CN104091089A - Infrared spectrum data PLS modeling method - Google Patents

Abstract

The invention discloses an infrared spectrum data PLS modeling method. Errors of PLS models of all partition regions and relevancy between the errors are combined so that the weight coefficients of the PLS models of all the partition regions can be determined and the obtained fused PLS model can have the minimum error. According to the method, spectrum information of all the partition regions can be made best use of, the method is easy and convenient to use, the process is visual, the calculating amount is small, and the characteristic wavelength region can be found fast. The weight coefficient determining method takes the errors of the models participating in fusion and the relevancy between the errors into consideration at the same time, and therefore it can be guaranteed that the fused model can have the minimum error.

Description

A kind of ir data PLS modeling method

Technical field

The invention belongs to infrared spectrum identification field, specifically a kind of data processing method that can promote infrared spectrum offset minimum binary modeling effect.

Background technology

In the multivariable ir data of small sample, PLS model can well solve variable collinearity problem and the dimension disaster that other modeling method runs into, and therefore in infrared spectrum identification, has obtained using widely.Although PLS can be directly to full spectrum modeling, theoretical and a large amount of wavelength that experimental results show that select to be still a kind of method of effective raising PLS model.Wavelength optimization selects to refer to the screening of carrying out characteristic wavelength or wave band by certain method before modeling.After wavelength is selected, institute's established model is owing to having rejected uncorrelated or non-linear variable, and therefore more full wavelength model is more simplified, and predictive ability and robustness are also better.Wherein iPLS (interval PLS-iPLS) is a kind of conventional Wavelength selecting method.The advantage of iPLS method be easy, visual, operand is little, can be very fast find characteristic wavelength interval.Shortcoming is only to utilize the spectral information of an interval section, may lose the useful spectral information of other interval sections.Therefore how the best spectral information that utilizes each interval section is problem demanding prompt solution.

Summary of the invention

Technical matters to be solved by this invention is, for above-mentioned the deficiencies in the prior art, to provide a kind of ir data PLS modeling method.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of ir data PLS modeling method, comprises the following steps:

1) largest interval interval number max_int_no, maximum latent variable be set count the tuple k of max_lv_no, bracketing method ₁and k ₂; Wherein, k ₁, k ₂all be not less than 2;

2) when counting period interval number is int_no, the cross validation error of corresponding fusion PLS model, the step of calculating is all 2.1 to 2.2, wherein 1≤int_no≤max_int_no:

2.1) the spectrum matrix X in infrared spectrum sample set data is equally divided into int_no interval section X _i: the columns of each interval section [] represents to round; I interval section X _i[(i-1) × l+1]～(i × l) data of row of corresponding spectrum matrix X; 1≤i≤int_no;

2.2) when calculating latent variable number is lv_no, fusion PLS model wherein 1≤lv_no≤max_lv_no, the step of calculating is all 2.2.1 to 2.2.5;

2.2.1) use k ₁retransposing method counting period number is int_no, when latent variable number is lv_no, and the cross validation error of the PLS model that each interval section is corresponding wherein y represents the actual value of the dependent variable matrix in infrared spectrum sample set data, represent the predicted value of the dependent variable matrix that PLS model that i latent variable number corresponding to interval section is lv_no obtains according to k1 retransposing method, e _ibe corresponding prediction residual matrix, n is the sample number of infrared spectrum sample set data;

2.2.2) counting period number is int_no, when latent variable number is lv_no, and the correlativity between the prediction residual matrix of the PLS model that each interval section is corresponding wherein, $\mathrm{cov}(e_i,e_j)=\frac{1}{n}<e_i,e_j>,i,j=\mathrm{1,2},...,\mathrm{int}\_\mathrm{no};$

2.2.3) calculate following formula by the method for nonlinear optimization,

$f=\min (\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_i\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{p>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_p{r}_{\mathrm{ip}}S\left(e_i\right)S\left(e_p\right))$

$s.t\left\{\begin{array}{c}\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i=1\\ 0\&le;{\mathrm{\&omega;}}_i\&le;1\end{array}\right.;$

Obtaining space-number is int_no, when latent variable number is lv_no, and the combination coefficient ω=[ω of the PLS model that each interval section is corresponding ₁..., ω _{int_no}] ':

2.2.4) use k ₂retransposing method counting period number is int_no, when latent variable number is lv_no, and the prediction residual matrix of the PLS model that each interval section is corresponding wherein represent that PLS model that i latent variable number corresponding to interval section is lv_no is according to k ₂the predicted value of the dependent variable matrix that retransposing method obtains, calculates

${\hat{f}}_{\mathrm{int}\_\mathrm{no}}^{\mathrm{lv}\_\mathrm{no}}=\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_{2i}\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{p>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_p{r}_{\mathrm{ip}}S\left(e_{2i}\right)S\left(e_{2p}\right);$

2.2.5) select minimum the cross validation error of the fusion PLS model while being int_no as interval section number, is designated as

3) select under all interval section numbers minimum this minimum corresponding interval section is counted int_bt, latent variable and is counted lv_bt and combination coefficient ω _ bt as optimum model parameter;

4) merge PLS model according to optimum model parameter structure: spectrum matrix X is equally divided into int_bt interval section, merges PLS model as follows:

$y^{*}=\underset{g=1}{\overset{\mathrm{int}\_\mathrm{bt}}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\_{\mathrm{bt}}_g(x_g\&times;b_g+c_g)$

Wherein, ω _ bt _gg the component of ω _ bt, y ^*it is the predicted value that merges the dependent variable of PLS model to sample; b _g, c _grespectively interval section X _gpartially minimum regression coefficient and intercept while being lv_bt with the corresponding latent variable number of dependent variable matrix Y; x _gg the ir data that interval section is corresponding.

Fusion PLS model of the present invention is the weighted array of multiple member's models.Member's model is exactly the PLS model that each interval section is corresponding.The quantity of the corresponding member's model of interval section number.The concrete form of i member's model is determined by the spectroscopic data of i interval section and the latent variable of extraction.

Compared with prior art, the beneficial effect that the present invention has is: the spectral information that utilizes each interval section that method of the present invention can be best, easy, visual, operand is little, can be very fast find characteristic wavelength interval; Definite method of the weight coefficient during we are bright, due to the correlativity of having considered between each error and error that participates in the model merging simultaneously, can ensure that the model after merging has minimum error.

Brief description of the drawings

Fig. 1 is method flow diagram of the present invention.

Embodiment

Now in conjunction with example, the present invention will be further described.

The spectra spectroscopic data that spectroscopic data adopts matlab2012a to carry, sample is gasoline, dependent variable is the octane value of sample.Original sample data collection comprises 60 samples, and the spectral variables length of each sample is 700.For convenience of description, this example only selects 1-6 spectral variables data of 1-6 sample as the spectroscopic data matrix of sample sets.The sample sets data that this example adopts are made up of spectroscopic data matrix X and dependent variable matrix Y, as follows respectively,

$X=\left[\begin{array}{cccccc}-0.0502& -0.0459& -0.0422& -0.0372& -0.0333& -0.0312\\ -0.0442& -0.0396& -0.0357& -0.0309& -0.0267& -0.0239\\ -0.0469& -0.0413& -0.0370& -0.0315& -0.0265& -0.0233\\ -0.0467& -0.0422& -0.0386& -0.03456& -0.0302& -0.0277\\ -0.0509& -0.0451& -0.0410& -0.0364& -0.0327& -0.0315\\ -0.0481& -0.0427& -0.0388& -0.0340& -0.0301& -0.0277\end{array}\right]$

$Y=\left[\begin{array}{c}85.3000\\ 85.2500\\ 88.4500\\ 83.4000\\ 87.9000\\ 85.5000\end{array}\right]$

Specific embodiment of the invention step is as follows:

Step 1, parameter setting: arrange that maximum interval section is counted Max_int_no=2, maximum latent variable is counted the tuple k of Max_lv_no=2, bracketing method ₁=4, k ₂=6.Arranging of these parameters can be adjusted according to actual needs.Here so just modeling procedure for convenience of explanation of parameters.

Step 2, when counting period interval number is int_no, corresponding fusion PLS model the step of calculating is all 2.1 to 2.2, and wherein 1≤int_no≤max_int_no, describes as an example of int_no=2 example below:

The spectrum matrix X in infrared spectrum sample set data is equally divided into int_no interval section X by step 2.1 _i.The columns of each interval section x ₁first row to the three examples of corresponding spectroscopic data matrix X, X ₂the 4th row of corresponding spectroscopic data matrix X are to the 6th row.X ₁, X ₂as follows respectively.

$X_1=\left[\begin{array}{ccc}-0.0502& -0.0459& -0.0422\\ -0.0442& -0.0396& -0.0357\\ -0.0469& -0.0413& -0.0370\\ -0.0467& -0.0422& -0.0386\\ -0.0509& -0.0451& -0.0410\\ -0.0481& -0.0427& -0.0388\end{array}\right]$

$X_2=\left[\begin{array}{ccc}-0.0372& -0.0333& -0.0312\\ -0.0309& -0.0267& -0.0239\\ -0.0315& -0.0265& -0.0233\\ -0.0345& -0.0302& -0.0277\\ -0.0364& -0.0327& -0.0315\\ -0.0340& -0.0301& -0.0277\end{array}\right]$

When step 2.2 is calculated latent variable number and is lv_no, merge the cross validation error of PLS model, wherein 1≤lv_no≤max_lv_no, the step of calculating is all 2.2.1 to 2.2.5; Describe as an example of lv_no=2 example below.

Step 2.2.1 k ₁retransposing method counting period number is int_no, the cross validation error of the PLS model that each interval section when latent variable number is lv_no is corresponding.

According to k ₁the predicted value of the PLS model that the latent variable number corresponding to first interval section of retransposing method calculating gained is lv_no to dependent variable matrix prediction residual matrix e ₁and e ₁standard deviation S (e ₁) as follows respectively,

${\hat{y}}_1=\left[\begin{array}{c}83.5924\\ 86.7554\\ 85.2694\\ 85.1904\\ 89.5037\\ 87.4816\end{array}\right],e_1=\left[\begin{array}{c}1.7076\\ -1.5054\\ 3.1806\\ 1.2096\\ -1.6037\\ -1.9816\end{array}\right],$ S(e ₁)＝2.1490。

According to k ₁the predicted value of the PLS model that the latent variable number corresponding to second interval section of retransposing method calculating gained is lv_no to dependent variable matrix prediction residual matrix e ₂and e ₂standard deviation S (e ₂) as follows respectively,

${\hat{y}}_2=\left[\begin{array}{c}80.1147\\ 86.4685\\ 86.9897\\ 86.9970\\ 81.4383\\ 84.1570\end{array}\right],e_2=\left[\begin{array}{c}5.1853\\ -1.2185\\ 1.4603\\ -3.5970\\ 6.4617\\ 1.3430\end{array}\right],$ S(e ₂)＝3.7823。

Step 2.2.2 counting period number is int_no, when latent variable number is lv_no, and the correlativity between the prediction residual matrix of the PLS model that each interval section is corresponding,

r ₁₁＝1.0000,r ₁₂＝-0.0900,r ₂₁＝-0.0900,r ₂₂＝1.0000。

Step 2.2.3 calculates following formula by the method for nonlinear optimization,

$f=\min (\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_i\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{j>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_j{r}_{\mathrm{ij}}S\left(e_i\right)S\left(e_j\right))$

$s.t\left\{\begin{array}{c}\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i=1\\ 0\&le;{\mathrm{\&omega;}}_i\&le;1\end{array}\right.$

Obtaining space-number is int_no, when latent variable number is lv_no, and the combination coefficient of the PLS model that each interval section is corresponding

ω＝[0.7376?0.2624]′。

Step 2.2.4 k ₂retransposing method counting period number is int_no, when latent variable number is lv_no, and the prediction residual matrix of the PLS model that each interval section is corresponding

${\hat{y}}_{21}=\left[\begin{array}{c}83.5924\\ 86.7554\\ 85.2694\\ 82.1904\\ 89.5037\\ 87.4816\end{array}\right],{\hat{y}}_{22}=\left[\begin{array}{c}80.1147\\ 86.4685\\ 86.9897\\ 86.9970\\ 81.4383\\ 84.1570\end{array}\right],e_{21}=\left[\begin{array}{c}1.7076\\ -1.5054\\ 3.1806\\ 1.2096\\ -1.6037\\ -1.9816\end{array}\right],e_{22}=\left[\begin{array}{c}5.1853\\ -1.2185\\ 1.4603\\ -3.5970\\ 6.4617\\ 1.3430\end{array}\right]$

respectively first, second interval corresponding latent variable number of the interval section predicted value of PLS model to dependent variable matrix that be lv_no.

Calculate ${\hat{f}}_{\mathrm{int}\_\mathrm{no}}^{\mathrm{lv}\_\mathrm{no}}=\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_{2i}\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{p>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_p{r}_{\mathrm{ip}}S\left(e_{2i}\right)S\left(e_{2p}\right)=1.7250$

Step 2.2.5 selects minimum the cross validation error of the fusion PLS model while being int_no as interval section number, is designated as in this example ${{\hat{f}}_1}^1=2.4440,{{\hat{f}}_1}^2=2.7208,{\hat{f}}_2^1=2.1265,$ therefore, when interval section is counted int_no=1, merge the cross validation error of PLS model when interval section is counted int_no=2, the cross validation error that merges PLS model is ${\hat{f}}_2=1.7250.$

Step 3, selects all interval sections and counts in int_no (1≤int_no≤Max_int_no) situation, merges the cross validation error minimum value of PLS model.In this example be minimum value, corresponding optimum model parameter is as follows: interval section is counted int_bt=2, and latent variable is counted lv_bt=2, combination coefficient ω _ bt=[0.7376 0.2624] '.

Step 4, merges PLS model according to optimum model parameter structure.B ₁=[64.4-2120.4 443.4] ', c ₁=1565.1 is respectively X ₁with latent variable number corresponding to Y be partial least squares regression coefficient and the intercept of 2 o'clock.B ₂=[105.8 596.31404.7] ', c ₂=-1544.9 is respectively X ₂with latent variable number corresponding to Y be partial least squares regression coefficient and the intercept of 2 o'clock.Final fusion PLS model is as follows,

y＝0.7376×(x ₁b ₁+64.4)+0.2624×(x ₂b ₂+105.8)。

The complete spectroscopic data x of a sample is by x ₁and x ₂form i.e. x=[x ₁x ₂].X ₁be first interval section corresponding spectroscopic data, x ₂second spectroscopic data that interval section is corresponding.Y is the predicted value that merges the dependent variable of PLS model to sample.

Claims (1)

1. an ir data PLS modeling method, is characterized in that, comprises the following steps:

1) largest interval interval number max_int_no, maximum latent variable be set count the tuple k of max_lv_no, bracketing method ₁and k ₂; Wherein, k ₁, k ₂all be not less than 2;

2) according to step 2.1) and step 2.2) counting period interval number is while being int_no, the cross validation error of corresponding fusion PLS model, wherein 1≤int_no≤max_int_no:

2.1) the spectrum matrix X in infrared spectrum sample set data is equally divided into int_no interval section X _i: the columns of each interval section [] represents to round; I interval section X _i[(i-1) × l+1]～(i × l) data of row of corresponding spectrum matrix X; 1≤i≤int_no;

2.2) according to step 2.2.1)～step 2.2.5) when calculating latent variable number and being lv_no, merge PLS model wherein 1≤lv_no≤max_lv_no:

2.2.1) use k ₁retransposing method counting period number is int_no, when latent variable number is lv_no, and the cross validation error of the PLS model that each interval section is corresponding wherein y represents the actual value of the dependent variable matrix in infrared spectrum sample set data, represent the predicted value of the dependent variable matrix that PLS model that i latent variable number corresponding to interval section is lv_no obtains according to k1 retransposing method, e _ibe corresponding prediction residual matrix, n is the sample number of infrared spectrum sample set data;

2.2.2) counting period number is int_no, when latent variable number is lv_no, and the correlativity between the prediction residual matrix of the PLS model that each interval section is corresponding wherein, $\mathrm{cov}(e_i,e_j)=\frac{1}{n}<e_i,e_j>,i,j=\mathrm{1,2},...,\mathrm{int}\_\mathrm{no};$

2.2.3) calculate following formula by the method for nonlinear optimization:

$f=\min (\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_i\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{p>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_p{r}_{\mathrm{ip}}S\left(e_i\right)S\left(e_p\right))$

$s.t\left\{\begin{array}{c}\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i=1\\ 0\&le;{\mathrm{\&omega;}}_i\&le;1\end{array}\right.;$

Obtaining space-number is int_no, when latent variable number is lv_no, and the combination coefficient ω=[ω of the PLS model that each interval section is corresponding ₁..., ω _{int_no}] ':

2.2.4) use k ₂retransposing method counting period number is int_no, when latent variable number is lv_no, and the prediction residual matrix of the PLS model that each interval section is corresponding wherein represent that PLS model that i latent variable number corresponding to interval section is lv_no is according to k ₂the predicted value of the dependent variable matrix that retransposing method obtains, calculates

${\hat{f}}_{\mathrm{int}\_\mathrm{no}}^{\mathrm{lv}\_\mathrm{no}}=\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i^2{S}^2\left(e_{2i}\right)+2\underset{i=1}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}\underset{p>i}{\overset{\mathrm{int}\_\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_p{r}_{\mathrm{ip}}S\left(e_{2i}\right)S\left(e_{2p}\right);$

2.2.5) select minimum the cross validation error of the fusion PLS model while being int_no as interval section number, is designated as

3) select under all interval section numbers minimum this minimum corresponding interval section is counted int_bt, latent variable and is counted lv_bt and combination coefficient ω _ bt as optimum model parameter;

4) merge PLS model according to optimum model parameter structure: spectrum matrix X is equally divided into int_bt interval section, merges PLS model as follows:

$y^{*}=\underset{g=1}{\overset{\mathrm{int}\_\mathrm{bt}}{\mathrm{\&Sigma;}}}\mathrm{\&omega;}\_{\mathrm{bt}}_g(x_g\&times;b_g+c_g)$

Wherein, ω _ bt _gg the component of ω _ bt, y ^*it is the predicted value that merges the dependent variable of PLS model to sample; b _g, c _grespectively interval section X _gpartially minimum regression coefficient and intercept while being lv_bt with the corresponding latent variable number of dependent variable matrix Y; x _gg the ir data that interval section is corresponding.