Clustering analysis driven high-precision missing data filling method

Abstract

The invention provides a clustering analysis-driven high-precision missing data filling method, which comprises the following steps of S1, acquiring data containing missing values, and preprocessing the data containing the missing values; s2, inputting the data matrix X, the mask matrix M, the prompt matrix H and the clustering label C1 into a generative adversarial network, and obtaining a filling matrix X'and a probability matrix P through nonlinear transformation; s3, inputting the filling matrix X'into the depth subspace clustering network to obtain a reconstructed data matrix and a self-expression layer coefficient matrix; s4, calculating the product of the matrix U and the transpose of the U, and adjusting to obtain an affinity matrix A; s5, distributing the samples to different clusters, and outputting a new clustering label C2; s6, repeating the steps S2 to S5, and outputting the filling matrix X'obtained in the step S2 at the moment as a high-precision filling data matrice.According to the method, the characteristics of potential structures and modes in data are captured through the clustering analysis technology, and the precision and quality of data filling are further improved.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a high-precision missing data filling method driven by cluster analysis. Background Art

[0002] Storing large amounts of data has become cheaper due to innovations in storage hardware and architecture. The information hidden in data resources has become an important knowledge base to aid the decision-making process in different fields such as business development, banking, healthcare, finance, and e-commerce. The presence of missing data has become a common phenomenon in quantitative research. Many real-world datasets may have missing values ​​due to various reasons, such as not knowing the value of the data at the data input stage or random noise. Missing values ​​may bring many serious problems, such as increased computational costs, output bias, and longer preprocessing time. Incomplete records may affect the predictions, descriptions, and inferences produced by analytical software. The data analysis process becomes complicated due to the bias caused by the difference between missing data and complete data.

[0003] Many studies have been conducted on the problem of missing value interpolation, such as simple imputation methods, model-based imputation methods, machine learning methods, deep learning methods, etc. Simple imputation methods, such as mean imputation, replace missing values ​​with the mean of the features in the data set, which is suitable for the case where the data is normally distributed, and mode imputation replaces missing values ​​with the most frequent value in the data set, which is suitable for categorical data or when some values ​​in the data set appear frequently. This method is simple and easy to operate; Model-based imputation methods, such as linear regression imputation, use other features in the known data as independent variables to build a regression model to predict the value of the feature where the missing value is located; Expectation maximization (EM) algorithm, iteratively estimates missing values ​​and model parameters until convergence; these model-driven methods usually provide more accurate imputation results than simple imputation techniques; Machine learning methods use advanced machine learning techniques to handle missing values. Random forest imputation methods use random forest algorithms to build a model that predicts missing values ​​by training existing data. Support vector machine imputation uses support vector machines for regression and predicts missing values ​​by training models. This method can handle complex nonlinear relationships and performs well for high-dimensional data; Deep learning-based imputation methods use the powerful functions of deep neural networks to handle missing values. For example, an autoencoder is an unsupervised learning neural network used to learn a compressed representation of data. The autoencoder consists of two parts: an encoder and a decoder. The encoder compresses the input data into a low-dimensional space, while the decoder reconstructs it. By training missing data on the autoencoder, the characteristics of the data can be learned and used to fill in the missing values; the generative adversarial network consists of a generator and a discriminator. The generator tries to generate data similar to the real data, while the discriminator distinguishes between the real data and the generated data. In the task of filling in missing values, reasonable estimates of the missing values ​​can be generated; these deep learning-based methods are able to handle complex data patterns and feature relationships, and generally provide higher filling accuracy than traditional methods.

[0004] At present, the existing missing value filling algorithms still have the following shortcomings: 1) Traditional missing data filling methods, such as mean filling, interpolation, and regression-based filling techniques, usually rely on simple statistics or local information. These methods cannot fully capture the potential structure and characteristics of the data when faced with high-dimensional and complex pattern data, thus affecting the accuracy and quality of the filling results; 2) Many existing filling methods, especially those based on complex models, require large computing resources and a large amount of training data, and have high computational overhead. These methods are inefficient when processing large-scale data sets, resulting in slow processing speeds and are not suitable for application scenarios that require real-time processing; 3) Traditional methods often ignore the internal structure and relationships between data. This limitation makes it impossible for the filling process to fully utilize the structural information of the data, and the filling effect is poor when the data contains complex relationships and patterns. Summary of the invention

[0005] In view of this, the purpose of the present invention is to propose a high-precision missing data filling method driven by cluster analysis, which performs missing value filling and clustering at the same time. The method associates missing value filling with the clustering process, uses clustering results that are more consistent with the internal structure of the data, enhances the learning ability of the generative adversarial network, and uses the filled data as a strong support for clustering. After multiple iterative training, high-precision filling of missing data is achieved, further improving the effect of existing filling technology.

[0006] The technical means adopted by the present invention are as follows:

[0007] A high-precision missing data filling method driven by cluster analysis includes the following steps:

[0008] S1, obtain data containing missing values, preprocess the data containing missing values, and obtain the data matrix X, mask matrix M, prompt matrix H, and initial clustering label C1;

[0009] S2, input the data matrix X, mask matrix M, prompt matrix H, and cluster label C1 into the generative adversarial network, and obtain the padding matrix X' and probability matrix P after nonlinear transformation; calculate the loss of the generator G and the discriminator D respectively, and optimize the generative adversarial network using the gradient descent method;

[0010] S3, input the padding matrix X' into the deep subspace clustering network to obtain the reconstructed data matrix and the self-expression layer coefficient matrix; calculate the losses of the three components in the deep subspace clustering network respectively, and optimize them as a whole using the gradient descent method;

[0011] S4, preprocessing the self-expression layer coefficient matrix, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix, adjusting the eigenvalues ​​and eigenvectors, obtaining the characteristic matrix U and normalizing it; calculating the product of the matrix U and the transpose of U, and obtaining the affinity matrix A after adjustment;

[0012] S5. Calculate the Laplace matrix based on the affinity matrix A and perform a normalization operation on the affinity matrix A to obtain the matrix L; perform eigendecomposition on the normalized Laplace matrix to construct a normalized eigenvector matrix F, where each row represents a sample; perform kmeans / GMM clustering on the normalized eigenvector matrix F, and assign the samples to different clusters based on the clustering results, and output a new cluster label C2;

[0013] S6. Input the new clustering label C2 as the new label of the generative adversarial network into S2, repeat S2 to S5 until the loss of the generative adversarial network converges and the loss of the deep subspace clustering network converges, and output the padding matrix X' obtained by S2 at this time as the high-precision padding data matrix.

[0014] Furthermore, S1 specifically includes the following steps:

[0015] S11, representing the acquired data containing missing values ​​as a data matrix X, where the data matrix X is two-dimensional table data; a row of the two-dimensional table data is represented as a piece of data, and a column of the two-dimensional table data is represented as an attribute or feature of the data, and performing a normalization operation on the data matrix X;

[0016] S12. According to the data matrix X, the mask matrix corresponding to the data matrix X is represented as M; in the mask matrix M, if the attribute observation value of the jth column of the i-th row observation data is missing, M i,j =0, otherwise M i,j =1;

[0017] S13, generating a binary matrix with the same shape as the mask matrix M according to the prompt rate of 0.9, wherein the probability of each element in the matrix being 1 is 0.9 and the probability of being 0 is 0.1. Multiplying the binary matrix and the mask matrix M element by element, obtaining the prompt matrix H;

[0018] S14. Assume that the data containing missing values ​​can be clustered into K classes. The initial cluster labels corresponding to the data containing missing values ​​in the K classes are represented as C1. The initial values ​​of the elements in the initial cluster label C1 are set to 0.

[0019] Further, in S2, the generative adversarial network includes a generator G and a discriminator D;

[0020] The generator G is used to accurately fill in the missing values ​​in the data matrix X. The network structure of the generator G is a fully connected layer;

[0021] The discriminator D is used to distinguish between observed data and filled data, and forms an adversarial relationship with the generator G, thereby improving the ability of the generator G. The discriminator D is a fully connected layer.

[0022] Furthermore, S2 specifically includes the following steps:

[0023] S21, the generator G in the generative adversarial network takes the concatenation of the data matrix X, the mask matrix M, and the clustering label C1 as input and obtains the hidden representation. After nonlinear transformation, the generator G finally outputs the padding matrix X';

[0024] S22, the discriminator D in the generative adversarial network receives the padding matrix X' and the prompt matrix H and obtains the hidden representation, and outputs the probability matrix P after nonlinear transformation;

[0025] S23, calculating the cross entropy loss between the probability matrix P and the mask matrix M, back-propagating the cross entropy loss to the discriminator D, and optimizing the discriminator D using the gradient descent method;

[0026] S24, calculating the mean square error loss between the non-missing data matrix X and the filling matrix X' and the logarithmic loss between the missing mask matrix M and the probability matrix P, back-propagating the logarithmic loss to the generator G, and optimizing the generator G using the gradient descent method;

[0027] S25. The generator G and the discriminator D are repeatedly trained against each other.

[0028] Further, in S3, the deep subspace clustering network is composed of a deep autoencoder and a self-expression layer;

[0029] The autoencoder is used to nonlinearly transform data into a latent space, thereby learning a low-dimensional representation of the data;

[0030] The self-expressive layer is located at the junction of the encoder and the decoder. It is a fully connected layer without bias and nonlinear activation. This fully connected layer encodes the self-expressive property of the data extracted from the union of the subspaces, that is, each data sample can be represented as a linear combination of other samples in the same subspace, and the pairwise affinity between all data points is learned through the standard back-propagation process.

[0031] Furthermore, S3 specifically includes the following steps:

[0032] S31, using the padding matrix X' as the input of the autoencoder of the deep subspace clustering network;

[0033] The data tuples in S32 and X' are mapped to latent vectors v through the encoder, and the transpose of v is used as the input of the self-expressive layer;

[0034] S33, the latent vector is passed through the self-expression layer coefficient matrix W s Fully connected, each latent vector is represented as a linear combination v' of other vectors;

[0035] S34, the linear combination vector v' is reconstructed through the decoder to obtain the reconstructed matrix X dec ;

[0036] S35. Calculate the square of the Frobenius norm between the reconstruction matrix and the padding matrix as the autoencoder loss; calculate the square of the Frobenius norm between the latent vector v and the linear combination vector v' as the self-expression loss; perform L-2 norm regularization on the self-expression layer coefficient matrix; and use the gradient descent method to optimize the entire clustering network.

[0037] Furthermore, S4 specifically includes the following steps:

[0038] S41, performing preprocessing operations of sparseness, symmetry and stabilization on the coefficient matrix of the self-expression layer;

[0039] S42, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix to extract a specified number of eigenvectors and eigenvalues;

[0040] S43, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of the matrix U;

[0041] S44, multiplying the matrix U processed by S43 by its own transposed matrix, and obtaining the affinity matrix A after adjustment.

[0042] Furthermore, S5 specifically includes the following steps:

[0043] S51, constructing an adjacency matrix W and a degree matrix D according to the affinity matrix A;

[0044] S52, calculating a Laplace matrix according to the adjacency matrix W and the degree matrix D and performing a normalization operation on the Laplace matrix to obtain a matrix L;

[0045] S53, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of U;

[0046] S54, calculating the smallest k eigenvalues ​​of the matrix L, obtaining the eigenvectors f corresponding to each of them, stacking these eigenvectors f by columns into an eigenvector matrix F, and further standardizing the eigenvector matrix F;

[0047] S55. Perform kmeans / GMM clustering on the rows in the feature vector matrix F, mark the original data corresponding to each cluster of the clustering result, output a new cluster label C2, and use it as a new label input for the generative adversarial network. Iterate the above S1 to S5 to obtain a high-precision filled data matrix.

[0048] The present invention also provides a storage medium, which includes a stored program, wherein when the program is run, any of the above-mentioned cluster analysis-driven high-precision missing data filling methods is executed.

[0049] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any one of the above-mentioned cluster analysis-driven high-precision missing data filling methods through the computer program.

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] The present invention first improves the data filling generative adversarial network. By taking clustering information as additional input, the generator in the network can better capture the category characteristics of the data. Under the guidance of the category characteristics, the generator can explore the underlying data structure and pattern, generate complete data that is more in line with the real data distribution, and thus improve the filling performance. On the other hand, clustering usually requires high-quality complete data. In this case, the deep subspace clustering network used for clustering uses the filled complete data as input to output accurate clustering results. The missing value filling task is interrelated with the clustering task and promotes each other.

[0052] In summary, the application of the technical solution of the present invention can take into account both missing value filling and downstream clustering tasks. By using clustering results that are more consistent with the internal structure of the data, we have enhanced the learning ability of the generative adversarial network, improved the quality and efficiency of the interpolation process, and used the filled data as a strong support for clustering. Through experimental verification, we found that the missing data filling method provided by this study can effectively improve the accuracy of filling and clustering. Compared with traditional methods, our method further improves the existing filling technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0054] Figure 1 It is the overall framework and flow chart of the missing value filling method of the present invention. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0056] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0057] like Figure 1 As shown, the present invention provides a high-precision missing data filling method driven by cluster analysis, comprising the following steps:

[0058] S1, obtain data containing missing values, preprocess the data containing missing values, and obtain the data matrix X, mask matrix M, prompt matrix H, and initial clustering label C1;

[0059] S11, representing the acquired data containing missing values ​​as a data matrix X, where the data matrix X is two-dimensional table data; a row of the two-dimensional table data is represented as a piece of data, and a column of the two-dimensional table data is represented as an attribute or feature of the data, and performing a normalization operation on the data matrix X;

[0060] S12. According to the data matrix X, the mask matrix corresponding to the data matrix X is represented as M; in the mask matrix M, if the attribute observation value of the jth column of the i-th row observation data is missing, M i,j =0, otherwise M i,j =1;

[0061] S13, generating a binary matrix with the same shape as the mask matrix M according to the prompt rate of 0.9, wherein the probability of each element in the matrix being 1 is 0.9 and the probability of being 0 is 0.1. Multiplying the binary matrix and the mask matrix M element by element, obtaining the prompt matrix H;

[0062] S14. Assume that the data containing missing values ​​can be clustered into K classes. The initial cluster labels corresponding to the data containing missing values ​​in the K classes are represented as C1. The initial values ​​of the elements in the initial cluster label C1 are set to 0.

[0063] S2, input the data matrix X, mask matrix M, prompt matrix H, and cluster label C1 into the generative adversarial network, and obtain the padding matrix X' and probability matrix P after nonlinear transformation; calculate the loss of the generator G and the discriminator D respectively, and optimize the generative adversarial network using the gradient descent method;

[0064] The generative adversarial network includes a generator G and a discriminator D;

[0065] The generator G is used to accurately fill in the missing values ​​in the data matrix X. The network structure of the generator G is a fully connected layer;

[0066] The discriminator D is used to distinguish between observed data and filled data, and forms an adversarial relationship with the generator G, thereby improving the ability of the generator G. The discriminator D is a fully connected layer.

[0067] S21, the generator G in the generative adversarial network takes the concatenation of the data matrix X, the mask matrix M, and the clustering label C1 as input and obtains the hidden representation. After nonlinear transformation, the generator G finally outputs the padding matrix X';

[0068] S22, the discriminator D in the generative adversarial network receives the padding matrix X' and the prompt matrix H and obtains the hidden representation, and outputs the probability matrix P after nonlinear transformation;

[0069] S23, calculating the cross entropy loss between the probability matrix P and the mask matrix M, back-propagating the cross entropy loss to the discriminator D, and optimizing the discriminator D using the gradient descent method;

[0070] S24, calculating the mean square error loss between the non-missing data matrix X and the filling matrix X' and the logarithmic loss between the missing mask matrix M and the probability matrix P, back-propagating the logarithmic loss to the generator G, and optimizing the generator G using the gradient descent method;

[0071] S25. The generator G and the discriminator D are repeatedly trained against each other.

[0072] S3, input the padding matrix X' into the deep subspace clustering network to obtain the reconstructed data matrix and the self-expression layer coefficient matrix; calculate the losses of the three components in the deep subspace clustering network respectively, and optimize them as a whole using the gradient descent method;

[0073] The deep subspace clustering network consists of a deep autoencoder and a self-expression layer;

[0074] The autoencoder is used to nonlinearly transform data into a latent space, thereby learning a low-dimensional representation of the data;

[0075] The self-expressive layer is located at the junction of the encoder and the decoder. It is a fully connected layer without bias and nonlinear activation. This fully connected layer encodes the self-expressive property of the data extracted from the union of the subspaces, that is, each data sample can be represented as a linear combination of other samples in the same subspace, and the pairwise affinity between all data points is learned through the standard back-propagation process.

[0076] S31, using the padding matrix X' as the input of the autoencoder of the deep subspace clustering network;

[0077] The data tuples in S32 and X' are mapped to latent vectors v through the encoder, and the transpose of v is used as the input of the self-expressive layer;

[0078] S33, the latent vector is passed through the self-expression layer coefficient matrix W s Fully connected, each latent vector is represented as a linear combination v' of other vectors;

[0079] S34, the linear combination vector v' is reconstructed through the decoder to obtain the reconstructed matrix X dec ;

[0080] S35. Calculate the square of the Frobenius norm between the reconstruction matrix and the padding matrix as the autoencoder loss; calculate the square of the Frobenius norm between the latent vector v and the linear combination vector v' as the self-expression loss; perform L-2 norm regularization on the self-expression layer coefficient matrix; and use the gradient descent method to optimize the entire clustering network.

[0081] S4, preprocessing the self-expression layer coefficient matrix, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix, adjusting the eigenvalues ​​and eigenvectors, obtaining the characteristic matrix U and normalizing it; calculating the product of the matrix U and the transpose of U, and obtaining the affinity matrix A after adjustment;

[0082] S41, performing preprocessing operations of sparseness, symmetry and stabilization on the coefficient matrix of the self-expression layer;

[0083] S42, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix to extract a specified number of eigenvectors and eigenvalues;

[0084] S43, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of the matrix U;

[0085] S44, multiplying the matrix U processed by S43 by its own transposed matrix, and obtaining the affinity matrix A after adjustment.

[0086] S5. Calculate the Laplace matrix based on the affinity matrix A and perform a normalization operation on the affinity matrix A to obtain the matrix L; perform eigendecomposition on the normalized Laplace matrix to construct a normalized eigenvector matrix F, where each row represents a sample; perform kmeans / GMM clustering on the normalized eigenvector matrix F, and assign the samples to different clusters based on the clustering results, and output a new cluster label C2;

[0087] S51, constructing an adjacency matrix W and a degree matrix D according to the affinity matrix A;

[0088] S52, calculating a Laplace matrix according to the adjacency matrix W and the degree matrix D and performing a standardization operation on the Laplace matrix to obtain a matrix L;

[0089] S53, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of U;

[0090] S54, calculating the smallest k eigenvalues ​​of the matrix L, obtaining the eigenvectors f corresponding to each of them, stacking these eigenvectors f by columns into an eigenvector matrix F, and further standardizing the eigenvector matrix F;

[0091] S55. Perform kmeans / GMM clustering on the rows in the feature vector matrix F, mark the original data corresponding to each cluster of the clustering result, output a new cluster label C2, and use it as a new label input for the generative adversarial network. Iterate the above S1 to S5 to obtain a high-precision filled data matrix.

[0092] S6. Input the new clustering label C2 as the new label of the generative adversarial network into S2, repeat S2 to S5 until the loss of the generative adversarial network converges and the loss of the deep subspace clustering network converges, and output the padding matrix X' obtained by S2 at this time as the high-precision padding data matrix.

[0093] Figure 1 The overall framework diagram of the proposed method is also shown, including the generative adversarial network (Imputer) and the deep subspace clustering network (Clusterer). The Imputer consists of a generator and a discriminator, and the Clusterer consists of an encoder, a self-expression layer, and a decoder.

[0094] Table 1 shows the effect comparison of the present invention in missing value filling, and Table 2 shows the effect comparison of clustering accuracy. The experiment used the Letter data set. We conducted experiments on both missing value filling and clustering tasks. The criterion for judging the filling effect is the RMSE value between the original data matrix and the filling matrix. The smaller the value, the smaller the difference between the filled data and the original data, that is, the better the effect. The criterion for judging the clustering effect is the Precision value between the original label and the clustering label. The larger the value, the smaller the difference between the clustering label and the original label, that is, the better the effect. It can be seen from this that this method is superior in filling tasks and clustering tasks.

[0095] Table 1 Comparison of the filling effect of the method described in the present invention (DACIN) and the existing filling technology

[0096] Missing rate (%) DACIN GAIN HI-VAE MCFlow SAITS MICE EM 10 0.09033 0.14595 0.18443 0.11621 0.10270 0.13143 0.10885 20 0.09360 0.15325 0.18767 O.13104 O.11616 0.14431 0.12352 30 0.09763 0.16590 0.19694 0.14656 0.12042 0.16163 0.14074 40 0.10058 0.18248 0.20713 0.15690 0.13688 0.18128 0.15011 50 0.11247 O.19295 O.22626 O.17913 O.14845 0.20069 0.16280

[0097] Table 2 Comparison of clustering effects between the method described in the present invention (DACIN) and existing filling technology

[0098] Missing rate (%) DACIN GAIN HI-VAE MCFlow SAITS MICE EM 10 0.88959 O.75415 0.71284 0.82627 0.84127 0.79026 0.81897 20 0.86886 0.71742 0.70107 0.81600 O.83503 0.78809 0.77049 30 0.83653 0.62609 0.68812 0.80179 0.82831 0.76403 0.76725 40 0.78991 O.61195 0.64208 0.65770 0.76256 0.73430 0.75945 50 0.77739 O.48982 0.62115 0.64987 0.75241 0.69326 0.72619

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-precision missing data filling method driven by cluster analysis, characterized in that: The steps include: S1, obtain data containing missing values, preprocess the data containing missing values, and obtain the data matrix X, mask matrix M, prompt matrix H, and initial clustering label C1; S2, input the data matrix X, mask matrix M, prompt matrix H, and cluster label C1 into the generative adversarial network, and obtain the padding matrix X' and probability matrix P after nonlinear transformation; Calculate the losses of the generator G and the discriminator D respectively, and use the gradient descent method to optimize the generative adversarial network; S3, input the padding matrix X' into the deep subspace clustering network to obtain the reconstructed data matrix and the self-expression layer coefficient matrix; calculate the losses of the three components in the deep subspace clustering network respectively, and optimize them as a whole using the gradient descent method; S4, preprocessing the self-expression layer coefficient matrix, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix, adjusting the eigenvalues ​​and eigenvectors, obtaining the characteristic matrix U and normalizing it; calculating the product of the matrix U and the transpose of U, and obtaining the affinity matrix A after adjustment; S5. Calculate the Laplace matrix based on the affinity matrix A and perform a normalization operation on the affinity matrix A to obtain the matrix L; perform eigendecomposition on the normalized Laplace matrix to construct a normalized eigenvector matrix F, where each row represents a sample; perform kmeans / GMM clustering on the normalized eigenvector matrix F, and assign the samples to different clusters based on the clustering results, and output a new cluster label C2; S6. Input the new clustering label C2 as the new label of the generative adversarial network into S2, repeat S2 to S5 until the loss of the generative adversarial network converges and the loss of the deep subspace clustering network converges, and output the padding matrix X' obtained by S2 at this time as the high-precision padding data matrix.

2. The high-precision missing data filling method driven by cluster analysis according to claim 1, characterized in that: S1 specifically includes the following steps: S11, representing the acquired data containing missing values ​​as a data matrix X, where the data matrix X is two-dimensional table data; a row of the two-dimensional table data is represented as a piece of data, and a column of the two-dimensional table data is represented as an attribute or feature of the data, and performing a normalization operation on the data matrix X; S12, according to the data matrix X, the mask matrix corresponding to the data matrix X is represented as M; Mask In the matrix M, if the attribute observation value of the jth column of the observation data in the i-th row is missing, M i,j =0, otherwise M i,j =1; S13, generating a binary matrix with the same shape as the mask matrix M according to the prompt rate of 0.9, wherein the probability that each element in the matrix is ​​1 is 0.9, and the probability that it is 0 is 0.1; multiplying the binary matrix by the mask matrix M element by element to obtain the prompt matrix H; S14. Assume that the data containing missing values ​​can be clustered into K classes. The initial cluster labels corresponding to the data containing missing values ​​in the K classes are represented as C1. The initial values ​​of the elements in the initial cluster label C1 are set to 0.

3. The high-precision missing data filling method driven by cluster analysis according to claim 1, characterized in that: In S2, the generative adversarial network includes a generator G and a discriminator D; The generator G is used to accurately fill in the missing values ​​in the data matrix X. The network structure of the generator G is a fully connected layer; The discriminator D is used to distinguish between observed data and filled data, and forms an adversarial relationship with the generator G, thereby improving the ability of the generator G. The discriminator D is a fully connected layer.

4. The high-precision missing data filling method driven by cluster analysis according to claim 3, characterized in that: S2 specifically includes the following steps: S21, the generator G in the generative adversarial network takes the concatenation of the data matrix X, the mask matrix M, and the clustering label C1 as input and obtains the hidden representation. After nonlinear transformation, the generator G finally outputs the padding matrix X'; S22, the discriminator D in the generative adversarial network receives the padding matrix X' and the prompt matrix H and obtains the hidden representation, and outputs the probability matrix P after nonlinear transformation; S23, calculating the cross entropy loss between the probability matrix P and the mask matrix M, back-propagating the cross entropy loss to the discriminator D, and optimizing the discriminator D using the gradient descent method; S24, calculating the mean square error loss between the non-missing data matrix X and the filling matrix X' and the logarithmic loss between the missing mask matrix M and the probability matrix P, back-propagating the logarithmic loss to the generator G, and optimizing the generator G using the gradient descent method; S25. The generator G and the discriminator D are repeatedly trained against each other.

5. The high-precision missing data filling method driven by cluster analysis according to claim 1, characterized in that: In S3, the deep subspace clustering network consists of a deep autoencoder and a self-expression layer; The autoencoder is used to nonlinearly transform data into a latent space, thereby learning a low-dimensional representation of the data; The self-expressive layer is located at the junction of the encoder and the decoder. It is a fully connected layer without bias and nonlinear activation. This fully connected layer encodes the self-expressive property of the data extracted from the union of the subspaces, that is, each data sample can be represented as a linear combination of other samples in the same subspace, and the pairwise affinity between all data points is learned through the standard back-propagation process.

6. The high-precision missing data filling method driven by cluster analysis according to claim 5, characterized in that: S3 specifically includes the following steps: S31, using the padding matrix X' as the input of the autoencoder of the deep subspace clustering network; The data tuples in S32 and X' are mapped to latent vectors v through the encoder, and the transpose of v is used as the input of the self-expressive layer; S33, the latent vector is passed through the self-expression layer coefficient matrix W s Fully connected, each latent vector is represented as a linear combination v' of other vectors; S34, the linear combination vector v' is reconstructed through the decoder to obtain the reconstructed matrix X dec ; S35, calculate the square of the Frobenius norm between the reconstruction matrix and the padding matrix as the autoencoder loss; The square of the Frobenius norm between the latent vector v and the linear combination vector v' is calculated as the self-expression loss; the coefficient matrix of the self-expression layer is regularized with the L-2 norm; and the entire clustering network is optimized using the gradient descent method.

7. The high-precision missing data filling method driven by cluster analysis according to claim 1, characterized in that: S4 specifically includes the following steps: S41, performing preprocessing operations of sparseness, symmetry and stabilization on the coefficient matrix of the self-expression layer; S42, performing singular value decomposition on the preprocessed self-expression layer coefficient matrix to extract a specified number of eigenvectors and eigenvalues; S43, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of the matrix U; S44, multiplying the matrix U processed by S43 by its own transposed matrix, and obtaining the affinity matrix A after adjustment.

8. The high-precision missing data filling method driven by cluster analysis according to claim 7, characterized in that: S5 specifically includes the following steps: S51, constructing an adjacency matrix W and a degree matrix D according to the affinity matrix A; S52, calculating a Laplace matrix according to the adjacency matrix W and the degree matrix D and performing a standardization operation on the Laplace matrix to obtain a matrix L; S53, performing a square root operation on the eigenvalue and multiplying it with the eigenvector to obtain a matrix U, and performing L2 normalization on each row of U; S54, calculating the smallest k eigenvalues ​​of the matrix L, obtaining the eigenvectors f corresponding to each of them, stacking these eigenvectors f by columns into an eigenvector matrix F, and further standardizing the eigenvector matrix F; S55. Perform kmeans / GMM clustering on the rows in the feature vector matrix F, mark the original data corresponding to each cluster of the clustering result, output a new cluster label C2, and use it as a new label input for the generative adversarial network. Iterate the above S1 to S5 to obtain a high-precision filled data matrix.

9. A storage medium, characterized in that: The storage medium includes a stored program, wherein when the program is run, the high-precision missing data filling method driven by clustering analysis as described in any one of claims 1 to 8 is executed.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: The processor executes the high-precision missing data filling method driven by clustering analysis as described in any one of claims 1 to 8 through the operation of the computer program.

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