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In this paper, partial least squares (PLS) regression (PLSR) model is established and the prediction performance is evaluated. In order to build a reliable model, we also implemented some common outlier detection and variable selection methods, which can remove potential outliers and “wash” your data using only a subset of selected variables.

steps

• PLS regression model was established
• PLS k-fold cross validation
• PLS monte Carlo cross validation (MCCV).
• Double cross validation of PLS (DCV)
• Monte Carlo sampling method was used to detect outliers
• CARS method was used for variable selection.
• Use moving window PLS (MWPLS) for variable selection.
• Monte Carlo uninformative variable elimination method (MCUVE) was used for variable selection
• Make variable selection

PLS regression model was established

This example illustrates how to build a PLS model using benchmark near infrared data.

plot(X'); % displays spectral data. Xlabel (' wavelength index '); Ylabel (' strength ');Copy the code

Parameter setting

A=6; % Number of potential variables (LVS). method='center'; % X internal preprocessing method PLS(X,y,A,method) for establishing PLS model; % command to create a modelCopy the code

The pls.m function returns an object PLS containing the list of components. Interpretation of results.

Regcoef_original: The regression coefficient connecting X and Y. X_scores: X scores. VIP: The importance of variables in the prediction, a criterion for evaluating the importance of variables. The importance of variables. RMSEF: root mean square error of the fit. Y_fit: the fitting value of y. R2: percentage of explanatory variation of Y.

PLS k-fold cross validation

clear; A=6; The number of % LV K=5; % Number of times of cross validationCopy the code

Plot (CV.RMSECV) % Plot the RMSECV value under each potential variable (LVs) quantity xLabel (' potential variable (LVs) quantity ') % Add xlabel ylabel('RMSECV') % Add Y labelCopy the code

Monte Carlo cross-validation (MCCV) with PLS

Explain how to MCCV PLS modeling. MCCV, like K-FOLD CV, is another method of cross-validation.

% parameter setting A=6; method='center'; N=500; % Number of Monte Carlo samples % run McCv.plot (McCv.rmsecv); % Draw the RMSECV value xlabel(' LVs number ') for each potential variable (LVs number);Copy the code

 
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MCCV
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MCCV is a structured data. Interpretation of results.

Ypred: predicted value Ytrue: true value RMSECV: root mean square error of cross verification. The smaller the error, the better. Q2: has the same meaning as R2, but is calculated by cross validation.

Double cross validation of PLS (DCV)

% parameter setting N=50; DCV (X, Y,A, K,method,N); DCVCopy the code

Outlier detection using Monte Carlo sampling method

Explain the use of outlier detection methods

A=6;
method='center';
F=mc(X,y,A,method,N,ratio);
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Interpretation of results.

PredError: sample prediction error per sample MEAN: average prediction error per sample STD: standard deviation of the prediction error per sample

Plot (F) % Diagnostic diagramCopy the code

Note: Samples with high MEAN or SD values are more likely to be outliers and should be considered to be removed before modeling.

CARS method was used for variable selection.

A=6;
fold=5;
car(X,y,A,fold);
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plotcars(CARS); % in the diagnosis of figureCopy the code

Use moving window PLS (MWPLS) for variable selection

load corn_m51; % example data width=15; % window size mw(X,y,width); plot(WP,RMSEF); Xlabel (' window position ');Copy the code

Note: From this figure, it is suggested to include the regions with low RMSEF values into the PLS model.

Monte Carlo uninformative variable elimination method (MCUVE) was used for variable selection

N=500;
method='center';

UVE
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plot(abs(UVE.RI))
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Make variable selection

A=6;
N=10000;
method='center';
FROG=rd_pls(X,y,A,method,N);


              N: 10000
              Q: 2
          model: [10000x700 double]
        minutes: 0.6683
         method: 'center'
          Vrank: [1x700 double]
         Vtop10: [505 405 506 400 408 233 235 249 248 515]
    probability: [1x700 double]
           nVar: [1x10000 double]
          RMSEP: [1x10000 double]
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Xlabel (' variable number '); Ylabel (' selection probability ');Copy the code

Interpretation of the results:

The model results in a matrix that stores the selection variables in each of the interrelationships. Probability: The probability that each variable is included in the final model. The bigger the better. This is a useful indicator of the importance of a variable.

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