A phenotype prediction method and system based on feature reduction and generalized inverse technology for adaptive fusion of linear and nonlinear effects

Abstract

The application provides a phenotype prediction method and system based on feature reduction and generalized inverse technology, which adaptively fuses linear and nonlinear effects, constructs a new model of adaptive fusion of linear and nonlinear effects of prediction factors for crop phenotype prediction, and evaluates the importance of different effects on the phenotype through the method of adaptive weight adjustment, so as to realize the function of comprehensively considering the influence of linear main effect and nonlinear relationship in crop phenotype prediction. When solving the model, the feature reduction is performed on the training data set, and the model is quickly and effectively solved by using the generalized inverse, so that the determination efficiency of the phenotype value of biological materials is improved. The learning set and the test set obtained by randomly dividing the experimental data set for multiple times are used for model learning, so that the system error of the model is reduced, and the stability of the phenotype prediction result is improved. The effectiveness of the application for phenotype prediction is verified based on DNA molecular marker genotype data and metabolite-based intermediate omics data.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent breeding, and particularly relates to a phenotype prediction method and system based on feature reduction and generalized inverse technology and fusing linear and nonlinear effects in an adaptive manner. BACKGROUND

[0002] Crop phenotype prediction is a process of predicting the phenotypic characteristics of crops by analyzing the genetic information, environmental factors or other related data of the crops. Traditional determination of crop agronomic trait phenotypic values is time-consuming and inefficient. In order to improve the determination efficiency of phenotypic values, a whole genome method is currently used to realize trait prediction.

[0003] Genomic selection (GS) uses high-density molecular markers distributed on the whole genome, such as single nucleotide polymorphism (SNP), to calculate the genetic value of the trait and estimate the breeding value. The GS method can capture all genetic effects that cause phenotypic variation, and the evaluation value of the phenotype can be obtained by using the genotype of an individual, so that early selection of potential superior varieties can be realized, the genetic gain per unit time can be improved, and the rapid improvement of the population can be ensured.

[0004] At present, the existing algorithms of GS mainly focus on genetic statistical methods and machine learning methods. The former includes best linear unbiased prediction (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) methods. The models solved by the algorithms are generally linear models (such as LASSO), mixed linear models (such as BLUP) and nonlinear models (such as RF, RKHS and DL). Among them, the linear or mixed linear model mainly captures the linear effects of the genome and the phenotype of the population, but ignores the nonlinear effects such as individual interaction and correlation between features; the nonlinear model considers the nonlinear relationship between individual sites, but ignores the influence of linear main effects. In terms of model solving, various methods often need multiple iterations to obtain a relatively stable solution.

[0005] In addition, the traditional GS only uses the genomic information of the population as a predictor. However, the process from genes to phenotypes involves complex biological processes such as transcription and translation, and only using 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 transcriptome, metabolome and other intermediate omics data, which are gradually applied as predictors in phenotype prediction. SUMMARY

[0006] The technical problem solved by the present application is to provide a phenotype prediction method and system based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects, which comprehensively considers the influence of linear main effects and nonlinear relationships in crop phenotype prediction.

[0007] The technical solution adopted by the present application to solve the above technical problem is a phenotype prediction method based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects, comprising the following steps:

[0008] S1: constructing a phenotype prediction model for fusing linear main effects and nonlinear effects according to adaptive weights;

[0009] S2: obtaining and proportionally dividing experimental data to obtain a learning set and a test set; using principal component analysis (PCA) and kernel principal component analysis (KPCA) to reduce the learning set, dimensionally reducing the learning set to construct a reduced basis, and further obtaining a reduced test set;

[0010] S3: substituting the reduced learning set into the model, using five-fold cross-validation, generalized inverse technology and Bayesian optimization algorithm to determine the model parameters;

[0011] S4: substituting the reduced test set into the learned model, and obtaining an index for evaluating the performance of the model by calculating the phenotype 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 parameters are used to represent the importance of linear main effects and nonlinear effects on the phenotype;

[0015] The kernel parameters are used to reflect the nonlinear relationship between features;

[0016] The linear main effect vectors and nonlinear effect vectors are used to represent the linear main effect features and nonlinear effect features of the prediction factors, respectively.

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

[0018] S21: randomly dividing a part of the experimental data according to a certain proportion as a learning set for model learning, and the remaining data as a test set for evaluating the performance of the model;

[0019] S22: Linear feature reduction subset of the learning set is obtained by using principal component analysis (PCA) method on the learning set, and nonlinear feature reduction subset of the learning set is obtained by using kernel principal component analysis (KPCA) method on the learning set, and the basis is constructed by reducing dimension on the learning set, and linear feature reduction subset and nonlinear feature reduction subset of the test set are obtained based on the basis.

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

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

[0022] S32: five-fold cross-validation is used on the feature reduction subset of the learning set, that is, the reduction subset is randomly divided into five equal parts, and four of them are used as the training set and one is used as the validation set;

[0023] S33: the training set is substituted into the model, and the linear main effect vector and the nonlinear effect vector corresponding to the preset weight parameter are obtained by using the generalized inverse;

[0024] S34: the model is obtained based on the preset weight parameter and the corresponding linear main effect vector and nonlinear effect vector; the validation set is substituted into the model, the phenotype prediction value of the validation set is calculated, and the correlation coefficient between the phenotype prediction value of the validation set and the phenotype observation value of the validation set is calculated;

[0025] S35: the training set and the validation set are rotated five times, and steps S33 to S34 are repeated, and the average of the correlation coefficients of five times is calculated, that is, the average validation accuracy;

[0026] S36: the hyperparameters including the weight parameter and the kernel parameter are learned by using the Bayesian optimization method, the value of the preset weight parameter with the highest average validation accuracy is taken as the optimization target, the hyperparameter search space is specified in advance, and the optimal weight parameter and kernel parameter are learned by iteration; based on the optimal weight parameter and the kernel parameter, the final linear main effect vector and the nonlinear effect vector of the model are calculated on the entire learning feature subset by using the generalized inverse technique.

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

[0028] The phenotype prediction value of the test set is calculated by substituting the test set into the model with the updated weight parameter, and the correlation coefficient between the phenotype prediction value of the test set and the phenotype observation value of the test set is calculated.

[0029] Further, the following steps are further included:

[0030] S5: the experimental data of step S2 are randomly divided into learning set and test set in the same proportion and reduced, and steps S3 to S4 are executed.

[0031] Further, the following steps are further included:

[0032] S6: repeating step S5 for several times, calculating the average of the correlation coefficients of the phenotype prediction value of the test set and the phenotype observation value of the test set obtained by each division, and evaluating the performance of the model according to the average.

[0033] A phenotype prediction system based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects, comprising

[0034] A model construction submodule for constructing a phenotype prediction model that fuses linear main effects and nonlinear effects according to adaptive weights;

[0035] A data preprocessing submodule for obtaining and proportionally dividing experimental data to obtain a learning set and a test set, reducing the learning set by using principal component analysis (PCA) and kernel principal component analysis (KPCA) to construct a reduced basis on the learning set, and further obtaining a reduced test set;

[0036] A parameter learning submodule for substituting the reduced learning set into the model, and determining model parameters by using five-fold cross-validation, generalized inverse technology, and a Bayesian optimization algorithm;

[0037] A model evaluation submodule for substituting the reduced test set into the learned model, and obtaining an index for evaluating the performance of the model by calculating the phenotype value of the test set.

[0038] Further, it further comprises a system error control submodule for re-randomly dividing the learning set and the test set according to the same proportion for several times, reducing the same experimental data, determining model parameters for representing weights, linear main effects, and nonlinear effects through model learning; and calculating the phenotype prediction value of the test set, the correlation coefficient of the phenotype prediction value of the test set and the phenotype observation value of the test set; averaging the correlation coefficients, and evaluating the performance of the model according to the average.

[0039] A computer memory having stored therein a computer program executable by a computer processor, the computer program performing a phenotype prediction method based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects.

[0040] The present application has the following advantages:

[0041] 1. The phenotype prediction method and system based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects of the present application construct a new model that adaptively fuses linear and nonlinear effects of prediction factors for crop phenotype prediction, and evaluate the importance of different effects on the phenotype by an adaptive weight adjustment method, thereby realizing the function of comprehensively considering the influence of linear main effects and nonlinear relationships in crop phenotype prediction.

[0042] 2. The model is solved, the training data set is respectively subjected to PCA linear feature reduction and KPCA nonlinear feature reduction, then the model is solved by one-step iteration of generalized inverse technology, and the determination efficiency of the biological material phenotype value is improved.

[0043] 3. The model is learned by multiple random division of the experimental data set to obtain learning set and test set, the system error of the model is reduced, and the stability of the phenotype prediction result is improved.

[0044] 4. The effectiveness of the phenotype prediction is verified on the genotype data based on DNA molecular markers and the intermediate omics data based on metabolites.

[0045] Of course, any product implementing the present application does not necessarily need to achieve all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

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

[0048] Figure 2 is a principle block diagram of the embodiment of the present application.

[0049] Figure 3 is a numerical comparison diagram of the genotype data (G) of rice 210 in the embodiment of the present application.

[0050] Figure 4 is a numerical comparison diagram of the genotype data (G) of corn 368 in the embodiment of the present application.

[0051] Figure 5 is a numerical comparison diagram of the genotype data (G) of corn NCII in the embodiment of the present application.

[0052] Figure 6 is a numerical comparison diagram of the metabolomics data (M) of rice 210 in the embodiment of the present application.

[0053] Figure 7 is a numerical comparison diagram of the metabolomics data (M) of corn 368 in the embodiment of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application.

[0055] Embodiment 1

[0056] Referring to Figure 1 The specific steps of the phenotype prediction method based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects are as follows:

[0057] S1: constructing a phenotype prediction model for fusing linear main effects and nonlinear effects according to adaptive weights;

[0058] S2: obtaining and proportionally dividing experimental data to obtain a learning set and a test set; reducing the learning set by using principal component analysis method PCA and kernel principal component analysis method KPCA to reduce the learning set, dimensionally constructing a basis on the learning set, and further obtaining a reduced test set;

[0059] S3: substituting the reduced learning set into the model, and determining the model parameters by using five-fold cross-validation, generalized inverse technology and Bayesian optimization algorithm;

[0060] S4: substituting the reduced test set into the learned model, and obtaining an index for evaluating the performance of the model by calculating the phenotype value of the test set.

[0061] Further, 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 represent the importance of linear main effects and nonlinear effects on the phenotype; the kernel parameters are used to reflect the nonlinear relationship between features; the linear main effect vectors and the nonlinear effect vectors are respectively used to represent the linear main effect features and the nonlinear effect features of the predictors.

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

[0063] S21: randomly dividing a part of the experimental data according to a certain proportion as a learning set for model learning, and dividing the remaining data as a test set for evaluating the performance of the model;

[0064] S22: performing linear feature reduction on the learning set by using principal component analysis method PCA to obtain a linear feature reduction subset of the learning set, performing nonlinear feature reduction on the learning set by using kernel principal component analysis method KPCA to obtain a nonlinear feature reduction subset of the learning set, dimensionally constructing a basis on the learning set, and obtaining a linear feature reduction subset and a nonlinear feature reduction subset of the test set based on the basis.

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

[0066] S31: preset weight parameter value range;

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

[0068] S33: the training set is substituted into the model, and the linear main effect vector and the nonlinear effect vector corresponding to the preset weight parameter are obtained by solving the generalized inverse;

[0069] S34: the model is obtained based on the preset weight parameter and the corresponding linear main effect vector and nonlinear effect vector; the validation set is substituted into the model, the phenotype prediction value of the validation set is calculated, and the correlation coefficient between the phenotype prediction value of the validation set and the phenotype observed value of the validation set is calculated;

[0070] S35: the training set and the validation set are rotated five times, and steps S33 to S34 are repeated, and the average of the correlation coefficients of the five times is calculated, i.e. the average validation accuracy;

[0071] S36: the hyperparameters including the weight parameter and the kernel parameter are learned by the Bayesian optimization method, the value of the preset weight parameter with the highest average validation accuracy is taken as the optimization target, the hyperparameter search space is specified in advance, and the optimal weight parameter and kernel parameter are learned by iteration; based on the optimal weight parameter and kernel parameter, the final linear main effect vector and nonlinear effect vector of the model are calculated on the entire learning feature subset by using the generalized inverse technique.

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

[0073] The phenotype prediction value of the test set is calculated by substituting the test set into the model with the updated weight parameter, and the correlation coefficient between the phenotype prediction value of the test set and the phenotype observed value of the test set is calculated.

[0074] Further comprising the following steps:

[0075] S5: the experimental data of step S2 are randomly divided into learning set and test set at the same proportion and reduced, and steps S3 to S4 are executed.

[0076] S6: step S5 is repeated several times, the average of the correlation coefficients between the phenotype prediction value of the test set and the phenotype observed value of the test set obtained by each division is calculated, and the performance of the model is evaluated according to the average.

[0077] The embodiment constructs a new model for crop phenotype prediction, which adaptively fuses the linear and nonlinear effects of the prediction factors, and evaluates the importance of different effects on the phenotype by adaptively adjusting the weight, thereby realizing the function of comprehensively considering the influence of the linear main effect and the nonlinear relationship in crop phenotype prediction.

[0078] Embodiment 2

[0079] See Figure 2 The steps in this embodiment are the same as in Embodiment 1, except that each step is applied to a specific instance. Specifically, it includes the following steps:

[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 proportionally divide the experimental data into a learning set and a test set, and preprocess the learning set and test set respectively; the specific steps are as follows:

[0084] Acquire experimental data and randomly divide the data; each time, randomly select 80% as the learning set X. sd Used for model learning, with the remaining 20% ​​as the test set X. test Used to evaluate model performance.

[0085] To improve computational efficiency, the learning set X is processed before model learning. sd and test set X test Perform feature reduction; to maintain consistency with the model, perform feature reduction on the training set X. sd The linear feature subset is obtained by extracting linear features using the PCA method. For learning set X sd The nonlinear feature subset is obtained by extracting nonlinear features using the KPCA method. The feature reduction subsets that make up the learning set are For test set X test Performing the same operation yields a linear feature subset. and nonlinear feature subsets The feature reduction subset that makes up the test set is

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

[0087] S31: The preset weight parameter ω has a range of values ​​of [0, 1];

[0088] S32: Standardize the learning set; reduce the features of the learning set to a subset using five-fold cross-validation. Randomly divide the data into five equal parts, four of which are used as training set X tr For learning the weight parameter ω, one part is used as validation set X val For cross-validation of the optimal weight parameter;

[0089] For the training set X tr Feature reduction is performed, and linear features are extracted using the PCA method to obtain a linear feature subset Nonlinear features are extracted using the KPCA method to obtain a nonlinear feature subset The feature reduction subset for the training set is composed of For the validation set X val Feature reduction is performed, and linear features are extracted using the PCA method to obtain a linear feature subset Nonlinear features are extracted using the KPCA method to obtain a nonlinear feature subset The feature reduction subset for the validation set is composed of

[0090] S33: The value ω of the preset weight parameter ω is determined * The feature reduction subset of the training set is brought into formula (1) The linear and nonlinear features are fused, and the generalized inverse is used to solve the preset weight parameter ω * The corresponding linear main effect vector α * And the nonlinear effect vector β * :

[0091]

[0092] Here [·] + Indicates the generalized inverse of the matrix;

[0093] S34: The preset weight parameter ω * And the corresponding linear main effect vector α * And the nonlinear effect vector β * Construct a model; bring the feature reduction subset of the validation set into the model Calculate the phenotype prediction value Y of the validation set pre :

[0094]

[0095] Calculate the phenotype prediction value Y of the validation set again pre And the correlation coefficient of the observed phenotype value Y val of the validation set;

[0096] S35: Rotate the training set and the validation set five times, repeat steps S33 to S34, and calculate the average of the correlation coefficients of the five times, 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 representing the linear main effect and the nonlinear effect; the specific steps are:

[0099] Substitute the feature reduction subset of the test set into the model with updated weight parameters, fuse the linear features and nonlinear features, solve the main effect vector a and the nonlinear effect vector β using the generalized inverse, and update the model.

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

[0101] S6: Repeat step S5 for 50 times to reduce the system error of the model, calculate the average of the correlation coefficients between the phenotype prediction values of the test sets obtained by 50 times of division and the phenotype observed values of the test sets, and evaluate the performance of the model according to the average.

[0102] In this embodiment, PCA linear feature reduction and KPCA nonlinear feature reduction are performed on the training data set, and then the generalized inverse technique is used to solve the model in one step iteration, which improves the efficiency of measuring the phenotype value of biological materials. In this embodiment, the learning set and the test set obtained by multiple random division of the experimental data set are used for model learning, which reduces the system error of the model and improves the stability of the phenotype prediction result.

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

[0104] Embodiment 3

[0105] 1. The related algorithm of this embodiment is implemented in Python3.7 environment, and the experimental data selected is the genotype data based on DNA molecular markers of rice 210, corn 368 and corn NCII, and the metabolomics data based on metabolites of rice 210 and corn 368.

[0106] Rice 210 consists of 210 rice recombinant inbred lines (RILs) derived from 9 rounds of selfing from a cross between Zhen Shan 97 and Ming Hui 63. The 210 RILs were sequenced using NGS technology, and 270,820 high-quality SNPs were identified as the genotypes of each individual, which were then combined into 1,619 bins, each of which adopted the same pattern. Thus, the genotype data of rice 210 was obtained as a 210 x 1619 matrix G. The metabolomics data included 683 metabolites measured from flag leaves and 317 metabolites measured from germinated seeds, and thus the metabolomics data matrix was obtained as 210 x 1000. For each sample, four important traits were collected for the experiment: yield per plant (yd), tiller number per plant (tp), grain number per panicle (gn), and 1000-grain weight (kgw), and the related trait data were obtained from field experiments of a university.

[0107] Maize 368 dataset consists of 368 maize inbred lines from a widely used maize association mapping panel. The 368 inbred lines were genotyped by multiple platforms, and about 1.25 million high-quality SNPs were selected as the features of the genotype data, and after reduction, 90,933 markers were obtained as the genotype data. Non-targeted primary metabolomics analysis of the 368 inbred lines across three environments can obtain 748 metabolite variable values as the metabolomics data. By removing samples containing missing features, finally 339 samples were obtained as experimental samples, and the corresponding genotype data and metabolomics data correspond to 339 x 90933, 339 x 748 data matrices, respectively. For each sample, 15 traits including heading date (HD), pollination (PS), silking time (ST), kernel number per panicle (KNPR), ear number (ERN), core diameter (CD), ear diameter (ED), ear length (EL), leaf number above ear (LNAE), ear branch number (TBN), ear main axis length (TMAL), ear leaf length (ELL), ear leaf width (ELW), ear height (EH), and plant height (PH) were collected for the experiment.

[0108] The maize NCII population includes 5820 F1 hybrid samples, which are obtained by crossing 194 maternal inbred lines selected from the maize CUBIC population and 30 different elite paternal lines. Through whole-genome resequencing and the process described in the literature of the CUBIC population, 13.8 million SNPs are obtained from 194+30=224 inbred lines. Through the PLINK software, the SNPs with MAF<0.05 or expected missing rate greater than 10% in the hybrid population are filtered out, and the SNPs with an LD threshold of 0.3 are pruned, finally 156268 SNPs are obtained, and the missing genotypes of the hybrid due to heterozygosity of the paternal or maternal line are interpolated by the Beagle V40 software. In 2015, the 5820 F1 hybrids were planted in B, H1, H2, J, and L five locations, and 18 agronomic traits were collected. This embodiment selects 5506 samples without missing values, randomly selects 20000 from 156268 SNPs markers, and forms a 5506x20000 genotype data matrix, and selects 15 trait data collected in B for each sample for experiments, and these traits include lean tip length (LBT), kernel weight per ear (KWPE), kernel number per row (KNPR), kernel number 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), tassel duration (DTT), silking duration (DTS), anther development duration (DTA), and ear axis weight (CW).

[0109] 2. The above embodiment adopts the classical principal component analysis method PCA for linear feature reduction, and the kernel principal component analysis method KPCA for nonlinear feature reduction. KPCA is a method based on kernel method, which is an extension of PCA. It converts data into high-dimensional space through nonlinear mapping, and then performs PCA analysis in the high-dimensional space. Because the PCA of the high-dimensional space only involves the inner product of the nonlinear mapping function, the inner product can be calculated by the kernel function, without explicitly writing the nonlinear mapping function. Both PCA and KPCA methods are realized by the library functions PCA and KPCA in the scikit-learn library of Python. For the rice 210 and maize 368 data, the number of principal components retained is the default number of training sample points; for the maize NCII data, considering that the number of sample points is large, the number of principal components retained by feature reduction is 500.

[0110] 3. The learning model (1) and the kernel function needed in KPCA nonlinear feature reduction, this embodiment uniformly adopts the Gaussian kernel function (also known as radial basis function) Here, σ is the kernel parameter, and for the rice 210, maize 368 and maize NCII data, the kernel parameter is 10, 5 and 0.1 respectively.

[0111] 4. Calculation of generalized inverse. The generalized inverse used in the above embodiments is a generalization of matrix inverse. For linear equation system y = Xa, when matrix X is not square, a = X + y is the least square solution of linear equation system y = Xa. The generalized inverse can be solved by pinv function in Numpy library in Python. To ensure numerical stability, in this embodiment, X + ≈(X T X+μI) -1 Xy is used to approximate solution, where I represents identity matrix and μ is the regularization parameter of least square. For rice 210, maize 368 and maize NCII, the regularization parameter is set to 8, 30 and 10 respectively.

[0112] 5. Comparative model of numerical comparison. To verify the effectiveness of the new model, in this embodiment, the fusion model (1) is compared with linear model (2) and nonlinear model (3) in numerical comparison. The kernel function in model (3) is completely consistent with that in model (1). Model (2) and (3) also use generalized inverse to solve. Before solving, PCA is used for linear feature reduction for model (2) and KPCA is used for nonlinear feature reduction for model (3).

[0113] Linear model:

[0114] y = a T x + ε (2)

[0115] Nonlinear model:

[0116] y = K(X, x) β + ε (3)

[0117] 6. Model evaluation and result analysis. In this embodiment, the average value of Pearson correlation coefficient between the phenotype prediction value and the phenotype observation value of the test set of 50 times is used as the evaluation index of model performance. The relevant experimental results are shown in Figures 3 to 7 , where PCA represents the result of model (2) based on PCA feature extraction and generalized inverse solution, KPCA represents the result of model (3) based on KPCA feature extraction and generalized inverse solution, and PCA+KPCA represents the result of the fusion model of the present application.

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

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

[0120] Embodiment 4

[0121] The embodiment is used to realize the principle of the above-mentioned method embodiment and construct a phenotype prediction system based on feature reduction and generalized inverse technology for adaptively fusing linear and nonlinear effects, which comprises 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 phenotype prediction model for fusing linear main effects and nonlinear effects according to weights. The data preprocessing module is used to obtain and divide experimental data according to a proportion to obtain a learning set and a test set, and pre-process 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 model parameters for representing weights through model learning. The linear effect parameter learning module is used to substitute the test set into the learned model, and determine model parameters for representing linear main effects and nonlinear effects.

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

[0123] Embodiment 5

[0124] This embodiment is based on embodiment 4, with the difference that it further comprises a system error control module for several times of re-randomly dividing the same experimental data into learning set and test set with the same proportion, and pre-processing, determining the model parameters for representing the weight, linear main effect and nonlinear effect by model learning, and calculating the phenotype prediction value of the test set obtained by each division, the correlation coefficient between the phenotype prediction value of the test set and the phenotype observation value of the test set, and averaging the correlation coefficients to evaluate the performance of the model according to the average value.

[0125] This embodiment aims to optimize the use of experimental data and improve the accuracy and reliability of model evaluation by the following steps: it can first randomly re-allocate the learning set and test set with the same proportion for the same experimental data set, and then perform refined processing on the two sets of data. On this basis, the module uses model learning to determine key parameters, which include weight, linear main effect and nonlinear effect, which together constitute the representation basis of the model. Further, it calculates the phenotype prediction value of the test set after each division, and evaluates the correlation coefficient between the prediction value and the actual observed phenotype value 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 fifty test correlation coefficients, the module can objectively evaluate the performance of the model according to the average value. The core purpose of this series of operations is to effectively alleviate the possible inconsistency between the learning set and the test set, thereby significantly enhancing the accuracy and practicality of the model evaluation index.

[0126] The modules of embodiment 4 and embodiment 5 are mainly used to realize the steps of the method embodiments, which are not described here.

[0127] It should be noted that according to the needs of implementation, each step / component described in this application can be split into more steps / components, or two or more steps / components or parts of the operation of the steps / components can be combined into a new step / component to achieve the purpose of the present application.

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

Claims

1. A phenotypic prediction method based on feature reduction and generalized inverse techniques, characterized in that: Includes the following steps: S1: Construct a phenotypic prediction model that integrates linear main effects and nonlinear effects with adaptive weights; S2: Obtain and proportionally divide the experimental data to obtain a learning set and a test set; reduce the learning set using Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA), construct a reduced basis on the learning set, and further obtain a reduced test set; the specific steps are as follows: S21: Randomly divide a portion of the experimental data into a learning set for model learning, and use the remaining data as a test set to evaluate model performance. S22: The learning set is linearly reduced by principal component analysis (PCA) to obtain a subset of linearly reduced features. The learning set is nonlinearly reduced by kernel principal component analysis (KPCA) to obtain a subset of nonlinearly reduced features. A basis is constructed on the learning set by dimensionality reduction. Based on the basis, the subsets of linearly reduced features and the subsets of nonlinearly reduced features of the test set are obtained respectively. S3: Substitute the reduced 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 performance index of the model by calculating the phenotypic value of the test set.

2. The phenotypic prediction method based on feature reduction and generalized inverse techniques according to claim 1, characterized in that: In step S1, The parameters of the phenotypic prediction model include weight parameters, kernel parameters, linear main effect vector, and nonlinear effect vector; The weighting parameters are used to represent the importance of linear main effects and nonlinear effects to the phenotype; Kernel parameters are used to reflect the nonlinear relationships between features; The linear main effect vector and the nonlinear effect vector are used to represent the linear main effect characteristics and nonlinear effect characteristics of the predictor, respectively.

3. The phenotypic prediction method based on feature reduction and generalized inverse techniques according to claim 1, characterized in that: The specific steps in step S3 are as follows: S31: Preset range of values ​​for weight parameters; S32: Five-fold cross-validation is used to reduce the feature subset of the learning set. That is, the reduced subset is randomly divided into five equal parts, and four of them are used as the training set and one part is used as the validation set. S33: Substitute the training set into the model and use the generalized inverse to solve for the linear main effect vector and nonlinear effect vector corresponding to the preset weight parameters; S34: Obtain the model based on the preset weight parameters and the corresponding linear main effect vector and nonlinear effect vector; substitute the validation set into the model, and calculate the phenotypic predicted value of the validation set and the correlation coefficient between the phenotypic predicted value of the validation set and the phenotypic observed value of the validation set; S35: Rotate the training set and validation set five times, repeat steps S33 to S34, and calculate the mean of the five correlation coefficients, i.e., the average validation accuracy. S36: Use Bayesian optimization to learn hyperparameters including weight parameters and kernel parameters. Take the preset weight parameter with the highest average verification accuracy as the optimization objective. Iterate learning in the pre-specified hyperparameter search space to learn the optimal weight parameters and kernel parameters. Based on the optimal weight parameters and kernel parameters, use the generalized inverse technique to calculate the final linear main effect vector and nonlinear effect vector of the model on the entire learned feature subset.

4. The phenotypic prediction method based on feature reduction and generalized inverse techniques according to claim 3, characterized in that: The specific steps in step S4 are as follows: Substitute the test set into the updated weight parameters of the model to calculate the phenotypic predicted values ​​of the test set and the correlation coefficient between the phenotypic predicted values ​​of the test set and the phenotypic observed values ​​of the test set.

5. The phenotypic prediction method based on feature reduction and generalized inverse techniques according to claim 4, characterized in that: It also includes the following steps: S5: The experimental data from step S2 are randomly re-divided into the learning set and the test set in the same proportion and reduced. Then, steps S3 to S4 are executed.

6. The phenotypic prediction method based on feature reduction and generalized inverse techniques according to claim 5, characterized in that: It also includes the following steps: S6: Repeat step S5 several times, calculate the mean of the correlation coefficient between the predicted phenotypic values ​​of the test set and the observed phenotypic values ​​of the test set obtained from each partition, and evaluate the performance of the model based on the mean.

7. A phenotypic prediction system based on feature reduction and generalized inverse techniques, characterized in that: include The model construction submodule is used to build a phenotypic prediction model that integrates linear main effects and nonlinear effects with adaptive weights. The data preprocessing submodule is used to acquire and proportionally divide the experimental data to obtain the learning set and the test set; the learning set is reduced using principal component analysis (PCA) and kernel principal component analysis (KPCA); the reduced basis is constructed on the learning set to further obtain the reduced 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 an indicator to evaluate the model's performance by calculating the phenotypic values ​​of the test set.

8. The phenotypic prediction system based on feature reduction and generalized inverse techniques according to claim 7, characterized in that: Also includes The systematic error control submodule is used to randomly redivide the same experimental data into learning and test sets in the same proportion several times and reduce them; determine the model parameters used to represent weights, linear main effects, and nonlinear effects through model learning; and calculate the phenotypic predicted values ​​of the test set obtained in each division, the correlation coefficient between the phenotypic predicted values ​​of the test set and the phenotypic observed values ​​of the test set; calculate the mean of the correlation coefficients, and evaluate the performance of the model based on the mean.

9. A computer memory, characterized in that: It contains a computer program that can be executed by a computer processor, which performs a phenotypic prediction method based on feature reduction and generalized inverse techniques, as described in any one of claims 1 to 6, which integrates linear and nonlinear effects.

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