CN113340874A - Quantitative analysis method based on combined ridge regression and recursive feature elimination - Google Patents
Quantitative analysis method based on combined ridge regression and recursive feature elimination Download PDFInfo
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Abstract
The invention relates to a quantitative analysis method based on combined ridge regression and recursive feature elimination, which comprises the following steps: acquiring spectral data and position information; performing full spectrum and normalization on the spectral data; dividing the training set and the verification set and standardizing; establishing a ridge regression calibration model for the training set, and recording the absolute value of the coefficient of the model; deleting the spectral features corresponding to the minimum coefficient absolute value to obtain a new feature subset; determining an evaluation model, modeling in a leave-one-out verification mode and recording RMSECV; repeating iteration until the algorithm jumps out of the loop; determining an optimal spectral feature subset and an element concentration calibration model according to RMSECV; and (5) taking the verification set data as the optimal model input to obtain a verification set RMSEP. The optimal calibration model of the method can realize more accurate quantitative analysis on the concentration of the element to be detected. The problems of overfitting in element calibration and multiple collinearity in spectral data are relieved, the search space of the feature subset is effectively reduced, and the root mean square error is effectively reduced under the condition of high judgment coefficient.
Description
Technical Field
The invention belongs to the field of spectral analysis and material composition analysis, and particularly relates to a quantitative analysis method based on combined ridge regression and recursive feature elimination.
Background
The Laser Induced Breakdown Spectroscopy (LIBS) technique uses a focusing lens to focus a laser beam on the surface of a sample, so that the surface of the sample is ablated and excited to generate transient plasma. And by collecting plasma emission spectral lines, qualitative and quantitative analysis is carried out on the element components in the substance to be detected. LIBS is widely used for analysis of various solid, liquid, gas and other substances with its advantages of being all-elemental, in-situ, on-line, rapid, requiring no sample preparation and the like. The complex sample usually contains abundant element information, and the determination of the analysis element is easily influenced by other elements, so that the reliability of experimental analysis cannot be met by adopting a univariate mode. The multivariate analysis method can fully utilize information in the spectrum to obtain a better analysis result, but too many features are used as model input, so that the complexity of the model is increased, and the overfitting problem is easy to form, so that feature selection is carried out on high-dimensional spectrum data, and the reduction of the dimension of the model input data is very necessary.
The currently generally adopted feature selection modes are classified into a filtering type mode, a wrapping type mode and an embedding type mode. The filtering type characteristic selection mode can be used for selecting the spectral characteristics by calculating a certain statistical index, so that single characteristic spectral lines can be screened, and finally, the spectral characteristics with a large number of similar properties are obtained. The wrapping method utilizes a random search algorithm to perform subset screening and evaluates the feature subset according to the fitting result of the final fitting model, an overfitting problem is usually generated, and the random search algorithm is used to perform subset screening, so that the subset search space is large and the calculation time is long. The embedded feature selection method only performs model training once, and the whole process excessively depends on a model fitting result.
Disclosure of Invention
Aiming at the defects in the prior art, the technical problem to be solved by the invention is to provide a spectral line automatic selection method based on combined ridge regression and recursive feature elimination, and train a concentration calibration model by using the spectral line information, thereby realizing quantitative analysis of element concentration.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a quantitative analysis method based on combined ridge regression and recursive feature elimination comprises the following steps:
obtaining original spectral data of a sample as input, screening characteristic spectral lines by combining ridge regression and recursive characteristic elimination algorithms to obtain a characteristic subset, evaluating the screened characteristic subset to select an optimal characteristic subset, and obtaining an optimal calibration model to carry out element concentration analysis on the material.
The method specifically comprises the following steps:
step 1: acquiring spectral data of a sample, and determining a wavelength range;
step 2: performing full spectrum and normalization on the spectral data;
and step 3: dividing the spectral data into a training set and a verification set;
step 4: standardizing each dimension of the training set data, and recording the mean value and the variance in the standardization process;
and 5: training and calibrating a ridge regression model by taking the standardized training spectrum data as input and the known standard sample concentration as output;
step 6: recording the absolute value of the model coefficient of the ridge regression calibration model;
and 7: sequencing the spectral features according to the obtained coefficient absolute value, and removing the spectral features corresponding to the minimum coefficient absolute value to obtain a new feature subset;
and 8: determining an evaluation model, taking the obtained new feature subset as evaluation model input, performing leave-one verification and recording a leave-one cross-verification root mean square error RMSECV of each element of training set data;
and step 9: repeating the step 4 to the step 8 until the feature numbers in the new feature subsets are completely deleted, and determining an optimal feature subset and a corresponding optimal element concentration calibration model according to the RMSECV result in each iteration process;
step 10: and (3) taking the verification set data as the input of the optimal element concentration calibration model to obtain the root mean square error RMSEP of each element of the verification set data output by the model, and comparing the known standard sample concentration to see that the verification set data is the optimal calibration model.
The sample is a standard sample, and LIBS spectral data of which the original spectral data is a wide-band spectrum are obtained and obtained through experimental measurement.
The element concentration in the standard sample is determined in advance.
The training set and the verification set are randomly drawn, the sample amount of the training set accounts for 80-90% of all data, and the test set accounts for 10-20%.
The normalization is to subtract the mean of each dimension of the spectral data and divide by the variance of the dimension.
The penalty coefficients of the ridge regression model are calibrated according to different elements, and the range of the corresponding different penalty coefficients is between 0.001 and 5.
The evaluation model for the optimal feature subset is a multivariate regression model and comprises a partial least squares regression (PLS) model, a Support Vector Regression (SVR) model and a Ridge regression model.
The leave-one-out verification comprises: and obtaining a new feature subset, modeling by adopting an N-1 sample on a training set, verifying and recording the root mean square error RMSECV of one cross verification left for each element of the data of the training set by using the remaining sample, recording the RMSECV of all samples after repeating N times, and judging the advantages and disadvantages of the feature subset according to the value of the RMSECV.
And the characteristic subset corresponding to the RMSECV value is optimal, and the corresponding PLS calibration model is an optimal element concentration calibration model.
The invention has the following advantages and beneficial effects:
1. and eliminating the least important features by utilizing the ridge regression fitting coefficient, and automatically screening the optimal feature spectral line. The spectral line obtained in the way relieves the common multiple collinearity problem in spectral data, and effectively reduces the search space of the feature subset.
2. The quality of the feature subset is evaluated in a leave-one-verification mode through the fitting model, the influence of the whole feature subset on the fitting result is considered, and the over-fitting problem generated when the final fitting model is used for evaluating the feature subset is relieved.
3. The method adopted by the invention is to apply a ridge regression and recursive feature elimination feature selection mode, find the optimal feature subset by continuously eliminating the feature spectral line, and evaluate the feature subset by using a leave-one-verification mode, thereby avoiding the over-fitting problem of directly using a final fitting model to evaluate the feature subset.
4. The method is suitable for, but not limited to, LIBS spectral data and can be used for feature selection and data dimension reduction in various broad-band spectrums.
Drawings
FIG. 1 is a flow chart of a method implementation of the present invention;
FIG. 2(a) is a graph showing the result of the quantitative analysis and calibration of the PLS model on Fe element in the aluminum alloy standard sample;
FIG. 2(b) is a graph showing the results of quantitative analysis and calibration of the PLS model by Si element in the aluminum alloy standard sample;
FIG. 2(c) is a graph showing the results of quantitative analysis and calibration of PLS model with Mg element in aluminum alloy standard samples;
FIG. 2(d) is a graph showing the results of quantitative analysis and calibration of the PLS model by Cu element of an aluminum alloy standard sample;
FIG. 2(e) is a graph showing the result of the quantitative analysis and calibration of the PLS model by Mn element in the aluminum alloy standard sample;
FIG. 2(f) is a graph showing the result of quantitative analysis and calibration of the PLS model on Zn element of the aluminum alloy standard sample.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention selects the optimal characteristic spectral line to analyze the element concentration aiming at different analysis elements in the LIBS signal.
As shown in fig. 1, taking LIBS spectral data as an example, after the method starts, original spectral data of a training sample obtained by a LIBS experimental platform is read as input, feature spectral lines are screened by combining ridge regression and a recursive feature elimination algorithm, and an optimal feature subset is selected by evaluating the screened feature subset by using a PLS model, so that an optimal calibration model is obtained to analyze the element concentration of a specific material. The method comprises the following concrete steps:
step 1: LIBS spectral data of the standard sample are obtained, and the wavelength range and all characteristic spectral position information in the wavelength range of the LIBS spectral data are determined. Wherein the standard sample has an accurate concentration; LIBS data were obtained by experimental measurements.
Reading LIBS data and position information of a standard sample, and reading the corresponding accurate concentration of the standard sample, wherein the measured LIBS data can fluctuate due to different experimental environments, actual measurement parameters and operations.
Step 2: LIBS spectral data were full-spectrum and normalized.
And step 3: and randomly dividing the standard sample into a training set and a verification set, wherein the training set accounts for 80-90% and the verification set accounts for 10-20%.
And 4, step 4: the mean of the dimensional data is subtracted from each of the dimensional data of the training spectral data and divided by the variance of the dimensional data. And recording the mean value and variance of the training set spectral data, and carrying out the same standardization operation on the verification set data. In order to avoid the influence of the magnitude of the spectral data with different dimensions on the ridge regression coefficient, the influence of the magnitude on the fitting coefficient is removed in a standardized mode.
The standardization specifically comprises the step of standardizing the spectral characteristics of each dimension of the spectral data. The specific normalization process is as follows:
wherein, XiIs the ith column, u, of the original dataiIs the mean, σ, of the ith column of the original data in the training setiIs the standard deviation, X 'of the ith column of the original data in the training set'iIs normalized for the data in column i.
And 5, using the normalized training spectrum data and the concentration data corresponding to the standard sample as input of a ridge regression model to carry out modeling, wherein the ridge regression penalty coefficient is (0.001-5) according to the concentration of different elements.
Step 6: and recording the coefficient absolute value of the ridge regression model and the corresponding wavelength position.
And 7: and 6, determining the spectral line position corresponding to the minimum coefficient absolute value according to the model coefficient absolute value obtained in the step 6, and eliminating the corresponding characteristic spectral line from the spectral characteristic set to obtain a new characteristic subset.
And 8: and (3) inputting the new feature subset obtained in the step (7) as a PLS model (the number of the PLS model principal components with different elements is between 5 and 30), training the classification model by using N-1 standard sample data of the training set, testing the model by using the remaining 1 standard sample, recording the RMSECV of the tested sample, and repeating the process on all N samples to finally obtain the RMSECV of all the samples.
And step 9: and (5) repeating the step 4 to the step 8 until the number of the features in the feature set is completely deleted, and at the moment, the algorithm jumps out of circulation. And finally, determining an optimal feature subset and a corresponding optimal PLS calibration model according to the RMSECV result in each iteration process. In the whole feature subset screening process, ridge regression is used for relieving the feature spectral line with the minimum absolute value of the overfitting dominance removal coefficient, and the scale of the feature space is gradually reduced.
Step 10: and (4) taking the verification set data as the input of the optimal PLS model obtained in the step 9 to obtain a verification set RMSEP.
Wherein, RMSECV refers to the root mean square error of each element of the training set data left a cross validation, and RMSEP refers to the root mean square error of each element of the validation set data. PLS is partial least squares regression.
Respectively analyzing the concentrations of 6 elements of Fe, Si, Mg, Cu, Zn and Mn in 51 standard aluminum alloy samples according to the method, taking 45 samples as training samples, taking the remaining 6 samples as verification samples, and testing the final effect of the method. The results are shown in FIG. 2(a) -FIG. 2(f) which are the calibration results of Fe, Si, Mg, Cu, Mn, Zn 6 elements, respectively
And
calculating a determination coefficient (Calibration LOOCV) for each element training set to leave a verification result
) Training set leave one validation result Root Mean Square Error (RMSECV) and validation set Root Mean Square Error (RMSEP) (among them)
Represents the ith prediction value, y, of the sampleiRepresenting the true value of its counterpart,
represents the mean of all samples, N represents the sample size of the calibration data set, NpRepresenting the sample size of the verification set), and finally obtaining the quantitative analysis result based on combined ridge regression and recursive feature elimination and the quantitative analysis result of the original spectrum, which are designed by applying the method, according to the following table, it can be seen that the method can effectively meet the requirements of quantitatively analyzing the concentration of the relevant elements of the sample, as shown in table 1 below.
TABLE 1
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A quantitative analysis method based on combined ridge regression and recursive feature elimination is characterized by comprising the following steps:
obtaining original spectral data of a sample as input, screening characteristic spectral lines by combining ridge regression and recursive characteristic elimination algorithms to obtain a characteristic subset, evaluating the screened characteristic subset to select an optimal characteristic subset, and obtaining an optimal calibration model to carry out element concentration analysis on the material.
2. The method of claim 1, wherein the method specifically comprises:
step 1: acquiring spectral data of a sample, and determining a wavelength range;
step 2: performing full spectrum and normalization on the spectral data;
and step 3: dividing the spectral data into a training set and a verification set;
step 4: standardizing each dimension of the training set data, and recording the mean value and the variance in the standardization process;
and 5: training and calibrating a ridge regression model by taking the standardized training spectrum data as input and the known standard sample concentration as output;
step 6: recording the absolute value of the model coefficient of the ridge regression calibration model;
and 7: sequencing the spectral features according to the obtained coefficient absolute value, and removing the spectral features corresponding to the minimum coefficient absolute value to obtain a new feature subset;
and 8: determining an evaluation model, taking the obtained new feature subset as evaluation model input, performing leave-one verification and recording a leave-one cross-verification root mean square error RMSECV of each element of training set data;
and step 9: repeating the step 4 to the step 8 until the feature numbers in the new feature subsets are completely deleted, and determining an optimal feature subset and a corresponding optimal element concentration calibration model according to the RMSECV result in each iteration process;
step 10: and (3) taking the verification set data as the input of the optimal element concentration calibration model to obtain the root mean square error RMSEP of each element of the verification set data output by the model, and comparing the known standard sample concentration to see that the verification set data is the optimal calibration model.
3. The method as claimed in claim 1 or 2, wherein the sample is a standard sample, and the LIBS spectrum data of the sample with wide-band spectrum is obtained by experimental measurement.
4. The method of claim 1 or 2, wherein the concentration of the element in the standard sample is determined in advance.
5. The method of claim 2, wherein the training set and the validation set are randomly selected, the training set comprises 80% -90% of all data, and the testing set comprises 10% -20%.
6. The method of claim 2, wherein the normalization is performed by subtracting a mean value of each dimension of the spectral data and dividing the mean value by a variance of the dimension.
7. The method as claimed in claim 2, wherein the ridge regression model penalty coefficients are scaled according to different elements, and the range of the corresponding different penalty coefficients is 0.001-5.
8. The method of claim 2, wherein the evaluation model for the optimal feature subset is a multivariate regression model, and comprises a partial least squares regression (PLS) model, a Support Vector Regression (SVR) model, and a Ridge regression model.
9. The method of claim 2, wherein the leave-one-out validation comprises: and obtaining a new feature subset, modeling by adopting an N-1 sample on a training set, verifying and recording the root mean square error RMSECV of one cross verification left for each element of the data of the training set by using the remaining sample, recording the RMSECV of all samples after repeating N times, and judging the advantages and disadvantages of the feature subset according to the value of the RMSECV.
10. The method of claim 2 or 9, wherein the subset of features corresponding to the minimum RMSECV value is optimal, and the corresponding PLS calibration model is an optimal element concentration calibration model.
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