CN112348238A - Egg yield prediction PSO-SVM regression model based on principal component analysis - Google Patents

Egg yield prediction PSO-SVM regression model based on principal component analysis Download PDF

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CN112348238A
CN112348238A CN202011163847.3A CN202011163847A CN112348238A CN 112348238 A CN112348238 A CN 112348238A CN 202011163847 A CN202011163847 A CN 202011163847A CN 112348238 A CN112348238 A CN 112348238A
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蒋敏兰
吴沛伦
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Abstract

The invention provides an egg yield prediction PSO-SVM regression model based on principal component analysis, which comprises the steps of analyzing the relationship between the egg laying rate of an egg chicken and the highest house temperature, the lowest house temperature, the weight, the age in day and the feed consumption by utilizing the principal component; according to the result of the principal component analysis, giving appropriate weight to each one-dimensional feature of the data; and taking the weight-endowed result as the input of a PSO-SVM, and establishing a regression model of five-dimensional characteristics of the laying rate of the laying hens, the highest house temperature, the lowest house temperature, the weight, the age of the day and the feed consumption by using a PSO-SVM algorithm. The method utilizes principal component analysis and correlation analysis to research the correlation between the laying rate of the laying hens and characteristics such as age in days, house temperature, weight, feed consumption and the like, weights are given to all the characteristics according to Pearson correlation coefficients of 6 characteristics, larger weights are given to the characteristics with larger influence on the laying rate, on the basis, egg yield regression modeling is carried out on weighted data by utilizing an SVM (support vector machine), and parameters of the SVM are optimized by utilizing a PSO (particle swarm optimization) algorithm, so that the method has the advantages of high precision, strong anti-interference performance and the like.

Description

Egg yield prediction PSO-SVM regression model based on principal component analysis
Technical Field
The invention relates to the technical field of data modeling, algorithm optimization and data analysis, in particular to an egg yield prediction PSO-SVM regression model based on principal component analysis.
Background
The eggs are used as the leading people of egg consumer products, provide abundant protein, fat, mineral substances, various vitamins and the like for human bodies, and have extremely high nutritional value. According to the statistics of world food and agricultural organizations, the global egg yield exceeds 7000 kilotons in 2015, and the yield of the first five egg-laying countries accounts for 55 percent of the total demand, wherein the egg yield of China is the first in the world. The characteristics causing the change of the egg yield are very complex, the change of the egg yield can reflect various characteristics such as environmental change in a farm, growth change of laying hens and the like in a time period, the economic benefit of the farm can be improved by predicting the egg yield data in advance, and meanwhile, an important reference basis is provided for how much production resources need to be put into the farm in the next stage. At present, most of egg yield prediction is modeled by using a traditional method, and the defects of low precision, poor interference resistance and the like exist.
Principal component analysis is one of multivariate analysis methods, which aims to convert a plurality of features into several comprehensive features, namely principal components, within the allowable range of information loss by using a dimension reduction idea. The principal components are not related to each other, but each principal component is a linear combination of the original features.
A Support Vector Machine (SVM) is a machine learning method provided by Vapnik, cortex and the like on the basis of a statistical learning theory, the method seeks the idea of risk minimization by utilizing the compromise between approximation precision and model complexity so as to achieve a good approximation effect, SVM regression maps actual sample data to a high-dimensional feature space by utilizing a kernel function through a nonlinear transformation method, and then a decision function is constructed to realize linear regression. The Support Vector Machine (SVM) has good performance in classification and regression after being proposed, but still has the problem of parameter selection, the selection of parameters c (penalty factor) and g (hyper-parameter generated after RBF kernel function is selected) can greatly influence the performance of the SVM, and the selection of a proper parameter becomes the problem to be solved. The method includes the steps that a Particle Swarm Optimization (PSO) simulates the behavior of bird clusters in flying foraging, the clusters are optimized through collective cooperation, and the optimal parameters can be selected for an SVM model.
Disclosure of Invention
In order to solve certain technical problems or some technical problems in the prior art, the invention provides the egg yield prediction PSO-SVM regression model based on principal component analysis, the egg yield regression model is established by utilizing a plurality of influence factors, and the egg yield prediction PSO-SVM regression model has the advantages of high precision, strong anti-interference performance and the like.
In order to solve the above-mentioned existing technical problem, the invention adopts the following scheme: a PSO-SVM regression model for egg yield prediction based on principal component analysis comprises a first step of analyzing the relationship between the influence on the egg laying rate of laying hens and the highest house temperature, the lowest house temperature, the body weight, the age in days and the feed consumption by using principal components;
secondly, giving appropriate weight to each one-dimensional characteristic of the data according to the result of the principal component analysis;
and step three, taking the weight-given result as the input of a PSO-SVM, and establishing a regression model of five-dimensional characteristics of the laying rate of the laying hens, the highest house temperature, the lowest house temperature, the weight, the age of the day and the feed consumption by using a PSO-SVM algorithm.
Further, the regression model modeling steps are sequentially as follows: begin → read data → principal component analysis → weight is given to each dimensional feature → data is saved and modeled as SVM input → PSO-SVM.
Further, the principal component analysis step comprises the steps of 1, selecting initial variables, and forming an analysis covariance matrix or an analysis correlation matrix according to whether measurement or value ranges in the selected initial variables are the same;
step 2, solving the eigenvalue and the corresponding eigenvector of the analysis covariance matrix or the analysis correlation matrix by using a Jacobian method, then solving the contribution rate by using a formula and selecting a principal component, wherein the expression is as follows:
Figure RE-GDA0002848850740000031
in the formula piFor each factor's correlation with egg production, EjIs a characteristic value of the principal component.
Further, the sample data of the initial variable is X ═ X (X)1，x2，x3，…，xi，…，x226)T226 samples each of which is data sample XiHas 6-dimensional characteristics, namely the age in days c1, the maximum cut temperature c2, the minimum cut temperature c3, the feed consumption c4, the body weight c5 and the laying rate c6, namely xi＝(xic1，xic2，…，xicj，…，xicj) Standardizing the raw data
Figure RE-GDA0002848850740000032
Wherein
Figure RE-GDA0002848850740000033
Is composed of
Figure RE-GDA0002848850740000034
Var(xj) Is composed of
Figure RE-GDA0002848850740000035
Further, the calculation mode of the sample correlation coefficient matrix correlation coefficient is calculated as
Figure RE-GDA0002848850740000036
Further, the contribution rate is calculated in the following manner:
Figure RE-GDA0002848850740000037
further, after non-equality constraints of the optimization problem in the SVM are replaced by equality constraints, an SLSVM model is formed, and the expression is as follows:
Figure RE-GDA0002848850740000038
wherein the constraint conditions are as follows:
yi(W*xi+b＝1)，i＝1，2，…，m。
further, an error is introduced to each sample in the SLSVM modelCharacteristic eiAnd adding an L2 regular term of error characteristics into the original function, wherein the expression of the optimization term is as follows:
Figure RE-GDA0002848850740000039
the constraint condition is
Figure RE-GDA0002848850740000041
Where λ is the regularization parameter.
Further, calculating the currently searched individual optimal solution to replace the global optimal solution by the particle swarm optimization algorithm (PSO), which comprises the following steps: start → read training data → read test data → initialize SVM parameter → initialize PSO parameter → generate random particle → SVM regression → calculate fitness → update optimal result → update particle → confirm whether stop condition is satisfied, if so, then finish, if not, then return to the SVM regression step from new to recalculate until the stop condition is satisfied.
Further, the calculation formula of the particle swarm optimization algorithm (PSO) is:
Figure RE-GDA0002848850740000042
where v is velocity, x is position, w is an inertia factor, c1、c2Is a learning factor, pbest is an individual optimal location, and gbest is a global optimal location.
Compared with the prior art, the invention has the beneficial effects that:
the method comprises the steps of carrying out principal component analysis on the day age, the highest house temperature, the lowest house temperature, the body weight, the feed consumption and the laying rate to obtain main components which are mutually irrelevant, analyzing which kinds of characteristics are linearly combined to form each main component to obtain characteristics with large relevance to the laying rate, measuring the internal characteristic relevance of each main component through a multivariate analysis method, distributing weights according to different influence degrees of the characteristics on the laying rate by taking correlation coefficients as the basis, and accordingly establishing a laying rate regression model by utilizing a plurality of influence factors.
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FIG. 1 is a principal component analysis flow chart of the present invention;
FIG. 2 is a flow chart of the PSO-SVM algorithm of the present invention;
FIG. 3 is a model flow chart of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and the detailed description, and it should be noted that any combination of the embodiments or technical features described below can be used to form a new embodiment without conflict.
As shown in figure 1, an egg yield prediction PSO-SVM regression model based on principal component analysis comprises a first step of analyzing the relationship between the influence on the laying rate of the laying hens and the maximum house temperature, the minimum house temperature, the weight, the age of day and the feed consumption by using the principal components;
secondly, giving appropriate weight to each one-dimensional characteristic of the data according to the result of the principal component analysis;
and step three, taking the weight-given result as the input of a PSO-SVM, and establishing a regression model of five-dimensional characteristics of the laying rate of the laying hens, the highest house temperature, the lowest house temperature, the weight, the age of the day and the feed consumption by using a PSO-SVM algorithm.
The regression model modeling steps are as follows in sequence: begin → read data → principal component analysis → weight is given to each dimensional feature → data is saved and modeled as SVM input → PSO-SVM.
Further, the principal component analysis step comprises the steps of 1, selecting initial variables, and forming an analysis covariance matrix or an analysis correlation matrix according to whether measurement or value ranges in the selected initial variables are the same;
step 2, solving the eigenvalue and the corresponding eigenvector of the analysis covariance matrix or the analysis correlation matrix by using a Jacobian method, then solving the contribution rate by using a formula and selecting a principal component, wherein the expression is as follows:
Figure RE-GDA0002848850740000051
in the formula piFor each factor's correlation with egg production, EjIs a characteristic value of the principal component.
The sample data of the initial variable is X ═ X1，x2，x3，…，xi，…，x226)T226 samples, each of which is xiHas 6-dimensional characteristics, namely the age in days c1, the maximum cut temperature c2, the minimum cut temperature c3, the feed consumption c4, the body weight c5 and the laying rate c6, namely xi＝(xic1，xic2，…，xicj，…，xicj) Standardizing the raw data
Figure RE-GDA0002848850740000061
Wherein
Figure RE-GDA0002848850740000062
Is composed of
Figure RE-GDA0002848850740000063
Var(xj) Is composed of
Figure RE-GDA0002848850740000064
The calculation mode of the correlation coefficient of the sample correlation coefficient matrix is
Figure RE-GDA0002848850740000065
In actual calculation, as shown in fig. 3, the results of principal component analysis are used to give weights to 5 features affecting the laying rate of the laying hens, and the weight formula is as shown in the formula
Figure RE-GDA0002848850740000066
Shown and used as the input of PSO-SVM, the primary data is subjected to principal component analysis, and 6 characteristics of total egg yield, maximum cut temperature, minimum cut temperature, body weight, age per day and feed consumption are selected as the characteristics to be analyzedThe characteristic is that after the normalized data is normalized, the correlation matrix between data is analyzed, the characteristic value and corresponding characteristic vector of the correlation coefficient matrix are solved by the Jacobian method, and then the formula is used
Figure RE-GDA0002848850740000067
The contribution ratio is obtained and the principal component is selected. Marking the sample data as X ═ X1，x2，x3，…，xi，…，x226)T226 samples, each of which is xiHas 6-dimensional characteristics, namely the age in days c1, the maximum cut temperature c2, the minimum cut temperature c3, the feed consumption c4, the body weight c5 and the laying rate c6, namely xi＝(xic1，xic2，…，xicj，…，xicj). Standardizing the raw data
Figure RE-GDA0002848850740000068
Wherein
Figure RE-GDA0002848850740000069
Is composed of
Figure RE-GDA00028488507400000610
Var(xj) Is composed of
Figure RE-GDA0002848850740000071
Then calculating the correlation coefficient of the sample correlation coefficient matrix in the way of
Figure RE-GDA0002848850740000072
Calculating the eigenvalue and corresponding eigenvector of the correlation coefficient matrix by using the Jacobi method and then using the formula
Figure RE-GDA0002848850740000073
The contribution ratio is obtained and the principal component is selected.
Wherein the contribution rateThe calculation method is as follows:
Figure RE-GDA0002848850740000074
in a further improvement, as shown in fig. 2, a Support Vector Machine (SVM) is a machine learning method proposed by Vapnik and cortex, etc. on the basis of a statistical learning theory, and the method seeks a risk minimization idea by using a trade-off between approximation accuracy and model complexity to achieve a good approximation effect. The SVM regression maps actual sample data to a high-dimensional feature space by using a kernel function through a nonlinear transformation method, and then constructs a decision function to realize linear regression.
LSSVM replaces the non-equality constraint of the optimization problem in SVM to equality constraint, and replaces the non-equality constraint of the optimization problem in SVM to equality constraint to form an SLSVM model, and the expression is as follows:
Figure RE-GDA0002848850740000075
wherein the constraint conditions are as follows:
yi(W*xi+b＝1)，i＝1，2，…，m。
to solve the situation that partial specific points exist, an error characteristic e is introduced into each sample in the SLSVM modeliAnd adding an L2 regular term of error characteristics into the original function, wherein the expression of the optimization term is as follows:
Figure RE-GDA0002848850740000081
the constraint condition is
Figure RE-GDA0002848850740000082
Where λ is the regularization parameter.
In a further improvement, the Particle Swarm Optimization (PSO) calculates an individual optimal solution currently searched to replace a global optimal solution, and the steps of the Particle Swarm Optimization (PSO) are sequentially: start → read training data → read test data → initialize SVM parameter → initialize PSO parameter → generate random particle → SVM regression → calculate fitness → update optimal result → update particle → confirm whether stop condition is satisfied, if so, then finish, if not, then return to the SVM regression step from new to recalculate until the stop condition is satisfied.
The particle swarm algorithm is a research on bird predation behaviors, a global optimal solution is replaced by a currently searched individual optimal solution, and food is searched in a bird swarm according to two principles:
1) information is shared between groups of birds flying towards where the group knows the most food.
2) According to his experience, fly towards the place where the food is known to be the most.
Abstracting a speed updating formula and a position updating formula according to the two behaviors, so as to obtain a calculation formula of the Particle Swarm Optimization (PSO) as follows:
Figure RE-GDA0002848850740000083
where v is velocity, x is position, w is an inertia factor, c1、c2Is a learning factor, pbest is an individual optimal location, and gbest is a global optimal location. Compared with other algorithms, the algorithm has the advantages of having a memory function and saving good solutions. In contrast to genetic algorithms, previous solutions vary with population variations, while PSOs do not have crossover and mutation operations. The particles are updated only according to the internal speed, the principle is simpler, the parameters are fewer, and the method is easier to realize.
As shown in fig. 2, there are two important hyper-parameters c, g in SVM, where c is a penalty factor, if c is too large, it is easy to over-fit, and if c is too small, it is easy to under-fit; g is a hyper-parameter generated after the RBF kernel function is selected, the distribution of the data after being mapped to a new feature space is determined, and the larger g is, the fewer support vectors are, and the smaller g value is, the more support vectors are. The selection of the proper hyper-parameter can improve the accuracy of SVM regression and the speed of convergence. The PSO algorithm has the characteristics of simple algorithm implementation, high speed, less needed adjustment parameters and the like, and is suitable for finding the optimal SVM parameter. The PSO-LSSVM prediction model pseudo-code based on principal component analysis is shown below.
Figure RE-GDA0002848850740000091
The pseudo code of the PSO-LSSVM prediction model based on principal component analysis as shown in FIG. 3 is as follows.
Figure RE-GDA0002848850740000101
The method comprises the steps of carrying out principal component analysis on the day age, the highest house temperature, the lowest house temperature, the body weight, the feed consumption and the laying rate to obtain main components which are mutually irrelevant, analyzing which kinds of characteristics are linearly combined to form each main component to obtain characteristics with large relevance to the laying rate, measuring the internal characteristic relevance of each main component through a multivariate analysis method, distributing weights according to different influence degrees of the characteristics on the laying rate by taking correlation coefficients as the basis, and accordingly establishing a laying rate regression model by utilizing a plurality of influence factors.
According to the method, the main component analysis and the correlation analysis are utilized to research the correlation between the laying rate of the laying hens and the characteristics such as the age of the day, the house temperature, the weight and the feed consumption, the weight is given to each characteristic according to the Pearson correlation coefficient of 6 characteristics, the characteristic with large influence on the laying rate is given with large weight, the result shows that the feed consumption and the laying hen weight are the most main characteristics influencing the laying rate, on the basis, egg yield regression modeling is carried out on weighted data by utilizing an SVM, and parameters in the SVM are optimized by utilizing a PSO algorithm. The experimental result shows that the mean square error of the model built in the method is 5.63 x 10 < -4 >, is reduced by 6.36 x 10 < -4 > compared with the mean square error of the existing SVM model, and achieves a better result.
The above embodiments are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited thereby, and any insubstantial changes and substitutions made by those skilled in the art based on the present invention are within the protection scope of the present invention.

Claims (10)

1. A PSO-SVM regression model for egg yield prediction based on principal component analysis is characterized in that: the method comprises the steps of analyzing the relationship between the influence on the laying rate of the laying hens and the highest house temperature, the lowest house temperature, the body weight, the age of the day and the feed consumption by utilizing main components;
secondly, giving appropriate weight to each one-dimensional characteristic of the data according to the result of the principal component analysis;
and step three, taking the weight-given result as the input of a PSO-SVM, and establishing a regression model of five-dimensional characteristics of the laying rate of the laying hens, the highest house temperature, the lowest house temperature, the weight, the age of the day and the feed consumption by using a PSO-SVM algorithm.
2. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 1, wherein: the regression model modeling steps are as follows in sequence: begin → read data → principal component analysis → weight is given to each dimensional feature → data is saved and modeled as SVM input → PSO-SVM.
3. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 2, wherein: the principal component analysis step comprises the steps of 1, selecting initial variables, and forming an analysis covariance matrix or an analysis correlation matrix according to whether measurement or value ranges in the selected initial variables are the same;
step 2, solving the eigenvalue and the corresponding eigenvector of the analysis covariance matrix or the analysis correlation matrix by using a Jacobian method, then solving the contribution rate by using a formula and selecting a principal component, wherein the expression is as follows:
Figure RE-FDA0002848850730000011
in the formula piFor each factor's correlation with egg production, EjIs a characteristic value of the principal component.
4. A principal component-based composition according to claim 3The analyzed egg yield prediction PSO-SVM regression model is characterized in that: the sample data of the initial variable is X ═ X1，x2，x3，…，xi，…，x226)T226 samples, each of which is xiHas 6-dimensional characteristics, namely the age in days c1, the maximum cut temperature c2, the minimum cut temperature c3, the feed consumption c4, the body weight c5 and the laying rate c6, namely xi＝(xic1，xic2，…，xicj，…，xicj) Standardizing the raw data
Figure RE-FDA0002848850730000021
Wherein
Figure RE-FDA0002848850730000022
Is composed of
Figure RE-FDA0002848850730000023
Var(xj) Is composed of
Figure RE-FDA0002848850730000024
5. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 4, wherein: the calculation mode of the correlation coefficient of the sample correlation coefficient matrix is
Figure RE-FDA0002848850730000025
6. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 3, wherein: the calculation mode of the contribution rate is as follows:
Figure RE-FDA0002848850730000026
7. according to claim 1The egg yield prediction PSO-SVM regression model based on principal component analysis is characterized in that: substituting non-equality constraint of the optimization problem in the SVM into equality constraint to form an SLSVM model, wherein the expression is as follows:
Figure RE-FDA0002848850730000027
wherein the constraint conditions are as follows: y isi(W*xi+b＝1)，i＝1，2，…，m。
8. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 7, wherein: introducing an error characteristic ei to each sample in the SLSVM model, and adding an L2 regular term of the error characteristic into the original function, wherein the optimization term is expressed as:
Figure RE-FDA0002848850730000028
the constraint condition is
Figure RE-FDA0002848850730000029
Where λ is the regularization parameter.
9. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 1, wherein: calculating the currently searched individual optimal solution to replace the global optimal solution through the Particle Swarm Optimization (PSO), wherein the Particle Swarm Optimization (PSO) sequentially comprises the following steps: start → read training data → read test data → initialize SVM parameter → initialize PSO parameter → generate random particle → SVM regression → calculate fitness → update optimal result → update particle → confirm whether stop condition is satisfied, if so, then finish, if not, then return to the SVM regression step from new to recalculate until the stop condition is satisfied.
10. The PSO-SVM regression model for egg production prediction based on principal component analysis as claimed in claim 9, wherein: the calculation formula of the particle swarm optimization algorithm (PSO) is as follows:
Figure RE-FDA0002848850730000031
where v is velocity, x is position, w is an inertia factor, c1、c2Is a learning factor, pbest is an individual optimal location, and gbest is a global optimal location.
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Application publication date: 20210209