: If FM index is recorded in C for sample pairs belonging to the same class, then FM index is used in C. * The proportion of sample pairs of the same class is p1, in C * If the proportion of sample pairs belonging to the same class in C is p2, then FM is the geometric mean of p1 and p2, with a value in the range [0,1]. The calculation process is shown in the formula:

[0141]

[0142] The method in this invention is represented by AnImpute in the figure. The ScImpute algorithm tends to treat identified zero values ​​as true zeros when processing real datasets, resulting in good performance on real datasets, second only to AnImpute. However, its performance on simulated datasets is unsatisfactory, possibly because simulated datasets contain more missing values ​​than true zeros. In contrast, the DrImpute algorithm tends to treat identified zero values ​​as missing zeros, leading to less than ideal performance on real datasets. The AutoImpute algorithm performs poorly on both datasets. On the hPSC dataset, this algorithm outperforms both ScImpute and DrImpute.

[0143] The AnImpute algorithm demonstrated excellent performance on all three real-world datasets, exhibiting relatively robust imputation results. Whether on the Trapnell, Usoskin, or hPSC datasets, AnImpute showed good clustering performance. This proves its superior performance in handling missing values ​​in real-world datasets. For clearer analysis, Table 1 presents a ranking of the four algorithms on the three real-world datasets, where 1 represents the best and 4 represents the worst.

[0144] Table 1. Ranking of clustering results of the four algorithms corresponding to three sets of real data.

[0145]

[0146] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for imputing scRNA-seq data based on nonnegative matrix factorization, characterized in that, The method specifically includes the following steps: Step 1: Filter the cells based on the gene data in the original single-cell RNA sequencing data to obtain the RNA sequencing data of the remaining cells after filtering. The RNA sequencing data of the remaining cells after filtering were normalized, and gene screening was performed based on the normalized data. Specifically, I gene data were screened out for each remaining cell after filtering. The specific process of gene selection is as follows: For a single cell, calculate the expression variability of each gene in the cell, sort the expression variability of each gene in the cell in descending order, and select the data of the gene with the highest expression variability. The matrix composed of the gene data of each selected cell is denoted as matrix. Then, for the matrix Perform logarithmic transformation to generate matrix ; Step 2: For the matrix Decompose: in, For the characteristic matrix, The dimension is ×r, The coefficient matrix, The dimension is × ; Step 3: Based on the feature matrix Construct the input matrix of the autoencoder, use the input matrix as the input of the autoencoder, and output the filled feature matrix through the autoencoder; The autoencoder includes an encoder and a decoder, and the loss function used to train the autoencoder is: in, It is an encoder matrix. It is a decoder matrix. It is the Sigmoid activation function. This indicates that the loss is calculated only for the non-zero counts present in R. It is the regularization coefficient. It is the F-norm; Step 4: Perform decomposition, logarithmic restoration, and inverse normalization on the filled feature matrix in sequence to obtain the complement value result.

2. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 1, characterized in that, The pair of matrices Perform logarithmic transformation to generate matrix Specifically: in, For the first One gene, It is the total number of genes in each cell of the matrix. For the first Each cell, , It is the total number of cells. For matrix The Middle Line number Column elements, For the generated matrix The Middle Line number The elements of the column.

3. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 2, characterized in that, The Less than ,and .

4. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 3, characterized in that, The and The calculation method is as follows: Step 2: Initialize the iteration count l=0 and randomly initialize the feature matrix. sum coefficient matrix ; Step 22: Update the feature matrix: in, Coefficient matrix transpose, This is the initially updated feature matrix; Steps two and three: If the feature matrix is ​​initially updated... If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated feature matrix. If the feature matrix is ​​initially updated If no elements in the set have negative values, then directly set them to... As the updated feature matrix ; Using the updated feature matrix Perform steps two and four; Step 24: Update the coefficient matrix: in, for transpose, This is the initially updated coefficient matrix; Step 25: If the coefficient matrix is ​​initially updated... If any element in the matrix has a negative value, then the negative value is set to 0 to obtain the updated coefficient matrix. If the coefficient matrix is ​​initially updated If no elements in the set have negative values, then directly set them to... As the updated coefficient matrix ; Using the updated coefficient matrix Perform step two six; Step 26: Determine whether the set iteration stop condition has been met; If the iteration stopping condition is met, then the feature matrix updated in the last iteration is used as... The coefficient matrix updated in the last iteration is used as... ; If the iteration stopping condition is not met, let l = l + 1 and return to step two.

5. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 4, characterized in that, The iteration stopping condition is that at least one of condition (1) and condition (2) is satisfied, wherein: Condition (1) The maximum number of iterations set has been reached; Condition (2): The change in the feature matrix obtained in two consecutive iterations is less than the threshold and the change in the coefficient matrix obtained in two consecutive iterations is less than the threshold.

6. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 5, characterized in that, The change is the Euclidean distance or KL divergence.

7. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 6, characterized in that, The feature matrix The input matrix of the autoencoder is constructed as follows: in, It is the Hadamard product, M is a binary mask containing 1s, and R is the input matrix of the autoencoder.

8. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 7, characterized in that, The filled-in feature matrix is: in, It is the ReLU activation function of the decoder. This is the feature matrix after filling in the missing parts.

9. The scRNA-seq data imputation method based on nonnegative matrix factorization according to claim 8, characterized in that, The decomposition and restoration of the filled feature matrix specifically involves: in, This is the result of decomposition and reduction.

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