ZHAO Zhong, LI Bin，WU Yan-xian, YUAN Hong-fu

1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China 2. College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China

Abstract Edible oil is a necessity in daily life. The nutritional value and price of different types of edible oils on the market vary a lot. Because of the spurious activities in the market, it is necessary to establish effective detection methods to classify the quality of the edible oils in the market. Traditional edible oil classification methods are usually time-consuming and requiring complex pre-treatment in the lab. Molecular spectroscopy can elucidate the sample information of both compositions and properties at the molecular level, and molecular spectra analysis has the advantages of fast speed detection and non-destructive testing for edible oil classification. Molecular spectra analysis combined with the chemometrics is becoming a popular method for rapid classification of edible oil. SIMCA (Soft Independent Modeling of Class Analogy) is widely applied to molecular spectra analysis. However, the Euclidean distance is used in SIMCA to classify the extracted features with PCA and F test. Therefore it is difficult to classify the irregular feature spaces. When the molecular spectral differences among the different types of samples are tiny such as edible oils, it is usually difficult to identify them with the traditional SIMCA method. SVDD(Support Vector Domain Description)algorithm is a support domain method for solving the one-class classification problem. SVDD can get a hypersphere to include as many objective samples as possible by solving the convex quadratic programming problem. In this work, a method of molecular spectra analysis based on SIMCA-SVDD method for rapid classification of edible oils is proposed. In order to accomplish recognition of the different types of edible oils, the attenuated total reflectance infrared spectra of four types of edible oil are scanned on ATR-FTIR. SIMCA is applied to extract the classification features T2 and Q. Since the extracted edible oil classification features T2 and Q distribute irregularly, instead of classification with Euclidean distance in SIMCA, Support Vector Domain Description (SVDD) is applied in this work to classify the extracted features. Since SVDD can map the extracted classification features to high dimensional space by mapping functions, then an optimal classification hypersphere can be trained to classify the irregular distributing feature spaces by solving the convex quadratic programming problem. Comparative experiments to identify the same molecular spectra samples with the proposed SIMCA-SVDD method and the SIMCA method have also been done. Comparative experiment results have verified that the classification results with the proposed SIMCA-SVDD method are obviously better than that with SIMCA. The proposed SIMCA-SVDD method has provided a new way to classify the edible oil rapidly based on molecular spectra analysis.

Keywords Edible oil；Molecular spectrum；SIMCA；Euclidean distance；SVDD

Introduction

Edible oil is a necessity of daily life. There are many kinds of edible oil such as the peanut oil, rapeseed oil, soybean oil, corn oil, tea seed oil, sesame oil and olive oil in the market. The nutritional value and prices of different types of edible oils vary a lot according to their composition change. In order to avoid market fraud, it is necessary to establish an effective detection method to classify edible oils. There are some methods that have been reported to detect the quality of edible oil[1-2]. However, these detection methods are usually time-consuming and requiring complex pre-treatment. Spectral analysisbased detection methods[3-4]have been developed to analyze the edible oils with the advantages of fast speed and non-destructive testing.

SIMCA (Soft Independent Modeling of Class Analogy)[5]is the widely applied method to molecular spectra analysis and chemometrics. In SIMCA, PCA and F test are used to extractT2andQas the classification features. Then, Euclidean distance is used to classify the extracted features. The range defined by Euclidean distance, which is a circle in the plane ofT2vsQ, can not accurately classify the extracted features distributing in irregular feature spaces. Support Vector Domain Description (SVDD)[6]is a supervised machine learning method based on SVM theory. SVDD can map the nonlinear feature data to the high-dimensional space with different kernel functions. A closed and compact sphere can be optimized to classify the nonlinear feature data. Since SVDD can be optimized with the distribution of the classification data, it can be used to classify the irregular feature spaces[7-8]. In this work, a method of molecular spectra analysis based on SIMCA-SVDD method for rapid classification of edible oil is proposed. Comparative experiments to identify the same samples with the proposed SIMCA-SVDD method, and SIMCA have also been done. Comparative experiment results have verified that the classification results with the proposed SIMCA-SVDD method are obviously better than that with SIMCA.

1 Methods

1.1 SIMCA

SIMCA is a supervised pattern recognition method, PCA is applied to decompose sample matrix of each class as

(1)

(2)

whereEis residual matrix. The fraction of the total variation can be estimated as

Q=1-PRESS/SS

(3)

where PRESS is the sum of squares of the prediction errors and SS is the sum of squares of the residuals of the previous component. According to selectedAcomponents, the HotellingT2for observationiis calculated as

(4)

(5)

(6)

(7)

1.2 SIMCA-SVDD

s.t. ‖xi-a‖2≤R2+ξi,ξi≥0

(8)

whereCis the penalty coefficient andξiis a relaxation factor. According to Eq. (8), the Lagrangian function is defined as

(9)

whereαi(αi≥0) andγi(γi≥0) are Lagrangian multipliers. The class center of the sphereaand the radiusRcan be obtained by solving MaxMinL(R,a,ξi,αi,γi). According to Eq.(9), there are

(10)

(11)

(12)

Substituting Eq.(10), Eq.(11) and Eq.(12) into Eq.(9), there is

(13)

Use kernel function to replace the inner product in Eq.(13) and maximizeL, then

(14)

According to Eq.(14) and definedC,αcan be solved for every feature sample. The radiusRcan be calculated as

(15)

wherepis the support vector. For multi-classification, the relative distance is defined as

(16)

According to the minimumDiin Eq.(16), the feature samples are classified.

2 Experimental

2.1 Materials

54 edible oil samples are provided by the National Institute of Metrology (NIM) of China，which belong to four types of edible oil. 43 samples are chosen as the calibration set and the remaining 11 samples are chosen as the validation set with the Rank-KS method[9]. The number of calibration set and validation set for each types of samplesis shown in Table 1.

Table 1 Statistics of samples

2.2 Spectra measurement

The infrared spectra of the samples are scanned by Attenuated Totalinternal Reflectance Fourier Transform Infrared (Agilent 5500) spectrometer. The spectra are collected from 650 to 4 000 cm-1with a resolution 4 cm-1and with 32 scans. Each sample is scanned three times and the average is used for analysis. The spectra of all samples measured on ATR instrument are shown in Fig.1.

Fig.1 Original spectrum of four types of oil samples measured on ATR spectrometer

2.3 Software

All data have been analyzed with MATLAB 2017a (The Mathworks Inc.).

2.4 Preprocessing

Eliminate the side effects of surface scattering and the change of optical path on infrared diffuse reflection spectra, and spectral mean centeringis applied to the spectral data.

2.5 Evaluation of classification results

Correct classification rate (CCR) is applied to evaluate the qualitative recognition results[9].

3 Results and discussion

3.1 Feature extractionwith SIMCA

Fig.2 PRESS and Q-T2 distributions for the spectra samples

3.2 Classification results

Fig.3 Euclidean distance discrimination for blended oil samples

Fig.4 SVDD discrimination for blended oil samples

The comparative experiments for edible oil classification based on molecular analysis with SIMCA and proposed SIMCA-SVDD have been done. The classification results are shown in Table 2. According to Fig.2, it is noticed that the extracted edible oil features based on molecular spectra analysis with SIMCA are different. Then, the extracted features can be used for classification. But, the extracted features based on molecular spectra analysis with SIMCA are not always linear separable. The discrimination area for feature spaces with Euclidean distance in SIMCA is a circle, and then it is difficult to classify the irregular feature spaces such as the linear inseparable feature spaces. SVDD can map the linear inseparable feature data to a high-dimensional space with kernel tricks. Then, the minimum hypersphereis trained with SQP to include as many class samples as possible. According to the comparative experiments, the blended oil samples in the validation set can be recognized with SIMCA-SVDD accurately.

Table 2 Classification results of SIMCA and SIMCA-SVDD

For SIMCA, the decision plane is a circle, and its indicator is the radius in which Judging indicator is too single. After the features are extracted, the characteristic distribution rules of single oil can be distinguished within the regular area. However, for mixed oil, changes in its composition lead to irregularities in the decision plane. The SIMCA-SVDD method can change the irregular decision area by the parameters of the kernel function, so better classification results are achieved.

4 Conclusions

In this work, a method of edible oil classification based on molecular spectra analysis with SIMCA-SVDD is proposed. The IR spectra of four types of edible oil are scanned on ATR-FTIR. For a single oil sample, SIMCA and the proposed SIMCA-SVDD method can better classify the sample. However, due to changes in the composition of the mixed oil and changes in the content of the components, SIMCA does not distinguish well between the mixed oil and the single oil. SIMCA-SVDD!can correctly distinguish mixed oils in many samples. SIMCA is applied to extract the classification featuresT2andQ. Instead of classification with Euclidean distance in SIMCA, SVDD is applied in this work to classify the extracted linear inseparable features. The comparative experiment results have verified that the proposed method had a better classification of edible oils than the traditional SIMCA method. The proposed method has provided a new way to classify the edible oil rapidly based onmolecular spectra analysis.