CN111474128B - Spectral wavelength combination method based on spectral separation degree - Google Patents

Abstract

The invention discloses a spectroscopic wavelength combination method based on spectral separation, comprising the following steps: measuring the spectrum of each negative and positive sample that needs to be discriminated; calculating the minimum value of the spectral absorbance of all negative and positive samples at each wavelength , maximum value, mean value, standard deviation; put forward the resolution spectrum and relative resolution spectrum of negative and positive spectral populations; determine the search range of the wavelength model, reorder the wavelengths according to the resolution value from large to small, and construct wavelength combinations in turn; The spectral data of the sample is used for discriminant analysis, the recognition accuracy is calculated, and the optimal model is determined according to the total recognition accuracy. The four separation degrees proposed by the present invention describe the separation degree of spectral populations from different angles. Prioritizing the selection of wavelengths for analysis based on the spectral separation can improve the similarity and difference characteristics of the same species of spectral populations, thereby improving the discrimination accuracy of instrumental analysis. It generally outperforms full search range models without wavelength selection, significantly reducing wavelength model complexity.

Description

A Spectral Wavelength Combination Method Based on Spectral Separation

technical field

The invention relates to the technical field of wavelength screening for spectral analysis, in particular to a spectroscopic wavelength combination method based on spectral separation.

Background technique

Molecular spectra mainly include ultraviolet-visible, near-infrared, mid-infrared and other spectral regions. With the development of detection technology and chemometrics, molecular spectroscopy has become an effective technical means for rapid detection of samples. Especially the near-infrared (NIR) spectrum, which reflects the double frequency and combined frequency absorption of the molecular hydrogen-containing functional group X-H (such as C-H, N-H, O-H, etc.), for most types of samples, no pretreatment (or Simple processing) can be measured.

At present, for the discriminative analysis of complex analytes in the full-band general-purpose near-infrared spectroscopy instrument, there is still a lack of wavelength selection based on the spectral population separation characteristics to improve the discriminative effect.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to provide a method for combining spectroscopic wavelengths based on spectral separation. The purpose of the present invention is achieved by the following technical solutions:

A kind of spectroscopic wavelength combination method based on spectral separation, is characterized in that comprising the following steps:

1. Measure the spectrum of each negative and positive sample that needs to be distinguished;

2. Calculate the minimum, maximum, mean and standard deviation of the spectral absorbance of all negative and positive samples at each wavelength;

3. Propose the separation spectrum and relative separation spectrum of negative and positive spectral populations;

4. Determine the search range of the wavelength model, reorder the wavelengths according to the resolution value from large to small, and construct wavelength combinations in turn;

5. Use the spectral data of the sample for discriminant analysis, calculate the recognition accuracy, and determine the optimal model based on the total recognition accuracy.

Further, the negative samples and positive samples are randomly or evenly divided into a calibration set and a prediction set, respectively. The calibration set is used to establish a discriminant analysis model and parameters based on the spectral data of the sample and the real category; the prediction set is used to judge the sample category based on the spectral data of the sample and the established discriminant analysis model, so as to test the model.

Further, step 3 includes four kinds of type I separation spectrum, type I relative resolution spectrum, type II resolution spectrum and type II relative resolution spectrum of negative and positive spectral populations.

Further, in step 4, the search range of the wavelength model is determined, and the search range of the wavelength combination is the full-scan spectral region; or the wavelength range specified according to the specific object.

Further, in step 5, negative, positive, calibration and predicted sample spectra are selected according to the wavelength combination model.

Further, in step 5, a spectral discriminant analysis model is established according to the wavelength combination data, and the relevant negative, positive, calibration, and predicted recognition accuracy rates are calculated; and the optimal model is determined according to the total identification accuracy rate.

Furthermore, a partial least squares discriminant analysis model or a principal component analysis-linear discriminant analysis model or other spectral discriminant analysis models are established according to the wavelength combination data.

Further, after step 5, the respective optimal models can be obtained from the priority combinations of different resolutions, and then the optimal wavelength model can be selected therefrom.

Furthermore, the type I separation degree (S _Ι (λ)), the type I relative separation degree (R _I (λ)), the type II separation degree (S _ΙΙ (λ)) and the II Type relative resolution (R _II (λ)), as follows:

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. The present invention is superior to the full search range model without wavelength selection, and significantly reduces the complexity of the wavelength model.

2. The method of the present invention is simple and easy to operate.

3. The present invention can provide a basis for the design of the spectroscopic system of the new special spectrometer.

Description of drawings

Fig. 1 is the flow chart of embodiment method.

Figure 2 is a schematic diagram of type I separation of two types of spectral populations, and the solid line and dotted line represent the spectral populations of negative and positive samples, respectively.

Fig. 3 is a schematic diagram of the type II separation degree of two types of spectral populations, and the solid line and dashed line represent the spectral populations of negative and positive samples, respectively.

Figure 4 is the type I separation spectrum and type I relative separation spectrum of negative and positive spectra mixed with rice seeds.

Fig. 5 is the type II separation spectrum and type II relative separation spectrum of negative and positive spectra mixed with rice seeds.

Fig. 6 is the type I separation degree spectrum and the type I relative separation degree spectrum of the negative and positive spectra of adulterated milk powder.

Fig. 7 is the type II separation degree spectrum and type II relative separation degree spectrum of the negative and positive spectra of adulterated milk powder.

Figure 8 is the type I separation spectrum and type I relative separation spectrum of negative and positive spectra for wine brand identification.

Figure 9 is the type II separation spectrum and type II relative separation spectrum of negative and positive spectra for wine brand identification.

Detailed ways

This patent takes (1) visible-near-infrared spectrum discrimination of mixed rice seeds; (2) visible-near-infrared spectrum discrimination of milk powder doping; (3) visible-near-infrared spectrum discrimination of wine brands as examples, and details Embodiments and effects of the separation degree priority combination (Separation Degree Priority Combination, SDPC) method, but the embodiments of the present invention are not limited thereto.

A method for combining spectroscopic wavelengths based on spectral separation, comprising the steps of:

S1. Sample collection: collect two types of samples that need to be identified, referred to as "negative" and "positive" samples respectively;

S2. Spectrum acquisition: Repeat multiple times to measure the spectrum of each sample;

计算全体阴性、阳性样品光谱吸光度的均值、标准偏差，分别记为

S3, at any wavelength λ, the minimum value, mean value and maximum value of the spectral absorbance of all negative and positive samples are recorded as

Calculate the mean and standard deviation of the spectral absorbance of all negative and positive samples, which are recorded as

S4. The type I separation spectrum, the type I relative resolution spectrum, the type II resolution spectrum and the type II relative resolution spectrum of the two spectral populations are sequentially presented below. Define type I resolution (S _Ι (λ)), type I relative resolution (R _I (λ)), type II resolution (S _ΙΙ (λ)) and type II relative resolution (R _II (λ) ),as follows:

S5. Sorting based on separation (taking S ₁ as an example): determine the required wavelength range, which can use the full scan spectrum area, or use a specific wavelength range (total number of wavelengths: n) according to the spectral characteristics of the actual object. The wavelengths are sorted according to the resolution value from large to small, as follows:

λ ₁ ,λ ₂ ,…,λ _n ;

S6. Wavelength combination with resolution priority: based on the resolution priority, construct n wavelength combination models in sequence as follows:

Ω _i ={λ ₁ ,λ ₂ ,...,λ _i }, i=1,2,...,n;

S7, using the spectral data of two types of samples, and dividing them into calibration and prediction sample sets, collecting and measuring the sample spectra; establishing a partial least squares discriminant analysis (PLS-DA) model (or Other spectral discriminant analysis models), calculate the relevant negative, positive, calibration, and predicted recognition accuracy; and determine the optimal model according to the total recognition accuracy (RAR _Total ), which is called the optimal SDPC model. The formula is as follows:

The corresponding optimal wavelength combination (number of wavelengths: N) is:

Ω _N ={λ ₁ ,λ ₂ ,...,λ _N }.

S8. Similarly, based on the priority combination method of the other three types of separation (R _I , S _II , R _II ), the respective optimal models can also be obtained respectively, and finally, be optimized from among them.

The above wavelength model is the optimal wavelength model selected.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. The four degrees of separation proposed by the present invention describe the degree of separation of spectral populations from different angles. Prioritizing the selection of wavelengths for analysis based on the spectral separation can improve the similarity and difference characteristics of the same species of spectral populations, thereby improving the discrimination accuracy of instrumental analysis. Compared with the full-spectrum model without wavelength selection, it significantly reduces the complexity of the wavelength model;

2. The present invention also has innovations in the spectral analysis method, and the method is simple and easy to operate. The wavelength combination obtained by screening is usually a combination of several wavebands. Therefore, it is a multi-band wavelength selection method. It is more flexible and applicable than the classical continuous wavelength selection method. It can overcome the defect that the continuous model is not suitable for analysis objects with multiple absorption bands;

3. The invention has the advantages of wide application range, simple method, good prediction effect, etc., and can provide a basis for the design of a spectroscopic system of a new type of special spectroscopic instrument.

Example 1

The authenticity identification of high-yield and high-quality rice seeds is an important basic problem in agricultural production. In this example, the visible-near-infrared spectrum discriminant analysis of mixed rice seeds is taken as an example to illustrate the applicability of the proposed spectral separation wavelength combination method based on spectral separation. By comparing the partial least squares discriminant analysis model (Full PLS-DA) based on the full spectrum, it is shown that the spectroscopic wavelength combination method based on the spectral separation degree proposed by the present invention is more suitable for the detection of rice seeds.

The specific implementation steps are as follows:

S1. Sample collection and preparation

Several bags of pure rice seeds of 5 different varieties confirmed by standard manual methods were collected from regular seed companies. They are Y Liangyou 900, Xiang Liangyou 900, Nei 5 You 8015, Jing Liang You Huazhan, and Huang Huazhan; they are abbreviated as R1, R2, R3, R4, R5 in sequence; R1 is a high-yield and high-quality hybrid seed, R2, R3 and R4 are hybrid seeds, and R5 is conventional seeds. The specific components and quantities for preparing target samples (negative) and contaminated samples (positive) are as follows:

218 negative samples: R1, 20g each;

148 positive samples: 1) pure positive samples, that is, four types of seeds R2, R3, R4, R5, 10 each, 40 in total, 20 grams each. 2) Miscellaneous samples, that is, different proportions of other Type 1 contaminated samples were mixed in R1, and the mixing ratio increased uniformly from 2.5% (tolerance 2.5%); there were 4 types of mixed samples, and a total of 108 samples were recorded, each 20g.

S2. Spectrum collection and sample division

The XDS Rapid Content ^TM near-infrared grating spectrometer (Denmark, FOSS) was used for collection, and the diffuse reflectance spectrum of each sample was collected 3 times (using the average spectrum) with a circular sample cup. The spectral scanning range of the instrument was 400-2498nm. The interval between the wavelength points is 2nm, and there are 1050 wavelengths in total (n=1050).

The negative samples (218) were randomly divided into the calibration set (116) and the prediction set (102), and the 40 pure positive samples were randomly divided into the calibration set (20) and the prediction set (20); A class of confounding samples are sorted according to the confounding ratio, extracted at intervals, and evenly divided into calibration sets (56) and prediction sets (52); in summary, the calibration set (negative 116, positive 76, 192 in total) and prediction set are obtained (negative 102, positive 72, 174 in total); Calculate the mean value and standard deviation of spectral absorbance of all negative and positive samples respectively.

S3-S4, with reference to above-mentioned S3-S4, obtain the I-type separation spectrum of the negative of rice seed, positive spectral population, I type relative separation spectrum, II type separation spectrum and II type relative separation spectrum, as Fig. 4, Figure 5 shows.

S5-S8. Referring to the methods of S5-S8 above, optimize the wavelength model of the resolution priority combination (SDPC) based on the four types of resolution respectively, and determine the respective optimal SDPC models, see Table 1. Wherein, N is the number of wavelengths of the selected model. According to the true category (positive, negative) of the sample, nine recognition accuracy rates (Recognition Accuracy Rate, RAR, unit %) about positive, negative, calibration, and prediction attributes are calculated. Among them, the positive, negative and total recognition accuracy of the samples in the calibration set are as follows:

The positive, negative and total recognition accuracy of the samples in the prediction set are as follows:

The overall positive, negative, and total recognition accuracy rates are as follows:

分别为阳性、阴性的定标、预测样品的真实个数；

分别为被准确识别的阳性、阴性的定标、预测样品的个数。并计算上述9个识别准确率的标准偏差，记为RAR_SD，用于描述针对不同样品属性(阳性、阴性、定标、预测等)的识别均衡性，也称为属性波动值。in

Respectively positive, negative calibration, the actual number of predicted samples;

Respectively, the number of positive and negative calibration and prediction samples that are accurately identified. And calculate the standard deviation of the above nine identification accuracy rates, which is recorded as RAR _SD , which is used to describe the identification balance for different sample attributes (positive, negative, calibration, prediction, etc.), also known as attribute fluctuation value.

The optimal band combination corresponding to the optimal model of the four types of separation is shown in Table 2. Then select from the optimal models of the four types of separation, and the model corresponding to S _II is the global optimal model. Compared with the results of Full PLS-DA based on the full-scan spectral region (400-2498nm), the optimal SDPC-PLS-DA model achieved significantly better prediction accuracy, and the attribute fluctuation value (RAR _SD ) also decreased. The number of wavelengths it uses is 341, which is only 32.5% of the full-spectrum wavelengths, indicating that the model complexity is also greatly reduced. See Table 3 for the results.

Table 1 The parameters and prediction accuracy of the four-class separation priority combination model of rice hybrid discriminant analysis

Table 2 The optimal band combination of the four-class separation priority combination model for hybrid discriminant analysis of rice

Table 3 Comparison of optimal SDPC-PLS-DA model and Full PLS-DA model for mixed discriminant analysis of rice

Experiments have proved that the wavelength combination screened out based on the spectroscopic wavelength combination method based on the spectral separation degree of the present invention is better than the prediction effect of the full spectrum, and the number of wavelengths is also significantly reduced. This method can form a naturally optimized piecewise continuous wavelength model, which cannot be realized by the continuous wavelength screening method, thereby broadening the wavelength screening method and application range, and is useful for establishing high-precision models, reducing model complexity and designing special spectrometers. Spectroscopic systems are of great significance.

Example 2

The identification of adulterated milk powder helps to protect the rights and interests of producers and consumers, and is an important food safety issue. In this example, the visible-near-infrared spectrum discriminant analysis of adulterated milk powder is taken as an example to illustrate the applicability of the proposed spectroscopic wavelength combination method based on spectral separation. By comparing the partial least squares discriminant analysis model (Full PLS-DA) based on full spectrum, it is shown that the spectral separation wavelength combination method based on spectral separation degree proposed by the present invention is more suitable for the identification of adulterated milk powder. However, the embodiments of the present invention are not limited thereto.

The specific implementation steps are as follows:

S1. Sample collection and preparation

Buy several bags of 3 different brands of milk powder (Beinmate, Yili and Junlebao) from regular stores, and denote them as I, II, and III in turn. The specific components and quantities for preparing target samples (negative) and adulterated samples (positive) are as follows:

64 parts of negative samples: 1, each 10g;

61 positive samples: 1) single doping sample, that is, doping II or III in I, the doping ratio increases uniformly from 3% (tolerance 3%); there are two types of doping, 22 copies each, total 44 servings of 10g each. 2) Double-doped samples, that is, I is doped with II and III at the same time, and the proportions of the two samples are uniformly increased from 2% (tolerance 2%); a total of 17 samples are recorded, each 10g.

S2. Spectrum collection and sample division

The XDS Rapid Content ^TM near-infrared grating spectrometer (Denmark, FOSS) was used for collection, and the diffuse reflectance spectrum of each sample was collected 5 times with a circular sample cup. The spectral scanning range of the instrument was 400-2498nm, and the wavelength point interval was 2nm. A total of 1050 wavelengths (n=1050).

Randomly divide the negative samples (64) into the calibration set (32) and the prediction set (32), 44 single-doped samples and 17 double-doped samples, sorted according to the doping ratio, interval extraction, uniform Divided into a calibration set (22 single-doped, 9 double-doped) and a prediction set (22 single-doped, 8 double-doped); in summary, the calibration set (negative 32, positive 31, total 63) and prediction set (negative 32, positive 30, total 62); respectively calculate the mean value and standard deviation of spectral absorbance of all negative and positive samples.

S3-S4, with reference to S3-S4 in "Example 1", obtain the type I separation degree spectrum, type I relative separation degree spectrum, type II separation degree spectrum and type II relative separation degree of the negative and positive spectrum populations adulterated with milk powder Spectrum, as shown in Figure 6 and Figure 7.

S5-S8. With reference to the method of S5-S8 in "Example 1", the wavelength model optimization of the resolution priority combination (SDPC) is carried out based on the four types of resolution respectively, and the respective optimal SDPC models are determined, see Table 4. And calculate the 9 identification accuracy rates and standard deviations RAR _SD about positive, negative, calibration, and prediction attributes.

The optimal band combination corresponding to the optimal model of the four types of separation is shown in Table 5. Then select from the optimal models of the four types of separation, and the model corresponding to S _I is the global optimal model. Compared with the results of Full PLS-DA based on the full-scan spectral region (400-2498nm), the optimal SDPC-PLS-DA model achieved significantly better prediction accuracy, and the attribute fluctuation value (RAR _SD ) also decreased significantly. The number of wavelengths it uses is 89, which is only 8.5% of the full-spectrum wavelengths, indicating that the model complexity is also greatly reduced. See Table 6 for the results.

Table 4 Parameters and prediction accuracy of the four-class separation priority combination model of adulterated milk powder discriminant analysis

Table 5 The optimal band combination of the four-class separation priority combination model for the discriminant analysis of adulterated milk powder

Table 6 Comparison of optimal SDPC-PLS-DA model and Full PLS-DA model for discriminant analysis of adulterated milk powder

The experiment also confirms that the wavelength combination screened out based on the spectral separation-based wavelength combination method of the present invention is much better than the prediction effect of the full spectrum, and the number of wavelengths is also significantly reduced. This method can form a naturally optimized piecewise continuous wavelength model, which cannot be realized by the continuous wavelength screening method, thereby broadening the wavelength screening method and application range, and is useful for establishing high-precision models, reducing model complexity and designing special spectrometers. Spectroscopic systems are of great significance.

Example 3

The identification of high-quality wine brands can avoid adulteration and fraud, and is of great significance to protecting the rights and interests of producers and consumers. This embodiment takes the visible-near-infrared spectrum discriminant analysis of wine brand identification as an example to clarify the applicability of the proposed spectral wavelength combination method based on spectral separation. By comparing the partial least squares discriminant analysis model (Full PLS-DA) based on the full spectrum, it is shown that the spectroscopic wavelength combination method based on the spectral separation degree proposed by the present invention is more suitable for the identification of wine brands. However, the embodiments of the present invention are not limited thereto.

The specific implementation steps are as follows:

S1. Sample collection and preparation

Several bottles of 4 different brands of wine (Great Wall, Chilean Aoyo, Dynasty and Changyu) were purchased from official channels, which are abbreviated as I, II, III, and IV in turn. The specific components and quantities of the target sample (negative) and interference sample (positive) were prepared as follows:

70 copies of negative samples: I, each 5mL;

210 positive samples: 70 each for II, III, and IV, each 5 mL.

S2. Spectrum collection and sample division

Collection uses XDS Rapid Content ^TM type near-infrared grating spectrometer (Denmark, FOSS), adopts 1mm quartz cuvette to collect the transmission spectrum of each sample three times (and calculates the average spectrum), and the spectral scanning range of the instrument is 400-2498nm , the wavelength point interval is 2nm, a total of 1050 wavelengths (n=1050).

Negative samples (70 copies) were randomly divided into the calibration set (40) and the prediction set (30), and each sample used three spectra, and the corresponding spectrum numbers were the calibration set (120) and the prediction set (90); the positive samples ( 210 copies) using only the average spectrum, II, III, and IV brand samples were randomly divided into the calibration set (40) and the prediction set (30), the total calibration set (120) and the prediction set (90); in summary, The calibration set (negative 120, positive 120, 240 in total) and prediction set (90 negative, 90 positive, 180 in total) were obtained; the mean and standard deviation of spectral absorbance of all negative and positive samples were calculated respectively.

S3-S4, with reference to S3-S4 in "Example 1", obtain the type I separation degree spectrum, type I relative separation degree spectrum, type II separation degree spectrum and type II relative separation degree spectrum of the negative and positive spectrum populations of each brand of wine Spectrum, as shown in Figure 8 and Figure 9.

S5-S8. Referring to the method of S5-S8 in "Example 1", respectively, optimize the wavelength model of the resolution priority combination (SDPC) based on the four types of resolution, and determine the respective optimal SDPC models, see Table 7. And calculate the 9 identification accuracy rates and standard deviations RAR _SD about positive, negative, calibration, and prediction attributes.

Taking the smallest total accuracy (RAR _Total ) and the smallest number of simultaneous wavelengths (N) as the standard, the optimal band combination corresponding to the optimal model of the four types of resolution is determined, as shown in Table 8. Then select from the optimal models of the four types of separation, and the models corresponding to S _II and R _II are the global optimal models. Compared with the results of Full PLS-DA based on the full-scan spectral region (400-2498nm), the overall accuracy of the optimal SDPC-PLS-DA model is 100% with that of the Full PLS-DA model, but the best The number of wavelengths used in the excellent SDPC-PLS-DA model is 14, which is only 1.3% of the full-spectrum wavelengths, indicating that the complexity of the model is greatly reduced. See Table 9 for the results.

Table 7 Parameters and prediction accuracy of the four-class separation priority combination model of wine brand discriminant analysis

Table 8 The optimal band combination of the four-class separation priority combination model of wine brand discriminant analysis

Table 9 Comparison of optimal SDPC-PLS-DA model and Full PLS-DA model for discriminant analysis of wine brands

The experiment proves that when the wavelength combination screened out based on the spectral separation-based spectral wavelength combination method of the present invention has the same prediction effect as the full spectrum, the number of wavelengths used for prediction is greatly reduced, and the model is greatly simplified. This method can form a naturally optimized piecewise continuous wavelength model, which cannot be realized by the continuous wavelength screening method, thereby broadening the wavelength screening method and application range, and is useful for establishing high-precision models, reducing model complexity and designing special spectrometers. Spectroscopic systems are of great significance.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (1)

1. A spectral wavelength combination method based on spectral separation is characterized by comprising the following steps:

s1, collecting samples: collecting two types of samples to be distinguished, which are called negative samples and positive samples for short respectively;

s2, spectrum collection: repeating the measuring of the spectrum of each sample a plurality of times;

s3, calculating the minimum value and the maximum value of the spectral absorbance of the whole negative and positive samples at each wavelength and recording the minimum value and the maximum value as the values

Calculating the average value and standard deviation of the spectral absorbance of the whole negative sample and the whole positive sample, and respectively recording the average value and the standard deviation as

S4, providing a type I separation degree spectrum, a type I relative separation degree spectrum, a type II separation degree spectrum and a type II relative separation degree spectrum of the two spectrum populations, and respectively definingDegree of separation of type I (S) _I (lambda)), degree of type I relative separation (R) _I (lambda)), type II separation degree (S) _II (lambda)) and type II relative separation degree (R) _II (λ)), as follows:

s5, sorting based on the separation degree, and regarding the type I separation degree S _I (λ): determining a required wavelength range, adopting a full scanning spectrum area, or adopting a specific wavelength range according to the spectral characteristics of an actual object, wherein the total number of wavelengths is n, and sorting the wavelengths from large to small according to a separation value as follows: lambda ₁ ，λ ₂ ，...，λ _n ；

S6, wavelength combination with preferential separation degree: based on the separation degree priority, n wavelength combinations are sequentially constructed as follows:

Ω _i ＝{λ ₁ ，λ ₂ ，...，λ _i }，i＝1，2，...，n；

s7, adopting the spectrum data of the two types of samples, dividing the spectrum data into a calibration sample set and a prediction sample set, and collecting the measured spectrum of the sample;

respectively establishing a partial least squares discriminant analysis (PLS-DA) model according to the data of the n wavelength combinations, and calculating 9 identification standards of the negative identification accuracy, the positive identification accuracy and the total identification accuracy of the relevant calibration sample set, the prediction sample set and the whole samplesThe accuracy was determined, and the standard deviation (RAR) of the above 9 recognition accuracies was calculated _SD ) (ii) a Total Recognition Accuracy (RAR) from the total population of samples _Total ) Determining the degree of separation S of type I _I (λ) an optimal wavelength model, called optimal SDPC model, with the following formula:

the corresponding optimal wavelength combination is:

Ω _N ＝{λ ₁ ，λ ₂ ，...，λ _N n is the number of wavelengths;

s8, similarly, based on the separation degrees R of other three types _I (λ)、S _II (λ)、R _II And (lambda) respectively obtaining respective optimal wavelength combinations, determining respective optimal SDPC models, finally determining a global optimal model from the optimal SDPC models with the four types of separation degrees, and correspondingly selecting the global optimal wavelength combinations.

Images