A model and method for predicting biological traits by integrating genetic background and variation information

Abstract

The application discloses a model and method for predicting biological traits by comprehensively integrating genetic background and variation information, and the model comprises: a Siamese network which generates and extracts genetic background and genetic correlation information between samples, establishes an embedding vector for each sample to represent the genetic background information; a genetic variation embedding network which uses a deep learning network to extract complex high-order information using whole genome variation information of each sample, establishes an embedding vector to represent the cumulative effect of genetic variation on traits; and a fusion and trait prediction module which realizes accurate prediction of traits by organically fusing the embedding vectors output by the above two modules. The application can solve the problem that genetic background information and genomic variation information cannot be effectively fused in the prior art, effectively capture the nonlinear effect between genes, and greatly improve the accuracy of genomic selection and the genetic architecture analysis capability of complex traits.

Description

TECHNICAL FIELD

[0001] The present application relates to the fields of biological trait prediction, plant and animal breeding and artificial intelligence, and specifically relates to a model method for predicting biological traits by integrating genetic background and variation information. BACKGROUND

[0002] Genotype-based phenotype prediction has wide applications in medicine, plant and animal genetics and biological research. In plant and animal breeding, the related methods are often referred to as whole genome selection. Existing prediction methods usually rely on linear models, and commonly used methods such as GBLUP and rrBLUP perform well in the prediction of some traits, but they cannot capture the nonlinear relationship between genes. These methods show limitations in prediction ability when dealing with complex traits.

[0003] Some deep learning methods are used for genotype-based phenotype prediction to improve nonlinear prediction ability. However, existing deep learning models are not effective in capturing the complex relationship of genetic variation. Most methods have good prediction accuracy for individual or partial test traits, but for the remaining traits, the prediction ability is often poor, lacking sufficient robustness. Existing methods also have shortcomings in the integration of genetic background information. Most methods focus on genomic variation and ignore the role of genetic background, resulting in low prediction accuracy and insufficient model robustness.

[0004] MMNet has the following characteristics:

[0005] 1. Accuracy and robustness of prediction performance of MMNet:

[0006] MMNet model performs well on 12 rice agronomic traits (such as yield, protein content, heading date, etc.), especially in prediction ability, significantly exceeding traditional linear models (such as GBLUP) and other existing deep learning models. Through its efficient prediction ability, MMNet achieves higher accuracy in multiple trait prediction.

[0007] 2. MMNet adaptive weight adjustment mechanism:

[0008] MMNet adaptively adjusts the relative amount of information between genetic background information and genomic variation during training. Specifically, the model can adaptively combine genetic background information and site variation information to achieve higher prediction accuracy. Through the adaptive learning mechanism of MMNet, the genetic architecture of unknown traits can be analyzed.

[0009] 3. MMNet captures nonlinear effects:

[0010] One of the highlights of MMNet is its ability to capture complex nonlinear effects, specifically in predicting plant height and heading date, it can capture information beyond additive genetic effects.

[0011] The application develops a new deep learning model based on genotype phenotype prediction, proposes a nonlinear deep learning network (MMNet) similar to a hybrid model, and solves the shortcomings of existing genotype phenotype prediction technology.

[0012] 1. Existing mainstream methods such as BLUP and GBLUP usually rely on linear models, although they have achieved certain results in the prediction of some phenotypes, but these methods have failed to effectively capture the nonlinear effects in complex traits. Although deep learning methods have been introduced into the field of genomic selection in recent years to improve this, existing deep learning models generally have the following problems: genetic background information and genomic variation information are not fully integrated, and the current deep learning model usually takes the effects of genetic background information and genomic variation as independent input variables, and fails to effectively integrate the complex interaction effects between the two into the prediction model. This processing method causes the model to fail to fully utilize the internal relationship between genetic variation and background information, thereby affecting the prediction accuracy.

[0013] We evaluated the performance of the MMNet model in predicting 12 agronomic traits of rice (such as yield, protein content, and heading date, etc.), and the results showed that MMNet outperformed the existing six models (XGBoost, MLP, RF, GBLUP_Gs, BayesC and DNNGP) in all traits. In terms of prediction performance, MMNet not only achieved the highest R 2 score in all traits, but also far exceeded other models in terms of average and median Pearson correlation coefficient (PCC). MMNet also performed well in error indicators such as NMSE, RRMSE, and MAPE, especially in predicting complex traits such as yield, protein content, and heading date, with the smallest error. Overall, MMNet demonstrates strong adaptability and accuracy, and can effectively deal with the diversity and complexity of rice agronomic traits.

[0014] 2. Lack of adaptability: The existing methods lack the ability to adaptively adjust the contribution of genetic background information and the impact of genomic variation. Because different traits often have completely different genetic architectures. Some traits, such as the growth period of rice planted in a single production area and many rare genetic diseases in humans, are often controlled by a small number of major genes. There are also many traits, such as rice yield or human height, type 2 diabetes, etc., which are often controlled by a large number of small effect genes. Traits with different genetic architectures have different contribution rates of genetic background and genomic variation to prediction accuracy. The existing model fails to dynamically adjust the contribution of the two according to the characteristics of different phenotypes, so that the prediction effect cannot be optimized. Further, the existing method ignores the potential importance of the genetic structure of the phenotype and the genetic background information, and lacks the ability to analyze the genetic structure of the trait.

[0015] We explored the contribution of ESN and VE subnetworks in MMNet to trait prediction. The results showed that the genetic structure of the trait determines the weight distribution of the genetic background information and the genomic variation information. For traits with similar genetic basis, such as heading date, plant height and stem length, prediction mainly relies on key genomic variations, and the weight of VE is greater than that of ESN. For traits affected by a large number of small effect genes, such as grain yield and protein content, MMNet relies more on genetic background information to improve prediction performance through the cumulative effect of small effect genes. This weight distribution reflects the genetic structure of the trait and has important genetic and breeding practice significance. The adaptive learning of MMNet is highly consistent with breeding practice, and can provide valuable guidance for complex trait breeding.

[0016] Overall, the present application aims to solve these problems in the existing method, and proposes a nonlinear deep learning network (MMNet) of a mixed model. MMNet adaptively adjusts the contribution of genetic background information and genomic variation during training, effectively analyzes the genetic structure of each trait, and improves the accuracy of whole genome selection. SUMMARY

[0017] The purpose of the present application is to provide a model method for predicting biological traits by integrating genetic background and variation information, and a nonlinear deep learning network (MMNet) of a mixed model is proposed. MMNet adaptively adjusts the contribution of genetic background information and genomic variation during training, effectively analyzes the genetic structure of each trait, and improves the accuracy of whole genome selection.

[0018] To achieve the above-mentioned purpose, the technical solutions adopted by the present application are as follows:

[0019] A model for predicting biological traits by integrating genetic background and variation information, the model is a nonlinear deep learning network model of a mixed model, comprising the following modules:

[0020] a Siamese network which generates and extracts genetic background information between samples and genetic correlation information between samples, to establish an embedding vector for each sample to represent its genetic background information;

[0021] a genetic variation embedding network which uses a deep learning network to extract complex high-order information using the whole genome variation information of each sample, to establish an embedding vector to represent the cumulative effect of genetic variation on traits;

[0022] a fusion and trait prediction module which realizes accurate prediction of traits by organically fusing the embedding vectors output by the above two modules.

[0023] Further, the embedding Siamese network comprises a backbone subnetwork and a weight sharing mechanism; the backbone subnetwork is composed of multiple fully connected layers, batch normalization layers, Leaky ReLU activation layers and Dropout layers, and the input is genotype and phenotype data, and the network is trained using label values; the weight sharing mechanism generates an embedding vector for each sample based on the backbone subnetwork through weight sharing; the genetic correlation between samples is measured by the Euclidean distance between embedding vectors, and the genetic correlation between a sample and the remaining samples is further generated into a corresponding embedding vector by a multilayer perceptron.

[0024] Further, the genetic correlation between samples is calculated according to the following formula:

[0025]

[0026] wherein qi and qj represent the embedding vectors of sample i and sample j respectively, and dis represents the Euclidean distance between embedding vectors.

[0027] Further, in the embedding Siamese network module, the genetic background information between samples provided by the user is directly used to generate relevant embedding vectors.

[0028] Further, the genetic variation embedding network is composed of two branches, the upper layer uses a residual unit which is composed of two 1x3 convolution layers, a Batch Normalization layer and an activation function are inserted after the first layer convolution, and a final Batch Normalization layer is connected after the second convolution; the skip connection is composed of a 1x1 convolution layer and a batch normalization layer; the lower branch includes fully connected layers, batch normalization layers, Leaky ReLU activation layers and Dropout layers; finally, the information of the upper and lower layers is fused by weighted summation.

[0029] Further, in the embedded Siamese network and the genetic variation embedded network, two scale embedding vectors are generated, and the embedding representation of the embedded Siamese network and the genetic variation embedded network is fused by the fusion and trait prediction module, and then a trait prediction result is generated through multiple fully connected layers.

[0030] A method for predicting biological traits by comprehensively considering genetic background and variation information, comprising the following steps:

[0031] Step 1, data preprocessing:

[0032] The preprocessed genetic data and corresponding phenotype data are used for subsequent model training;

[0033] Step 2, constructing a network model as in the above scheme:

[0034] The network model is divided into three parts: an embedded Siamese network, a genetic variation embedded network, and a fusion and trait prediction module.

[0035] Step 3, training the model and evaluating the contribution in the model training process.

[0036] Based on principal component analysis algorithm or network weight, the contribution of the embedded Siamese network and the genetic variation embedded network is evaluated.

[0037] Further, the principal component analysis algorithm is specifically: for N samples in the data set, all embedding vectors Z1,…,ZN form a matrix Z of size N×2p; apply principal component analysis (PCA) based on singular value decomposition (SVD) to the matrix Z; calculate the contribution of each principal component to the original feature, and perform weighted summation on the weight of ESN and VE based on the variance contribution, thereby obtaining the contribution weight W of each subnetwork to the final prediction result. VE and W ESN :

[0038]

[0039] U and V are matrices obtained in the complete SVD of matrix Z, where U contains left singular vectors and V contains right singular vectors, is the jth component of the ith eigenvector V i , and η i is the ith eigenvalue.

[0040] A computer device comprising a memory, a processor, and computer readable instructions stored in the memory and executable on the processor, wherein the processor executes the computer readable instructions to implement the method in the above scheme.

[0041] A readable storage medium storing computer readable instructions, which when executed by one or more processors, cause the one or more processors to perform the steps in the above solutions.

[0042] The beneficial effects of the present application are as follows:

[0043] (1) Improve prediction accuracy: by fusing gene background and gene variation information, MMNet can better capture nonlinear effects and complex genetic structures, improving the prediction ability of complex traits.

[0044] (2) Shorten the breeding cycle: the efficient prediction ability of MMNet makes the breeding decision more accurate, thereby greatly shortening the breeding period.

[0045] (3) Analyze the genetic architecture of the phenotype: MMNet not only can predict the phenotype, but also can reveal the genetic structure of the phenotype, helping to deeply understand the complex relationship between genotype and phenotype. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a detailed introduction of MMNet network. Figure a is an overview of MMNet network; the extended Siamese network is used to extract the embedding of genetic background information; at the same time, the genetic variation embedding network based on CNN is used to extract the embedding of genomic variation information; the embedding of the two layers is aligned and integrated, which is used for network training in the fusion layer, and finally the trait prediction is realized. Figure b is a detailed introduction of ESN module in figure a; a simple neural network is trained using genotype data and phenotype data, and the embedding representation of each sample in the network is extracted one by one. The genetic relationship between samples is obtained by evaluating the embedding of different samples, and then the embedding vector representing the genetic relationship is obtained. Figure c is a detailed introduction of the residual unit used in the VE module of figure a; it is composed of two convolutions combined with batch normalization and Leaky ReLU activation function, and the jump connection part is directly processed by a convolution combined with a batch normalization.

[0047] Figure 2 is a comparison chart with other commonly used methods, and MMNet performs well on multiple rice agronomic traits. The column chart of figure a shows the R 2 of 12 rice phenotypes predicted by various models, and the maximum indicates that it has the highest prediction accuracy; the box plot of figure b shows that the mean and median of the correlation coefficient of MMNet in 12 phenotypes are the highest, indicating that its model is robust; figure c is the error of the phenotype under three different genetic architectures is the smallest.

[0048] Figure 3 is the prediction ability of plant height and growth period exceeds the additive genetic force of the corresponding phenotype, which indicates that nonlinear effects have been detected.

[0049] Figure 4 is the dynamic pattern of the contribution of ESN embedding and VE embedding in the training process. Among the 12 agronomic traits, the VE (genomic variation information) contribution of traits such as heading date, plant height and stem length is significantly higher than the ESN (genetic background information) contribution. The ESN contribution of other traits is much higher than the VE contribution, which matches the phenotype genetic architecture.

[0050] Figure 5 is the prediction ability of MMNet on 12 agronomic traits and the change of PVE with LD threshold. a. The change trend of R2 (red line) and PVE (blue line) with LD threshold in the range of 0.1-0.5. b. The correlation coefficient column chart of prediction ability (R2) and PVE of 12 traits. c. The prediction ability (R2) and PVE growth percentage column chart of three LD threshold intervals (0.1→0.5, 0.1→0.3, 0.3→0.5). It is illustrated that the model prediction ability is regulated by the genotype to explain the variance of the trait. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all embodiments.

[0052] Embodiment one

[0053] A model for predicting biological traits by integrating genetic background and variation information, specifically proposes a nonlinear deep learning network (MMNet) model of a mixed model type, realizes the precise prediction of phenotypes of animals and plants, human physiological indicators or disease conditions by using whole genome genetic variation; the model comprises the following modules:

[0054] Embedding Siamese network (Embedding Siamese Network, ESN), which generates and extracts genetic background and genetic correlation information between samples, establishes an embedding vector for each sample to represent its genetic background information;

[0055] Variation embedding network (Variation Embedding Network, VE), which uses deep learning network to extract complex high-order information using whole genome variation information of each sample, establishes an embedding vector to represent the cumulative effect of genetic variation on traits;

[0056] The fusion and trait prediction module realizes the precise prediction of traits by organically fusing the embedding vectors output by the above two modules.

[0057] The embedding Siamese network includes a backbone subnetwork and a weight sharing mechanism. The backbone subnetwork is composed of multiple fully connected layers, batch normalization layers, Leaky ReLU activation layers and Dropout layers. The input is the genotype (1 x M) and phenotype data, and the network is trained using the label value; and the weight sharing mechanism generates an embedding vector (1 x T) for each sample based on the backbone subnetwork through weight sharing. The genetic correlation (GR) between samples is measured by the Euclidean distance between the embedding vectors. The genetic correlation between a sample and the remaining samples is further generated by a multilayer perceptron to generate a corresponding embedding vector.

[0058] In the embedding Siamese network module, the genetic background information between samples provided by the user can be directly used to generate relevant embedding vectors.

[0059] The genetic variation embedding network is composed of two branches. The upper layer uses a residual unit (Residual Unit) composed of two 1x3 convolution layers. The first layer is inserted with a Batch Normalization layer and an activation function after convolution, and the second convolution is followed by a final Batch Normalization layer. The Skip Connection is composed of a 1x1 convolution layer and a batch normalization layer. The lower branch includes fully connected layers, batch normalization layers, Leaky ReLU activation layers and Dropout layers. Finally, the information of the upper and lower layers is fused by weighted summation.

[0060] Embodiment two

[0061] Step 1: data preprocessing;

[0062] First, the rice genotype and phenotype data are subjected to quality control (QC) processing to ensure the integrity of the data and the reliability of the analysis. Data quality control includes the following three steps: variation screening: first, exclude genetic markers with a missing value rate of more than 25%; then exclude genetic markers with a MAF (minor allele frequency) of less than 0.05. The quality-controlled genetic variation data is encoded as 1 and -1 for homozygous and heterozygous genotypes, respectively, and the missing genotype value is filled with 0.

[0063] We performed a normality test on the phenotype data. For phenotype data that does not meet the normal distribution, we use a specific mathematical transformation to convert the relevant phenotype data to meet the normal distribution. The 12 rice agronomic traits shown in this application all pass the normality test.

[0064] The preprocessed genetic data and corresponding phenotype data are used for subsequent model training.

[0065] Step 2: construct MMnet network;

[0066] The MMnet network is mainly divided into three parts: an embedding Siamese network (ESN), a variation embedding network (VE), and an embedding fusion module. The following is a detailed introduction.

[0067] (1) ESN module

[0068] This embodiment proposes a new Siamese network architecture, which enhances the learning ability of the network for the genetic correlation between samples by introducing embedding and weight sharing mechanism. The ESN module includes two main parts.

[0069] Backbone subnetwork: The backbone subnetwork is used to train the embedding of the sample, and the input includes the genotype and phenotype data of each sample. The subnetwork is composed of multiple fully connected layers, batch normalization layers, Leaky ReLU activation layers, and Dropout layers. The input is the genotype (1xM) and phenotype data, and the network is trained using the label value.

[0070] Weight sharing mechanism: Based on the backbone subnetwork, the weight sharing mechanism is used to generate the embedding vector (1xT) of each sample. The genetic correlation (GR) between samples is measured by the Euclidean distance between the embedding vectors, and the specific calculation formula is as follows:

[0071]

[0072] where q i and q j represent the embedding vectors of sample i and sample j, respectively, and dis represents the Euclidean distance between the embedding vectors.

[0073] (2) VE module

[0074] The VE module processes the genotype data and extracts genomic information through two branches.

[0075] Upper branch: The upper layer uses a residual unit (Residual Unit), which is composed of two 1x3 convolution layers. The first layer is followed by a Batch Normalization layer and an activation function, and the second convolution is followed by a final Batch Normalization layer. The Skip Connection is composed of a 1x1 convolution layer and a batch normalization layer. The convolution operation of the upper layer effectively captures the local features in the genotype data and reduces the gradient vanishing problem through the residual unit.

[0076] Lower branch: The lower branch includes fully connected layers, batch normalization layers, Leaky ReLU activation layers, and Dropout layers. Finally, the information of the upper and lower branches is fused by weighted summation, and a 1024-dimensional embedding based on gene variation information is output.

[0077] The role of the VE module is to convert the input genotype data from (N x M) to an embedding representation of (N x 1024), extract complex gene variation information, and enhance the information mining capability of the network.

[0078] (3) Embedding fusion module

[0079] The embedding fusion module splices the embedding vectors (1 x p) from the ESN and VE subnetworks to form a new vector (1 x 2p). After batch normalization processing, the fusion vector is input to the scoring unit for final prediction. The scoring unit includes multiple fully connected layers, Leaky ReLU activation layers, and Dropout layers, and finally outputs the predicted phenotype value.

[0080] During training, to ensure that the contributions of gene background information and genomic variation information are fairly evaluated, in addition to calculating the loss through the final predicted value, the embedding of each subnetwork is also passed through the scoring unit and added to the final loss, so that the network is more comprehensively trained.

[0081] Step 3: Contribution evaluation during model training

[0082] To evaluate the contributions of the ESN and VE subnetworks, this embodiment proposes an algorithm based on principal component analysis (PCA). Specifically, for N samples in the dataset, all embedding vectors Z1,…,Z N A matrix Z of size (N x 2p) is formed. Apply principal component analysis (PCA) based on singular value decomposition (SVD) to the matrix Z. Calculate the contribution of each principal component to the original features, and based on the variance contribution, perform weighted summation on the weights of ESN and VE, to obtain the contribution weight (W VE and W ESN ) of each subnetwork to the final prediction result.

[0083]

[0084] U and V are matrices obtained from the complete SVD of matrix Z, where U contains left singular vectors and V contains right singular vectors, is the jth component of the ith feature vector Vi, and ηi is the ith eigenvalue.

[0085] The scheme of the patent is based on the cross principle of deep learning and genetics, and the accuracy of phenotype prediction is improved by combining nonlinear modeling methods (such as Siamese network, convolutional neural network, residual connection, etc.) with statistical analysis methods such as PCA. The scheme can adapt to different genomic data and phenotype characteristics, dynamically adjust the contribution of genetic background and variation information, and thus show excellent performance in the prediction of various complex traits.

[0086] Through the above technical scheme, the present application can solve the problem that genetic background information and genomic variation information cannot be effectively fused in the prior art, and effectively capture the nonlinear effect between genes, greatly improving the accuracy of genomic selection and the genetic architecture analysis ability of complex traits.

[0087] In summary, the present application can be applied in the following aspects:

[0088] Plant and animal breeding: can be widely applied to whole genome selection, realizing efficient breeding of crops and animals.

[0089] Genetic research: MMNet provides a new method for geneticists to analyze the genetic architecture of traits, and can fully utilize nonlinear effects to assist trait prediction.

[0090] Biological trait prediction: MMNet can be used for phenotype prediction of different plants or animals based on genomic information, especially for complex traits (quality, yield, etc.).

[0091] Disease prediction: MMNet can predict the incidence mode and physiological indicators of specific diseases based on human genomic information.

[0092] The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the above examples do not limit the protection scope of the present application in any form, and any technical solutions obtained by equivalent replacement or the like fall within the protection scope of the present application. The parts not involved in the present application are the same as or can be realized by the prior art.

Claims

1. A method for predicting biological traits by comprehensively considering genetic background and variation information, characterized in that, Includes the following steps: Step 1, Data Preprocessing: The preprocessed gene data and corresponding phenotypic data are used for subsequent model training; Step 2: Construct the network model, which is a hybrid-model-like nonlinear deep learning network model, including the following modules: The Siamese network is embedded, which generates and extracts genetic background and genetic correlation information between samples, and establishes an embedding vector for each sample to represent its genetic background information. Genetic variation embedding networks utilize deep learning networks to extract complex high-order information from the whole genome variation information of each sample and establish embedding vectors to characterize the cumulative effect of genetic variation on traits. The fusion and trait prediction module achieves accurate trait prediction by organically fusing the embedding vectors output by the two modules mentioned above. Step 3: Train the model and evaluate its contribution during the training process; The contributions of the two sub-networks, the Siamese embedding network and the genetic variation embedding network, are evaluated based on principal component analysis or network weights.

2. The method for predicting biological traits by integrating genetic background and variation information according to claim 1, characterized in that, The embedded Siamese network includes a backbone subnetwork and a weight sharing mechanism. The backbone subnetwork consists of multiple fully connected layers, batch normalization layers, Leaky ReLU activation layers, and Dropout layers. The input is genotype and phenotype data, and the network is trained using label values. The weight sharing mechanism generates an embedding vector for each sample based on the backbone subnetwork through weight sharing. The genetic correlation between samples is measured by the Euclidean distance between the embedding vectors. The genetic correlation between a sample and the other samples is further used to generate corresponding embedding vectors through a multilayer perceptron.

3. The method for predicting biological traits by integrating genetic background and variation information according to claim 2, characterized in that, The specific formula for calculating the genetic correlation between samples is as follows: ， Where qi and qj represent the embedding vectors of sample i and sample j, respectively, and dis represents the Euclidean distance between the embedding vectors.

4. The method for predicting biological traits by integrating genetic background and variation information according to claim 1, characterized in that, In the embedded Siamese network module, the genetic background information between user-provided samples is directly used to generate relevant embedding vectors.

5. The method for predicting biological traits by integrating genetic background and variation information according to claim 1, characterized in that, The genetic variation embedding network consists of two branches. The upper layer uses residual units, which are composed of two 1×3 convolutional layers. After the first convolution, a batch normalization layer and an activation function are inserted, and after the second convolution, a final batch normalization layer is connected. The skip connection consists of a 1×1 convolutional layer and a batch normalization layer. The lower branch includes a fully connected layer, a batch normalization layer, a Leaky ReLU activation layer, and a dropout layer. Finally, the information from the upper and lower layers is fused by weighted summation.

6. The method for predicting biological traits by integrating genetic background and variation information according to claim 1, characterized in that, Embedding vectors at two scales are generated by embedding Siamese networks and genetic variation embedding networks. By fusing the embeddings, trait prediction results are produced.

7. The method for predicting biological traits by integrating genetic background and variation information according to claim 1, characterized in that, The principal component analysis algorithm is as follows: For N samples in the dataset, all embedding vectors Z1,…,ZN form a matrix Z of size N × 2p; Principal component analysis (PCA) based on singular value decomposition (SVD) is applied to matrix Z; the contribution of each principal component to the original features is calculated, and the weights of ESN and VE are weighted and summed based on the variance contribution to obtain the contribution weight W of each sub-network to the final prediction result. VE and W ESN : ， ， ， U and V are matrices obtained from the complete SVD of matrix Z, where U contains the left singular vectors and V contains the right singular vectors. It is the i-th eigenvector V i The j-th component, η i It is the i-th eigenvalue.

8. A computer device comprising a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor, characterized in that, The processor implements the method as described in any one of claims 1 to 7 when executing the computer-readable instructions.

9. A readable storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the steps of any one of claims 1 to 7.

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