CN109459408A - A kind of Near-Infrared Quantitative Analysis method based on sparse regression LAR algorithm - Google Patents
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Abstract
The building of quantitative analysis regression model based near infrared spectrum is the core link during entire Near-Infrared Spectra for Quantitative Analysis, and link the most complicated.Minimum angles return (Least angle regression, LAR), are a kind of sparse regression algorithms based on linear model.Minimum angles recurrence is similar with the process that forward direction returns paragraph by paragraph, but keeps computational efficiency higher using mathematical formulae.It is no longer that the step that multiple very littles and length are fixed is carried out on current variable, the appropriate length of step is calculated by mathematical method to be determined, until the correlation of next variable is caught up with.Also, for minimum angles homing method without the coefficient adjustment of small step is carried out in turn between currently having chosen variable until another variable enters model, this method directly jumps to that suitable point according to determining step-length.LAR and other conventional methods the difference is that, irrelevant variable is abandoned to generate a sparse model;It is influenced to less by noise.The present invention proposes that the Near-Infrared Spectra for Quantitative Analysis detection method based on sparse regression LAR algorithm, opposite conventional method have a clear superiority.
Description
Technical field
The quantitative analysis detection method based near infrared spectrum that the present invention relates to a kind of.
Background technique
The building of quantitative analysis regression model based near infrared spectrum, during being entire Near-Infrared Spectra for Quantitative Analysis
Core link, and link the most complicated.Near-Infrared Spectra for Quantitative Analysis is high dimensional and small sample size problem, and spectral Dimensions are general
All thousands of or even thousands of dimensions, and there are highly linear cross-correlation between each dimension spectroscopic data.Effectively believe near infrared spectrum
It is number faint, it needs to extract small-signal relevant with target quality parameter in the huge spectral information of higher-dimension, and establish back
Return prediction model, this is challenging task.And this be exactly in machine learning homing method be good at it is to be solved
Problem.It is other that the homing method of machine learning can be divided into linear and nonlinear method two major classes.Wherein based on the machine of linear model
Learning method is easy to understand because its is simple and quick, is widely welcome, and is the most frequently used near infrared spectrum quality quantitative detection
Method.Offset minimum binary (Partial least squares, PLS) is that most wide side is used to obtain in linear regression method again
Method;Other such as multiple linear regression (Multiple linear regression, MLR) and principal component regressions
(Principal component regression, PCR) is also often used.
Multiple linear regression MLR is earliest near-infrared regression modeling method.Since the High Linear between spectroscopic data is related,
Simple multiple linear regression effect is generally not fine.PLS is most widely used homing method in near-infrared spectrum analysis.
PLS is used for the quantitative analysis detection of a large amount of near infrared spectrum.Due to overcoming the highly linear relevant issues between spectrum, PLS
Prediction effect be generally preferred over MLR.Principal component regression PCR is that linear regression is carried out in principal component.Since it is simply easy to real
Existing, PCR is also employed in some researchs, but effect is not so good as PLS.
Non-linear machine learning method is also successfully applied to the Near-Infrared Quantitative Analysis detection of quality of agricultural product.So
And in terms of the comprehensibility of model, in terms of such as finding maximally related spectral band by model, the machine based on linear model
Learning method is more preferable than nonlinear.Although some special technologies are proposed to find and select most important spy
Sign, these methods are all very complicated and calculation amount is very big, and relatively easy directly based on linear method, and are easy to understand
With use.For this reason that the PLS method based on linear model is most common method in near-infrared spectrum analysis.
Due to containing complicated physics and optical phenomena in near-infrared (near-infrared, NIR) spectra collection, closely
It inevitably include noise in infrared spectroscopy.It is generally acknowledged that noise has smaller variance than signal.In order to reduce noise,
PCR abandons the direction of small variance.PLS also tends to compress small variance direction, but can amplify some high variance directions again simultaneously.
This, which will lead to PLS, has a bit unstable.Also, PLS reduces the weight of noise characteristic, but does not abandon them;Therefore it largely makes an uproar
Sound still influences whether the estimated performance of PLS.And high cross-correlation variable tends to be chosen simultaneously, causes to exist in selected variables set
A large amount of redundancy.
Summary of the invention
Minimum angles return (Least angle regression, LAR), are a kind of sparse times based on linear model
Reduction method.LAR and PLS scheduling algorithm the difference is that, by irrelevant variable abandon to generate a sparse model;To
It is less to be influenced by noise.LAR and lasso (Least absolute shrinkage and selection
Operator) it is closely related, in fact the variant of LAR provides the algorithm for calculating the ultrahigh in efficiency in the complete path lasso.
To gradually before minimum angles recurrence (Least angle regression, LAR) and traditional model selection method
Recurrence is closely related.Forward stepwire regression, since all coefficients are all zero, then one variable of primary addition gradually, structure
A series of model is built, and updates least square coefficient.Forward stepwire regression once selects a variable that model is added to obtain
Best least square fitting.This process is continued for the standard until reaching some stoppings.Forward stepwire regression is greedy calculation
Method is because it seeks the influence that is optimal and ignoring its future of each single step.
Forward direction returns negative effect similar with forward stepwire regression, but focusing on reducing greedy behavior in successive Regression paragraph by paragraph
Fruit.In successive Regression, the most useful variable is all added in model by each step, and the coefficient of the variable is leapt to most from zero
Small two multiplying factors value.Forward direction returns first variable of selection as successive Regression paragraph by paragraph, but only changes its coefficient one
Lesser amount.Then reselection and the maximally related variable of current residue, this variable may be the same change selected by back
Amount.The coefficient of this same variable only changes a little.This process continues always in this way.When a variable is than other changes
When amount has apparent initial advantage, this variable will have continuous multiple steps and be selected.Thereafter, when there is multiple variables in model
When, this selection process will carry out in turn between these variables.The coefficient that the coefficient ratio stepwise regression method generated in this way obtains
It is more stable.
Minimum angles recurrence is similar with the process that forward direction returns paragraph by paragraph, but keeps computational efficiency higher using mathematical formulae.
It is no longer that the step that multiple very littles and length are fixed is carried out on current variable, the appropriate length of step passes through mathematical method and calculates
It determines, until the correlation of next variable is caught up with.Also, minimum angles homing method is without currently choosing variable
Between carry out the coefficient adjustment of small step in turn until another variable enters model, this method is directly jumped to according to determining step-length
That suitable point.
The absolute value of related coefficient between first covariant of residual sum is than the related coefficient between other covariants
Absolute value is big.When the regression coefficient of first covariant shifts to its least square value (phase relation between this point and residual error
Number will become zero) when, and the related coefficient of residual error constantly reduces, and it is related between residual error finally always to have another covariant
Coefficient is equal thereto.At this moment that variable is just used as second activity variable (selected variable) that model is added.Then the two are assisted
The coefficient of variable is all mobile to their least square value, until the related coefficient of third variable is caught up with.It is returned in higher-dimension
In problem, model will be finally added in other covariants, when the related coefficient between all activity variables and residual error drop to and other
The same level of covariant.
Assuming that a total of n measurement sample, each sample have p covariant measurement and a response measurement value.VectorIt isA length be n covariant (=1,2 ..., p), y is in response to variable (length is also n),It is comprising returning
The length of coefficient is the vector of p,It isA covariant regression coefficient (=1,2 ..., p), regression residuals r is long
The vector (the corresponding sample of each element) that degree is n.The process of LAR algorithm can be summarized as follows:
1) all covariants of near infrared spectrum data are standardized, make their mean value zero and variance is 1.Residual error
The initial value of r is equal to the response variable after placed in the middleization: (It is the mean value of y).All regression coefficients are zero:;
2) it finds out and the maximally related covariant of residual error r;
3) regression coefficientFrom 0 to its least square coefficient <(With the inner product of residual error r) it is mobile, until it is some its
Its covariantIt is caught up with the related coefficient of current residueRelated coefficient;
4) simultaneously along current residue () on joint least-squares coefficient direction, mobile regression coefficientWith,
Until some other covariantRelated coefficient catch up with;
5) continue this process, be equal to until covariant number in model or model is added in all covariants.Work as institute
After having covariant that LAR model is added, as a result as common least square.
According to above algorithm steps, the covariant chosen sequentially enters model according to its significance level.Optimal mould
Type can generally abandon some unrelated or unessential covariant, such as, k covariant before only retaining.Hyper parameter k, model
Middle retained covariant number, can be determined by cross validation.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, the present invention is carried out
It is further described.
The quantitative analysis of agricultural product interior quality detects, and is that one of the quantitative analysis tech based near infrared spectrum is important
The field of research and application.And the quantitative analysis application based near infrared spectrum of different research objects, used in method
It communicates.Experiment illustration is used as using the quantitative analysis of the interior quality of navel orange.
The near infrared spectra collection of all samples, the absorption spectrum acquired using near infrared spectrometer in reflective-mode
(log1/R).The wave-length coverage of scanning is from 1000nm to 2499nm, wavelength interval 1nm.Two 14.5 halogen lamp are as light
Source.Spectrometer detection probe is perpendicular to sample fruit surface, apart from 10 millimeters of fruit surface.
Near infrared spectrum measures at the equator position of fruit sample.The maximum circumference institute of equator position, that is, fruit surface perimeter
At position.The reflectance spectrum for being separated by about 120 degree of three points measurement pericarp surfaces each other is selected on the position of equator.These three point institutes
Spectrum is surveyed to be averaged as the fruit sample ambitus surface spectrum measured value.
Interior quality data determination.Total soluble solids (Total Soluble Solids, TSS), titratable acid
The true value of (Titratable Acidity, TA) and vitamin C (Vitamin C, VC) three kinds of inside quality parameters is by passing
Destructive test chemical method of uniting measures.Total soluble solids (TSS) are that the sugar of one of most common index of quality and navel orange contains
It measures also highly relevant.Titratable acid (TA) is the key parameter for embodying fruit internal quality, is the most important index for influencing taste
One of.
Total soluble solids (TSS), titratable acid (TA) and vitamin C (VC), are that can reflect navel orange inside quality more comprehensively
Three kinds of important parameters.Another important common index of quality is maturity (Gu sour ratio), is total soluble solids and titratable
The ratio of acid, can also be calculated by surveyed parameter.The actual value of parameter passes through traditional destructive test method measurement.
Total soluble solids TSS assay: it squeezes the juice, is then filtered with double gauze, and make after navel orange sample removal pericarp
Fruit juice is uniformly mixed.Then take supernatant therein at room temperature with Japan produce hand-held digital display refractometer (ATAGO, PAL-ES3,
Japan total soluble solids TSS content) is measured.Titratable acid TA assay: using determination of acid-basetitration fruit containing acid
Amount.Accurate 10mL fruit juice of drawing adds distilled water to be settled to scale and shakes up, take dilution 10mL extremely into 100mL volumetric flask
In 100mL triangular flask, 1% phenolphthalein indicator 2 is added to drip, to terminal with sodium hydroxide solution titration, solution is aobvious uniformly pink
For titration end-point.Record titrates consumed sodium hydroxide solution volume, calculates acid content according to the volume of consumption.Vitamin C
Assay: fruit Vitamin C content is measured using 2,6- sodium dichlorphenol indophenolate method.It is accurate to draw 10mL raw juice extremely
In 100mL volumetric flask, mass concentration is that the oxalic acid solution of 1g/100mL is settled to scale and shakes up, and takes dilution 2mL extremely
In 50mL triangular flask, to terminal with the titration of 2,6- sodium dichlorphenol indophenolate standard solution, solution is titration end-point in uniform light red.
Vitamin C content is calculated according to the 2,6- sodium dichlorphenol indophenolate liquor capacity of consumption.
3/4ths in these data samples are selected as training dataset, for constructing prediction inside quality parameter
Regression model;Another a quarter sample is used as the estimated performance that test data set carrys out assessment models.
Precision of prediction is core and important performance indicator the most for machine learning algorithm with regress analysis method.If cannot
Reach the precision of prediction in tolerance interval, then the regression forecasting result of quantitative analysis is with regard to nonsensical.Model prediction accuracy
Evaluation index, has used trained coefficient R, and training root-mean-square error RMSEC tests correlation coefficient r, tests root-mean-square error
Five kinds of indexs of RMSEP, deviation Bias etc..This five kinds of indexs are also to carry out comprehensive and accurate evaluation to forecast of regression model precision
Most common index.
Near infrared spectrum data inevitably includes noise.Before being used to detect navel orange quality parameter, in order to mitigate
Influence of noise, near infrared spectrum data have used rolling average smoothing method and standard normal variable to correct (standard
Normal variate, SNV) method pre-processes.Rolling average smoothing method is the pretreatment side for removing high-frequency noise
Method;It is a kind of row transform method that standard normal variable, which corrects SNV, carries out placed in the middle and change of scale to each individual spectrum, makes
Each spectrum average is that 0 variance is 1, for removing light scattering effect bring influence of noise.
Minimum angles return LAR algorithm and are used to construct the Quantitative Analysis Model based near infrared spectrum, predict navel orange
Several most important inside quality parameters, total soluble solids TSS, titratable acid TA and vitamin C.
The result shows that the estimated performance that LAR is returned is always than most widely used method --- PLS returns more preferable.It is non-linear
Homing method least square method supporting vector machine LS-SVM is the prediction generally acknowledged in current many Near-Infrared Spectra for Quantitative Analysis researchs
The highest method of precision.The precision of prediction of LAR algorithm is larger better than the amplitude of PLS, and more connects with the precision of prediction of LS-SVM
Closely, gap is little.
Claims (1)
1. a kind of Near-Infrared Quantitative Analysis method based on sparse regression LAR algorithm, which is characterized in that including following main step
It is rapid: (1) all covariants of near infrared spectrum data to be standardized, make their mean value zero and variance is 1, residual error
The initial value of r is equal to the response variable after placed in the middleization, and all regression coefficients are zero;
(2) it finds out and the maximally related covariant of residual error;
(3) regression coefficientFrom 0 to its least square coefficient <(With the inner product of residual error r) it is mobile, until it is some its
Its covariantIt is caught up with the related coefficient of current residueRelated coefficient;(4) simultaneously along current residue () on
Joint least-squares coefficient direction, mobile regression coefficientWith, until some other covariantRelated coefficient
It catches up with;
(5) continue this process, be equal to until covariant number in model or model is added in all covariants, work as institute
After having covariant that LAR model is added, as a result as common least square;
(6) according to above algorithm steps, the covariant chosen sequentially enters model, optimal model according to its significance level
Some unrelated or unessential covariant can be generally abandoned, such as, k covariant before only retaining, hyper parameter k, in model
The covariant number retained can be determined by cross validation.
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CN113345525A (en) * | 2021-06-03 | 2021-09-03 | 谱天(天津)生物科技有限公司 | Analysis method for reducing influence of covariates on detection result in high-throughput detection |
CN116486969A (en) * | 2023-06-25 | 2023-07-25 | 广东工业大学 | Genetic algorithm-based material optimal correlation relation acquisition method and application |
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CN105203498A (en) * | 2015-09-11 | 2015-12-30 | 天津工业大学 | Near infrared spectrum variable selection method based on LASSO |
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CN113345525A (en) * | 2021-06-03 | 2021-09-03 | 谱天(天津)生物科技有限公司 | Analysis method for reducing influence of covariates on detection result in high-throughput detection |
CN116486969A (en) * | 2023-06-25 | 2023-07-25 | 广东工业大学 | Genetic algorithm-based material optimal correlation relation acquisition method and application |
CN116486969B (en) * | 2023-06-25 | 2023-09-26 | 广东工业大学 | Genetic algorithm-based material optimal correlation relation acquisition method and application |
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