Characteristic reduction and generalized inverse technology-based phenotype prediction method and system capable of adaptively fusing linear and nonlinear effects

Abstract

The invention provides a feature reduction and generalized inverse technology-based phenotype prediction method and system for self-adaptive fusion of linear and nonlinear effects, and constructs a new model for self-adaptive fusion of linear and nonlinear effects of prediction factors for crop phenotype prediction. And the importance degree of different effects on the phenotype is evaluated through a self-adaptive weight adjustment method, so that the function of comprehensively considering the influence of the linear main effect and the nonlinear relationship in crop phenotype prediction is realized. When the method is used for solving the model, the training data set is subjected to feature reduction, and the model is rapidly and effectively solved by using the generalized inverse, so that the determination efficiency of the phenotype value of the biological material is improved. According to the invention, model learning is carried out through the learning set and the test set obtained by multiple times of random division of the experimental data set, the system error of the model is reduced, and the stability of the phenotype prediction result is improved. The effectiveness of phenotype prediction is verified on genotype data based on DNA molecular markers and intermediate omics data based on metabolites.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent breeding, and specifically relates to a phenotypic prediction method and system based on feature reduction and generalized inverse technology that adaptively integrates linear and nonlinear effects. Background Art

[0002] Crop phenotypic prediction is the process of predicting crop phenotypic characteristics by analyzing crop genetic information, environmental factors or other relevant data. The traditional determination of crop agronomic phenotypic values ​​is time-consuming and inefficient. In order to improve the efficiency of phenotypic value determination, whole genome-based methods are currently often used to achieve trait prediction.

[0003] Genomic selection (GS) uses high-density molecular markers distributed throughout the genome, such as single nucleotide polymorphisms (SNPs), to calculate the genetic value of traits and estimate breeding values. The GS method can capture all genetic effects that lead to phenotypic variation, and the phenotype evaluation value can be obtained using the individual genotype, thereby achieving early selection of potential superior varieties, increasing genetic gain per unit time, and ensuring rapid population improvement.

[0004] At present, the existing algorithms for GS mainly focus on genetic statistics and machine learning methods. The former includes best linear unbiased estimation (GBLUP), Bayesian regression, least absolute shrinkage and selection operator (LASSO), etc., and the latter includes support vector machine (SVM), random forest (RF), reproducing kernel Hilbert space (RKHS) and deep learning (DL) and other methods. The models solved by the algorithm are generally linear models (such as LASSO), mixed linear models (such as BLUP), and nonlinear models (such as RF, RKHS, DL). Among them, linear or mixed linear models mainly capture the linear effects of the genome and phenotype of the population, but ignore nonlinear effects such as multi-individual interactions and correlation between characteristics; nonlinear models take into account the nonlinear relationship between individual sites, but ignore the influence of linear main effects. In terms of model solving, various methods often require multiple iterations to obtain a relatively stable solution.

[0005] In addition, traditional GS only uses the genomic information of the population as a predictor. However, complex biological processes such as transcription and translation are involved between genes and phenotypes, and using only genotype information may not be enough to capture all the information between genotype and phenotype. In recent years, various omics technologies have been widely used, generating a large amount of intermediate omics data such as transcriptomes and metabolomes, which are gradually used as predictors in phenotypic prediction. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a phenotypic prediction method and system based on feature reduction and generalized inverse technology that adaptively fuses linear and nonlinear effects, so as to comprehensively consider the influence of linear main effects and nonlinear relationships in crop phenotypic prediction.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a phenotypic prediction method based on feature reduction and generalized inverse technology that adaptively integrates linear and nonlinear effects, comprising the following steps:

[0008] S1: Construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to adaptive weights;

[0009] S2: Obtain and divide the experimental data in proportion to obtain a learning set and a test set; use the principal component analysis method PCA and the kernel principal component analysis method KPCA to simplify the learning set, reduce the dimension on the learning set to construct a simplified basis, and further obtain a simplified test set;

[0010] S3: Substitute the simplified learning set into the model and use five-fold cross validation, generalized inverse technique and Bayesian optimization algorithm to determine the model parameters;

[0011] S4: Substitute the reduced test set into the learned model and obtain the indicator for evaluating the model performance by calculating the phenotypic value of the test set.

[0012] According to the above scheme, in step S1,

[0013] The parameters of the phenotype prediction model include weight parameters, kernel parameters, linear main effect vectors, and nonlinear effect vectors;

[0014] The weight parameter is used to indicate the importance of linear main effects and nonlinear effects on the phenotype;

[0015] The kernel parameter is used to reflect the nonlinear relationship between features;

[0016] The linear main effect vector and nonlinear effect vector are used to represent the linear main effect characteristics and nonlinear effect characteristics of the predictors, respectively.

[0017] Furthermore, in step S2, the specific steps are:

[0018] S21: Randomly divide the experimental data into a certain proportion as a learning set for model learning, and use the remaining data as a test set to evaluate model performance;

[0019] S22: Use principal component analysis method PCA to perform linear feature simplification on the learning set to obtain a linear feature simplification subset of the learning set. Use kernel principal component analysis method KPCA to perform nonlinear feature simplification on the learning set to obtain a nonlinear feature simplification subset of the learning set. Reduce the dimension on the learning set to construct a basis, and based on the basis, obtain the linear feature simplification subset and nonlinear feature simplification subset of the test set respectively.

[0020] Furthermore, in step S3, the specific steps are:

[0021] S31: preset the value range of the weight parameter;

[0022] S32: A five-fold cross validation is performed on the feature reduction subset of the learning set, i.e. the reduction subset is randomly divided into five equal parts, four of which are used as training sets and one as a validation set;

[0023] S33: Substitute the training set into the model and use the generalized inverse solution to obtain the linear main effect vector and the nonlinear effect vector corresponding to the preset weight parameters;

[0024] S34: obtaining a model based on preset weight parameters and corresponding linear main effect vectors and nonlinear effect vectors; substituting the validation set into the model, and calculating the phenotypic prediction value of the validation set and the correlation coefficient between the phenotypic prediction value of the validation set and the phenotypic observation value of the validation set;

[0025] S35: Alternate the training set and the validation set five times, repeat steps S33 to S34, and calculate the average of the five correlation coefficients, i.e., the average validation accuracy;

[0026] S36: Use the Bayesian optimization method to learn the hyperparameters including weight parameters and kernel parameters, take the value of the preset weight parameter with the highest average verification accuracy as the optimization target, iteratively learn in the pre-specified hyperparameter search space, and learn the optimal weight parameters and kernel parameters; based on the optimal weight parameters and kernel parameters, use the generalized inverse technology to calculate the final linear main effect vector and nonlinear effect vector of the model on the entire learning feature subset.

[0027] Furthermore, in step S4, the specific steps are:

[0028] Substitute the test set into the model with updated weight parameters to calculate the phenotypic prediction value of the test set and the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set.

[0029] Furthermore, the method further comprises the following steps:

[0030] S5: The experimental data in step S2 is randomly re-divided into the learning set and the test set according to the same proportion and simplified, and steps S3 to S4 are executed.

[0031] Furthermore, the method further comprises the following steps:

[0032] S6: Repeat step S5 several times, calculate the mean of the correlation coefficients between the phenotypic prediction values ​​of the test set obtained in each division and the phenotypic observation values ​​of the test set, and evaluate the performance of the model based on the mean.

[0033] A phenotypic prediction system based on feature reduction and generalized inverse techniques that adaptively fuses linear and nonlinear effects, including

[0034] The model construction submodule is used to construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to adaptive weights;

[0035] The data preprocessing submodule is used to obtain and divide the experimental data in proportion to obtain the learning set and the test set; the principal component analysis method PCA and the kernel principal component analysis method KPCA are used to simplify the learning set, and the dimensionality reduction is used to construct a simplified basis on the learning set to further obtain the simplified test set;

[0036] The parameter learning submodule is used to substitute the reduced learning set into the model and determine the model parameters using five-fold cross validation, generalized inverse technique and Bayesian optimization algorithm;

[0037] The model evaluation submodule is used to substitute the reduced test set into the learned model and obtain the index for evaluating the model performance by calculating the phenotypic value of the test set.

[0038] Furthermore, it also includes a system error control submodule, which is used to randomly re-divide the learning set and the test set and simplify the same experimental data in the same proportion for several times, and determine the model parameters used to represent weights, linear main effects and nonlinear effects through model learning; and is used to calculate the phenotypic prediction value of the test set obtained from each division, and the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set; average the correlation coefficients, and evaluate the performance of the model based on the average.

[0039] A computer memory stores a computer program executable by a computer processor, wherein the computer program executes a phenotype prediction method based on feature reduction and generalized inverse technology to adaptively fuse linear and nonlinear effects.

[0040] The beneficial effects of the present invention are:

[0041] 1. The present invention provides a phenotypic prediction method and system that adaptively fuses linear and nonlinear effects based on feature reduction and generalized inverse technology. A new model of adaptively fused linear and nonlinear effects of prediction factors is constructed for crop phenotypic prediction. The importance of different effects on the phenotype is evaluated by adaptively adjusting weights, thereby realizing the function of comprehensively considering the influence of linear main effects and nonlinear relationships in crop phenotypic prediction.

[0042] 2. When solving the model, the present invention performs PCA linear feature simplification and KPCA nonlinear feature simplification on the training data set, and then uses the generalized inverse technology to solve the model quickly and effectively in one-step iteration, thereby improving the efficiency of determining the phenotypic value of the biomaterial.

[0043] 3. The present invention performs model learning by randomly dividing the experimental data set multiple times to obtain a learning set and a test set, thereby reducing the systematic error of the model and improving the stability of the phenotype prediction results.

[0044] 4. The effectiveness of the present invention in phenotype prediction has been verified on both genotype data based on DNA molecular markers and intermediate omics data based on metabolites.

[0045] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 work.

[0047] Figure 1 is a flow chart of an embodiment of the present invention.

[0048] Figure 2 It is a principle block diagram of an embodiment of the present invention.

[0049] Figure 3 4 is a numerical comparison diagram of the genotype data (G) of the rice 210 according to the embodiment of the present invention.

[0050] Figure 4 It is a numerical comparison diagram of the genotype data (G) of corn 368 according to an embodiment of the present invention.

[0051] Figure 5 It is a numerical comparison diagram of the maize NCII genotype data (G) according to an embodiment of the present invention.

[0052] Figure 6 4 is a numerical comparison diagram of the metabolomics data (M) of the rice 210 according to an embodiment of the present invention.

[0053] Figure 7 It is a numerical comparison diagram of the maize 368 metabolomics data (M) according to an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0055] Example 1

[0056] See also Figure 1 ,The specific steps of a phenotypic prediction method based on feature reduction and generalized inverse technology for adaptive fusion of linear and nonlinear effects are as follows:

[0057] S1: Construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to adaptive weights;

[0058] S2: Obtain and divide the experimental data in proportion to obtain a learning set and a test set; use the principal component analysis method PCA and the kernel principal component analysis method KPCA to simplify the learning set, reduce the dimension on the learning set to construct a simplified basis, and further obtain a simplified test set;

[0059] S3: Substitute the simplified learning set into the model and use five-fold cross validation, generalized inverse technique and Bayesian optimization algorithm to determine the model parameters;

[0060] S4: Substitute the reduced test set into the learned model and obtain the indicator for evaluating the model performance by calculating the phenotypic value of the test set.

[0061] Furthermore, in step S1, the parameters of the phenotype prediction model include weight parameters, kernel parameters, linear main effect vectors and nonlinear effect vectors; the weight parameters are used to indicate the importance of linear main effects and nonlinear effects to the phenotype; the kernel parameters are used to reflect the nonlinear relationship between features; the linear main effect vectors and nonlinear effect vectors are used to indicate the linear main effect characteristics and nonlinear effect characteristics of the prediction factors, respectively.

[0062] In the step S2, the specific steps are:

[0063] S21: Randomly divide the experimental data into a certain proportion as a learning set for model learning, and use the remaining data as a test set to evaluate model performance;

[0064] S22: Use principal component analysis method PCA to perform linear feature simplification on the learning set to obtain a linear feature simplification subset of the learning set. Use kernel principal component analysis method KPCA to perform nonlinear feature simplification on the learning set to obtain a nonlinear feature simplification subset of the learning set. Reduce the dimension on the learning set to construct a basis, and based on the basis, obtain the linear feature simplification subset and nonlinear feature simplification subset of the test set respectively.

[0065] In the step S3, the specific steps are:

[0066] S31: preset the value range of the weight parameter;

[0067] S32: A five-fold cross validation is performed on the feature reduction subset of the learning set, i.e. the reduction subset is randomly divided into five equal parts, four of which are used as training sets and one as a validation set;

[0068] S33: Substitute the training set into the model and use the generalized inverse solution to obtain the linear main effect vector and the nonlinear effect vector corresponding to the preset weight parameters;

[0069] S34: obtaining a model based on preset weight parameters and corresponding linear main effect vectors and nonlinear effect vectors; substituting the validation set into the model, and calculating the phenotypic prediction value of the validation set and the correlation coefficient between the phenotypic prediction value of the validation set and the phenotypic observation value of the validation set;

[0070] S35: Alternate the training set and the validation set five times, repeat steps S33 to S34, and calculate the average of the five correlation coefficients, i.e., the average validation accuracy;

[0071] S36: Use the Bayesian optimization method to learn the hyperparameters including weight parameters and kernel parameters, take the value of the preset weight parameter with the highest average verification accuracy as the optimization target, iteratively learn in the pre-specified hyperparameter search space, and learn the optimal weight parameters and kernel parameters; based on the optimal weight parameters and kernel parameters, use the generalized inverse technology to calculate the final linear main effect vector and nonlinear effect vector of the model on the entire learning feature subset.

[0072] In the step S4, the specific steps are:

[0073] Substitute the test set into the model with updated weight parameters to calculate the phenotypic prediction value of the test set and the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set.

[0074] The following steps are also included:

[0075] S5: The experimental data in step S2 is randomly re-divided into the learning set and the test set according to the same proportion and simplified, and steps S3 to S4 are executed.

[0076] S6: Repeat step S5 several times, calculate the mean of the correlation coefficients between the phenotypic prediction values ​​of the test set obtained in each division and the phenotypic observation values ​​of the test set, and evaluate the performance of the model based on the mean.

[0077] This embodiment constructs a new model for crop phenotype prediction that adaptively integrates the linear and nonlinear effects of prediction factors, and evaluates the importance of different effects on the phenotype by adaptively adjusting weights, thereby realizing the function of comprehensively considering the influence of linear main effects and nonlinear relationships in crop phenotype prediction.

[0078] Example 2

[0079] See also Figure 2 The steps of this embodiment are the same as those of embodiment 1, except that each step is applied to a specific example. Specifically, the following steps are included:

[0080] S1: Construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to weight parameters:

[0081] y=ωα T x+(1-ω)K(X,x)β+ε (1)

[0082] Where y is the phenotypic value of the predicted sample x, X is the training set, K(X,x) is the kernel function for calculating the training set X and the predicted sample x, ω is the weight parameter, α is the linear main effect vector, β is the nonlinear effect vector, and ε is the random error.

[0083] S2: Obtain and divide the experimental data into learning set and test set in proportion, and preprocess the learning set and test set respectively; the specific steps are:

[0084] Get the experimental data and randomly divide it; randomly take 80% as the learning set X each time sd For model learning, the remaining 20% ​​is used as the test set X test Used to evaluate model performance.

[0085] In order to improve the computational efficiency, the learning set X is sd and the test set X test Perform feature simplification; to be consistent with the model, the learning set X sd Extract linear features using PCA to obtain linear feature subsets For the learning set X sd Using KPCA method to extract nonlinear features to obtain nonlinear feature subsets The reduced subset of features that make up the learning set is For the test set X test Perform the same operation to obtain the linear feature subset and nonlinear feature subsets The reduced subset of features that make up the test set is

[0086] S3: Substitute the learning set into the model and determine the model parameters used to represent the weights through model learning; the specific steps are:

[0087] S31: Preset the value range of the weight parameter ω to [0, 1];

[0088] S32: Standardize the learning set; use five-fold cross validation to reduce the features of the learning set to a subset Randomly divide into five equal parts, four of which are used as training set X tr Used to learn the weight parameter ω, and one as the validation set X val Used to cross-validate the optimal weight parameters;

[0089] For the training set X tr Perform feature simplification and use the PCA method to extract linear features to obtain linear feature subsets Using KPCA method to extract nonlinear features to obtain nonlinear feature subsets The reduced subset of features that make up the training set is For the validation set X val Perform feature simplification and use the PCA method to extract linear features to obtain linear feature subsets Using KPCA method to extract nonlinear features to obtain nonlinear feature subsets The reduced subset of features that make up the validation set is

[0090] S33: Preset the value of the weight parameter ω * , reduce the features of the training set to a subset The model introduced into formula (1) integrates linear features and nonlinear features, and uses generalized inverse to solve the preset weight parameter ω * The corresponding linear main effect vector α * and the nonlinear effect vector β * :

[0091]

[0092] here[·] + represents the generalized inverse of a matrix;

[0093] S34: Preset weight parameter ω * and the corresponding linear main effect vector α * and the nonlinear effect vector β * Construct the model; reduce the features of the validation set to a subset Bring it into the model and calculate the phenotypic prediction value Y of the validation set pre :

[0094]

[0095] Then calculate the phenotypic prediction value Y of the validation set pre and the phenotypic observations Y of the validation set val The correlation coefficient of

[0096] S35: Alternate the training set and the validation set five times, repeat steps S33 to S34, and calculate the average of the five correlation coefficients, i.e., the average validation accuracy;

[0097] S36: Take the value of the preset weight parameter with the highest average verification accuracy as the optimal weight parameter, and update the model.

[0098] S4: Substitute the test set into the learned model to determine the model parameters used to represent linear main effects and nonlinear effects; the specific steps are:

[0099] Reduce the features of the test set to a subset Substitute the updated weight parameters into the model, integrate the linear and nonlinear features, use the generalized inverse to solve the main effect vector α and the nonlinear effect vector β, and update the model.

[0100] S5: re-randomly divide the experimental data of step S2 into a learning set and a test set according to the same proportion and perform preprocessing, and execute steps S3 to S4; calculate the phenotypic prediction value of the test set, and then calculate the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set;

[0101] S6: Repeat step S5 for a total of 50 times to reduce the systematic error of the model, calculate the mean of the correlation coefficient between the phenotypic prediction value of the test set obtained by 50 divisions and the phenotypic observation value of the test set, and evaluate the performance of the model based on the mean.

[0102] When solving the model in this embodiment, PCA linear feature simplification and KPCA nonlinear feature simplification are performed on the training data set, and then the generalized inverse technology is used to iterate in one step to quickly and effectively solve the model, thereby improving the efficiency of determining the phenotypic value of the biological material. In this embodiment, the learning set and the test set obtained by randomly dividing the experimental data set for multiple times are used for model learning, thereby reducing the systematic error of the model and improving the stability of the phenotypic prediction results.

[0103] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0104] Example 3

[0105] 1. The relevant algorithms of this embodiment are implemented in Python 3.7 environment. The experimental data are genotype data based on DNA molecular markers of rice 210, corn 368 and corn NCII, as well as metabolomics data based on metabolites of rice 210 and corn 368.

[0106] Rice 210 consists of 210 rice recombinant inbred lines (RILs) obtained by 9 rounds of selfing from the cross between Zhenshan 97 and Minghui 63. The 210 RILs were sequenced using NGS technology, and 270,820 high-quality SNPs were identified as the genotype of each individual. The SNPs were then merged into 1,619 bins, each of which used the same pattern. Thus, the genotype data of rice 210 was obtained as a 210×1,619 matrix G. The metabolomics data included 683 metabolites measured from flag leaves and 317 metabolites measured from germinated seeds, resulting in a 210×1,000 metabolomics data matrix. For each sample, four important traits were collected for the experiment: yield per plant (yd), number of tillers per plant (tp), number of grains per panicle (gn), and weight of 1,000 grains (kgw). The relevant trait data were collected from field experiments at a university.

[0107] The Maize 368 dataset consists of 368 maize inbred lines from a widely used maize association mapping panel. The 368 inbred lines were genotyped using multiple platforms, and about 1.25 trillion high-quality SNPs were selected as genotype data features. After simplification, 90,933 markers were obtained as genotype data. Non-targeted primary metabolomics analysis of the 368 inbred lines across three environments can obtain 748 metabolic variable values ​​as metabolome data. By removing samples with missing features, 339 samples were finally obtained as experimental samples, and the corresponding genotype data and metabolome data corresponded to data matrices of 339×90,933 and 339×748, respectively. For each sample, 15 traits including heading date (HD), pollination (PS), silking time (ST), kernel number per ear (KNPR), ear number (ERN), core diameter (CD), ear diameter (ED), ear length (EL), leaves number per ear (LNAE), branches per ear (TBN), ear main axis length (TMAL), ear leaf length (ELL), ear leaf width (ELW), ear height (EH), and plant height (PH) were collected for experiment.

[0108] The maize NCII population includes 5820 F1 hybrid samples, which are obtained by crossing 194 maternal inbred lines and 30 different superior paternal lines extracted from the maize CUBIC population. Through whole genome resequencing and the process described in the literature of the CUBIC population, 13.8 million SNPs were obtained from 194+30=224 inbred lines. SNPs with MAF<0.05 or expected missing rate greater than 10% in the hybrid population were filtered out by PLINK software, and SNPs with an LD threshold of 0.3 were trimmed. Finally, 156,268 SNPs were obtained, among which the missing genotypes of the hybrids caused by paternal or maternal heterozygosity were interpolated using Beagle V40 software. In 2015, these 5820 F1 hybrids were planted in five locations, B, H1, H2, J, and L, and 18 agronomic traits were collected. In this embodiment, 5506 samples without missing values ​​were selected, and 20,000 SNPs markers were randomly selected from 156,268 to form a genotype data matrix of 5506×20,000. Each sample selected 15 trait data collected in B for experiment. These traits include barren tip length (LBT), grain weight per ear (KWPE), number of grains per row (KNPR), number of grains per ear (KNPE), ear weight (EW), ear row number (ERN), ear leaf width (ELW), ear leaf length (ELL), ear length (EL), ear height (EH), ear diameter (ED), days to male ear (DTT), days to silking (DTS), days to anther development (DTA), and cob weight (CW).

[0109] 2. The above embodiment uses the classic principal component analysis method PCA for linear feature simplification, and uses the kernel principal component analysis method KPCA for nonlinear feature simplification. KPCA is an extension method of PCA based on the kernel method. It transforms the data into a high-dimensional space through nonlinear mapping, and then performs PCA analysis in the high-dimensional space. Because PCA in high-dimensional space only involves the inner product of the nonlinear mapping function, the inner product can be calculated using the kernel function without explicitly writing the nonlinear mapping function. Both PCA and KPCA methods are implemented through the library functions PCA and KPCA of the scikit-learn library in Python. For rice 210 and corn 368 data, the number of principal components retained defaults to the number of training sample points; for corn NCII data, considering the large number of sample points, the number of principal components retained by feature simplification is taken as 500.

[0110] 3. The kernel function required for learning model (1) and KPCA nonlinear feature reduction, in this embodiment, Gaussian kernel function (also called radial basis function) is uniformly used. Here, σ is the kernel parameter. For the three data sets of rice 210, corn 368, and corn NCII, the kernel parameters are 10, 5, and 0.1, respectively.

[0111] 4. Calculation of generalized inverse. The generalized inverse used in the above embodiment is a generalized form of matrix inverse. For the linear equation system y=Xα, when the matrix X is not a square matrix, α=X + y is the least square solution of the linear equation system y = Xα. The generalized inverse can be solved using the pinv function in the Numpy library in Python. To ensure numerical stability, X is used in this embodiment. + ≈(X T X+μI) -1 Xy is used to approximate the solution, where I represents the unit matrix, μ is the regularization parameter of the least squares, and for the three groups of data of rice 210, corn 368, and corn NCII, the regularization parameter is 8, 30, and 10, respectively.

[0112] 5. Comparison model for numerical comparison. To verify the effectiveness of the new model, this embodiment compares the fusion model (1) with the linear model (2) and the nonlinear model (3). The kernel function in model (3) is exactly the same as that in model (1). Models (2) and (3) also use generalized inverse solution. Before solving, PCA is used to simplify the linear features of model (2), and KPCA is used to simplify the nonlinear features of model (3);

[0113] Linear Model:

[0114] y=α T x+ε (2)

[0115] Nonlinear Models:

[0116] y=K(X,x)β+ε (3)

[0117] 6. Model evaluation and result analysis. This example uses the average value of the Pearson correlation coefficient between the phenotypic prediction value and the phenotypic observation value of 50 test sets as the evaluation index of model performance. Figure 3 to Figure 7 As shown, PCA represents the result based on PCA feature extraction and generalized inverse solution model (2), KPCA represents the result based on KPCA feature extraction and generalized inverse solution model (3), and PCA+KPCA represents the result of the fusion model of the present invention.

[0118] From the results, it can be seen that the nonlinear model performs the worst among the three models. On the genotype data of rice 210, corn 368 and corn NCII, the average trait accuracy of the linear model is 62.45%, 51.57% and 79.67%, and the average trait accuracy of the adaptive fusion model is 64.86%, 51.61% and 80.76%, which are much higher than the results of the nonlinear model (the average trait accuracy is only 17.98%, 8.44% and 45.22%). The new adaptive fusion model is slightly higher than the linear model, and its advantage in the tp trait of rice 210 is more obvious, which is 5.29 percentage points higher. In the phenotypic prediction of metabolomics data based on metabolites, except for the PS trait of corn 368, the results of the linear model are lower than those of the nonlinear model. In other cases, the linear model and the fusion model are better than the nonlinear model. Among them, the performance of the fusion model is significantly better than that of the linear model. In the tp and yd traits of rice 210, the fusion model was 5.4 and 3.57 percentage points higher than the linear model, respectively. In the 15 traits of corn 368, the average accuracy of the linear model, nonlinear model and fusion model were 23.60%, 15.98% and 31.92%, respectively. The accuracy of the fusion model was significantly higher than that of the pure linear model and the pure nonlinear model. These results show that in phenotypic prediction, the linear main effect is still the main factor affecting the phenotype, and although the nonlinear effect of the predictor is not the main influencing factor of the phenotypic value, it can effectively improve the prediction performance after integration.

[0119] The effectiveness of this embodiment for phenotype prediction has been verified on both genotype data based on DNA molecular markers and intermediate omics data based on metabolites.

[0120] Example 4

[0121] The present embodiment is used to implement the principle of the above-mentioned method embodiment to construct a phenotypic prediction system that adaptively integrates linear and nonlinear effects based on feature reduction and generalized inverse technology, including: a model construction module, a data preprocessing module, a weight parameter learning module and a linear effect parameter learning module; the model construction module is used to construct a phenotypic prediction model that integrates linear main effects and nonlinear effects by weight; the data preprocessing module is used to obtain and divide the experimental data in proportion to obtain a learning set and a test set, and preprocess the learning set and the test set respectively; the weight parameter learning module is used to substitute the learning set into the model, and determine the model parameters used to represent the weights through model learning; the linear effect parameter learning module is used to substitute the test set into the learned model, and determine the model parameters used to represent the linear main effects and nonlinear effects.

[0122] Each module is mainly used to implement each step of the method embodiment, which will not be described in detail here.

[0123] Example 5

[0124] This embodiment is based on Embodiment 4, but differs in that it also includes a system error control module, which is used to randomly re-divide the learning set and the test set in the same proportion for the same experimental data for several times and perform preprocessing, and determine the model parameters used to represent weights, linear main effects and nonlinear effects through model learning; and is used to calculate the phenotypic prediction value of the test set obtained from each division, and the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set; the correlation coefficients are averaged, and the performance of the model is evaluated based on the average.

[0125] This embodiment aims to optimize the use of experimental data and improve the accuracy and reliability of model evaluation through the following steps: it can first randomly redistribute the learning set and the test set in the same proportion for the same experimental data set, and then streamline the two sets of data. On this basis, the module uses model learning to determine key parameters, which cover weights, linear main effects, and nonlinear effects, and together constitute the characterization basis of the model. Further, it calculates the phenotypic prediction value of the test set after each division, and evaluates the correlation coefficient between these prediction values ​​and the actual observed phenotypic values ​​of the test set. This process is carefully repeated fifty times to ensure the stability and statistical significance of the results. Finally, by calculating the average value of the correlation coefficients of these fifty tests, the module can objectively evaluate the performance of the model based on this mean. The core purpose of this series of operations is to effectively alleviate the distribution inconsistency problem that may exist between the learning set and the test set, thereby significantly enhancing the accuracy and practicality of the model evaluation indicators.

[0126] The modules of Example 4 and Example 5 are mainly used to implement the steps of the method embodiments, which will not be described in detail here.

[0127] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0128] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A phenotypic prediction method based on feature reduction and generalized inverse technology that adaptively integrates linear and nonlinear effects, characterized by: The following steps are involved: S1: Construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to adaptive weights; S2: Obtain and divide the experimental data in proportion to obtain a learning set and a test set; use the principal component analysis method PCA and the kernel principal component analysis method KPCA to simplify the learning set, reduce the dimension on the learning set to construct a simplified basis, and further obtain a simplified test set; S3: Substitute the simplified learning set into the model and use five-fold cross validation, generalized inverse technique and Bayesian optimization algorithm to determine the model parameters; S4: Substitute the reduced test set into the learned model and obtain the indicator for evaluating the model performance by calculating the phenotypic value of the test set.

2. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptive fusion of linear and nonlinear effects according to claim 1, characterized in that: In the step S1, The parameters of the phenotype prediction model include weight parameters, kernel parameters, linear main effect vectors, and nonlinear effect vectors; the weight parameters are used to indicate the importance of linear main effects and nonlinear effects on the phenotype; The kernel parameter is used to reflect the nonlinear relationship between features; The linear main effect vector and nonlinear effect vector are used to represent the linear main effect characteristics and nonlinear effect characteristics of the predictors, respectively.

3. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptive fusion of linear and nonlinear effects according to claim 2, characterized in that: In the step S2, the specific steps are: S21: Randomly divide the experimental data into a certain proportion as a learning set for model learning, and use the remaining data as a test set to evaluate model performance; S22: Use principal component analysis method PCA to perform linear feature simplification on the learning set to obtain a linear feature simplification subset of the learning set. Use kernel principal component analysis method KPCA to perform nonlinear feature simplification on the learning set to obtain a nonlinear feature simplification subset of the learning set. Reduce the dimension on the learning set to construct a basis, and based on the basis, obtain the linear feature simplification subset and nonlinear feature simplification subset of the test set respectively.

4. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptive fusion of linear and nonlinear effects according to claim 3, characterized in that: In the step S3, the specific steps are: S31: preset the value range of the weight parameter; S32: A five-fold cross validation is performed on the feature reduction subset of the learning set, i.e. the reduction subset is randomly divided into five equal parts, four of which are used as training sets and one as a validation set; S33: Substitute the training set into the model and use the generalized inverse solution to obtain the linear main effect vector and the nonlinear effect vector corresponding to the preset weight parameters; S34: obtaining a model based on preset weight parameters and corresponding linear main effect vectors and nonlinear effect vectors; substituting the validation set into the model, and calculating the phenotypic prediction value of the validation set and the correlation coefficient between the phenotypic prediction value of the validation set and the phenotypic observation value of the validation set; S35: Alternate the training set and the validation set five times, repeat steps S33 to S34, and calculate the average of the five correlation coefficients, i.e., the average validation accuracy; S36: Use the Bayesian optimization method to learn the hyperparameters including weight parameters and kernel parameters, take the value of the preset weight parameter with the highest average verification accuracy as the optimization target, iteratively learn in the pre-specified hyperparameter search space, and learn the optimal weight parameters and kernel parameters; based on the optimal weight parameters and kernel parameters, use the generalized inverse technology to calculate the final linear main effect vector and nonlinear effect vector of the model on the entire learning feature subset.

5. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptively integrating linear and nonlinear effects according to claim 4, characterized in that: In the step S4, the specific steps are: Substitute the test set into the model with updated weight parameters to calculate the phenotypic prediction value of the test set and the correlation coefficient between the phenotypic prediction value of the test set and the phenotypic observation value of the test set.

6. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptive fusion of linear and nonlinear effects according to claim 5, characterized in that: The following steps are also included: S5: The experimental data in step S2 is randomly re-divided into the learning set and the test set according to the same proportion and simplified, and steps S3 to S4 are executed.

7. The phenotypic prediction method based on feature reduction and generalized inverse technology and adaptively integrating linear and nonlinear effects according to claim 6, characterized in that: The following steps are also included: S6: Repeat step S5 several times, calculate the mean of the correlation coefficients between the phenotypic prediction values ​​of the test set obtained in each division and the phenotypic observation values ​​of the test set, and evaluate the performance of the model based on the mean.

8. A phenotypic prediction system based on feature reduction and generalized inverse technology that adaptively integrates linear and nonlinear effects, characterized by: include The model construction submodule is used to construct a phenotypic prediction model that integrates linear main effects and nonlinear effects according to adaptive weights; The data preprocessing submodule is used to obtain and divide the experimental data in proportion to obtain the learning set and the test set; the principal component analysis method PCA and the kernel principal component analysis method KPCA are used to simplify the learning set, and the dimensionality reduction is used to construct a simplified basis on the learning set to further obtain the simplified test set; The parameter learning submodule is used to substitute the reduced learning set into the model and determine the model parameters using five-fold cross validation, generalized inverse technique and Bayesian optimization algorithm; The model evaluation submodule is used to substitute the reduced test set into the learned model and obtain the index for evaluating the model performance by calculating the phenotypic value of the test set.

9. The phenotypic prediction system based on feature reduction and generalized inverse technology for adaptive fusion of linear and nonlinear effects according to claim 8, characterized in that: Also includes The system error control submodule is used to randomly re-divide the learning set and the test set in the same proportion for the same experimental data several times and simplify them, determine the model parameters used to represent weights, linear main effects and nonlinear effects through model learning; and calculate the correlation coefficient between the phenotypic prediction value of the test set obtained from each division and the phenotypic prediction value of the test set and the phenotypic observation value of the test set; average the correlation coefficients and evaluate the performance of the model based on the average.

10. A computer memory, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes a phenotypic prediction method based on adaptive fusion of linear and nonlinear effects based on feature reduction and generalized inverse technology as described in any one of claims 1 to 7.

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