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Determination of α-linolenic acid and linoleic acid in edible oils using near-infrared spectroscopy improved by wavelet transform and uninformative variable elimination
Analytica Chimica Acta 634 (2009) 166–171
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Analytica Chimica Acta journal homepage: www.elsevier.com/locate/aca
Determination of ␣-linolenic acid and linoleic acid in edible oils using near-infrared spectroscopy improved by wavelet transform and uninformative variable elimination Di Wu a,1 , Xiaojing Chen a,b,1 , Pinyan Shi a , Sihan Wang a , Fengqin Feng a,∗ , Yong He a,∗ a b
College of Biosystems Engineering and Food Science, Zhejiang University, 268 Kaixuan Road, Hangzhou 310029, China Department of Physics, Xiamen University, Xiamen 361005, China
a r t i c l e
i n f o
Article history: Received 15 October 2008 Received in revised form 4 December 2008 Accepted 10 December 2008 Available online 24 December 2008 Keywords: Near-infrared spectroscopy ␣-Linolenic acid and linoleic acid Edible oils Wavelet transform (WT) Uninformative variable elimination (UVE)
a b s t r a c t This paper proposes an analytical method for simultaneous near-infrared (NIR) spectrometric determination of ␣-linolenic and linoleic acid in eight types of edible vegetable oils and their blending. For this purpose, a combination of spectral wavelength selection by wavelet transform (WT) and elimination of uninformative variables (UVE) was proposed to obtain simple partial least square (PLS) models based on a small subset of wavelengths. WT was firstly utilized to compress full NIR spectra which contain 1413 redundant variables, and 42 wavelet approximate coefficients were obtained. UVE was then carried out to further select the informative variables. Finally, 27 and 19 wavelet approximate coefficients were selected by UVE for ␣-linolenic and linoleic acid, respectively. The selected variables were used as inputs of PLS model. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The coefficient of determination (r2 ) and root mean square error prediction set (RMSEP) for prediction set were 0.9345 and 0.0123 for ␣-linolenic acid prediction by WT-UVE-PLS model. The r2 and RMSEP were 0.9054, 0.0437 for linoleic acid prediction. The good performance showed a potential application using WT-UVE to select NIR effective variables. WT-UVE can both speed up the calculation and improve the predicted results. The results indicated that it was feasible to fast determine ␣-linolenic acid and linoleic acid content in edible oils using NIR spectroscopy. © 2008 Elsevier B.V. All rights reserved.
1. Introduction ␣-Linolenic acid, systematically named all-cis-9, 12, 15octadecatrienoic acid 18:3 (n−3), and linoleic acid, systematically named cis, cis-9, 12-octadecadienoic acid, 18:2 (n−6) are two kinds of essential fatty acids for human beings. The lack of ␣-linolenic acid and linoleic acid may cause lipid metabolic turbulence and forgettery, fatigue and immunity depression, especially will lead to cardiovascular diseases and cancer. The intellective development of infants will be greatly hindered if they could not have enough ␣-linolenic acid or linoleic acid. However, these two acids could not be synthesized in human body, and must be taken in from diet. Therefore, it is very important to know the contents of these two fatty acids in various edible oils.
∗ Corresponding authors. Tel.: +86 571 86971143; fax: +86 571 86971143. E-mail addresses: [email protected] (D. Wu), [email protected] (F. Feng), [email protected] (Y. He). 1 The first two authors contribute equally to this paper. 0003-2670/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2008.12.024
Usually, the contents of fatty acids are determined using GC or HPLC, but they are destructive, with high cost and could not satisfy the need for rapid analyzing of the fatty acids. Thus, a rapid online method to determine the content of ␣-linolenic acid and linoleic acid is badly needed. Nowadays, near-infrared (NIR) spectroscopy are widely employed as alternatives to wet chemistry procedures for qualitative and quantitative analysis in agriculture and food quality evaluation [1,2]. It is non-invasive, fast, and has a potential for the industrial online application. NIR spectroscopy can avoid the generation of harmful chemical residues because in most analyses no reagents or solvents are required. NIR spectrometers can be more easily deployed in industrial facilities without strict environmental control, compared with mid-infrared instruments [3]. In 1992, De Pedro et al. (1992) used NIR spectroscopy to predict the subcutaneous fat content of oleic, linoleic, palmitic and stearic acids in Iberian pork compared with those obtained by gas chromatography [4]. González-Martıˇın et al. used NIR spectroscopy to determine fatty acid composition in intramuscular fat of Iberian pork loin [5] and in the subcutaneous fat of Iberian breed swine [6]. The ability of Vis/NIR spectroscopy to accurately predict linolenic acid in animal products has been reported by other workers in the
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past [7,8]. Pla et al. predicted the fatty acid content in rabbit meat by NIR [9]. In their study, prediction of linoleic was excellent (r2 = 0.91) while prediction of a-linolenic FA (r2 = 0.59) needs more precision. In the study on quality evaluation of edible oils, Armenta et al. determined acidity and peroxide index in edible oils using NIR [10]. Costa Pereira et al. used NIR spectroscopy to determine acidity, refractive index and viscosity in four types of edible vegetable oils (corn, soya, canola and sunflower) [11]. However, few contributions can be found on the use of NIR for quantitative determination of essential fatty acids in edible oils. NIR spectrum comprises a complex overlapping of various combinations and overtones of fundamental vibrational transitions [3,12,13], which constitutes a significant challenge for multivariate calibration. However, with hundreds or thousands wavelengths as input variables and hundreds of samples, NIR spectral data are too complicated to be trained directly in the chemomtric models. The training procedure is time-consuming and not convenient to fulfill the high-speed features of spectroscopic techniques. Some wavelengths or wavelength bands in full spectral regions may contain useless or irrelevant information for calibration model like noise and background than relevant information to models, which can worsen the predictive ability of the whole model. The selection of variables would affect the quality of multivariate calibration models [14]. Better quantitative calibration model may be obtained by selecting characteristic information such as samplespecific or component-specific instead of the full-spectrum. The elimination of uninformation variables can predigest calibration modeling and improve prediction results in terms of accuracy and robustness. Characteristic wavelengths instead of full spectra as input variables for calibration model might obtain better quantitative results. In this work, a hybrid variable selection method, which combined wavelet transform (WT) and elimination of uninformative variables (UVE), was applied for NIR spectral variable selection. The aim of this study is the simultaneous evaluation of essential fatty acids in edible oils, such as ␣-Linolenic acid and linoleic acid, by means of a fast and clean methodology based on NIR spectrometry combined with chemometric analysis (spectral wavelengths selection by WT and elimination of uninformative variables, and content determination by partial least square (PLS)).
2. Materials and methods 2.1. Sample preparation and spectral measurement The edible oils which were used in the experiment included the grinding sesame oil (Haining Yufeng brewage Co. Ltd.), the benne oil (Henan Licheng ),the purified benne oil (Zhoushan vegetable oil Co. Ltd.), the purified olive oil (Fanyu Hexing oil Co. Ltd.), peanut oil (Shandong Luhua group Co. Ltd.), the camellia oil (Changshan Shanshen camellia oil Co. Ltd.), the soya oil (Shanghai Jiali industrial Co. Ltd.), the Hippophae rhamnoides L fruit oil and seed oil (Qinghai Kangpude biological product Co. Ltd.).There are one hundred and fifty-five samples which were prepared by mixing two (1:1) or three (1:1:1) different kinds of pure edible oils and the samples were all transparent homogeneous. The samples were randomly divided into two groups, seventy-eight of which were used to establish the model, and the remained seventy-seven were used for prediction. A FT-IR-4100 spectrometer (JASCO, Tokyo, Japan) was applied for the spectral scanning, and the resolution of the spectrometer was 4.0 cm−1 . Transmission mode was applied and only the nearinfrared spectroscopy region (1280–2500 nm) was used for further calibration analysis. The sample was dropped into the fixed liquid cell with a 1.0 mm light path length, and then the fixed liquid cell was placed in the sample holder, which was mounted in the sample compartment.
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2.2. GC analysis The fatty acid was analyzed by SP-GC (Shandong Ruihong chemical industrial instrument Co. Ltd.). The SP-GC system was equipped with a FID and a capillary column DB-23 (60 m × 0.250 mm × 0.25 m) bought from Agligent Corporation. The temperature of the injection port and detector were set at 320 ◦ C and 330 ◦ C, respectively. The oven temperature was programmed at 190 ◦ C for 15 min. All fatty acid ester in samples can be eluded out the column at this condition. The carrier gas was nitrogen and its flow rate was 50 mL min−1 . The data was collected and analyzed by chromatograph workstation N-2000 with dual pathways of intellect information engineering research center of Zhejiang University. The steps of sample preparation for GC analysis: saponification: 100 mg samples were weighed accurately, and were put in the flask of 50 mL, and then 4 mL internal standard C19:0 (1 mg mL−1 ), 4 mL NaOH in methanol (2%) and zeolite were added in sequence. The fixed flask was circum-flowed on the water bath (60 ◦ C) for 15 min until no oil drop were left. esterification: 5 mL boron trifluoridemethanol was added in the flask, continue to boil for 2 min, and then 3 mL Hexane was added and continue to boil for one more minute, stopped heating let the flask to cool down to room temperature. After taken down the flask, a little saturated sodium chloride solution was added with shaking, then continued to add saturated sodium chloride until the flask was full, taken 1 mL top clear solution into a test tube and removed the trace water by adding some Na2 SO4 removing sterol: The sep-pak filter column was washed by sherwood oil firstly, then the sample was loaded and filtered quickly, 2 mL sherwood oil was used to wash the sample test tube and transferred to the sep-pak column, and then about 3 mL 5% aether in sherwood oil was used to wash the column drop by drop and the filtrate was collected in a clean test tube. The sep-pak column was washed using 2 to 3 mL mixed solvent of chloroform and methanol (chloroform: methanol was 2:1) to remove the adsorbed sterol, and then washed several times by sherwood oil for next use. The filtrate in the clean test tube was dried by blowing with nitrogen gas, and then resolved with 0.1 mL N-hexane of chromatographic pure grade, 1 L sample was taken for GC analysis. C19:0 was used as internal standard. The quantity ratio of ␣linolenic acid and linoleic acid and C19:0 was based as X-axis, and the peak area ratio of ␣-linolenic acid and linoleic acid and C19:0 was based as Y-axis, respectively. The two standard curves were drawn .The content of ␣-linolenic acid and linoleic acid was determined by testing the peak area ratio of ␣-linolenic acid and linoleic acid and C19:0, respectively. Gas chromatogram of the mixture of sesame oil and soya oil (1:1) sample is shown as Fig. 1. The corresponding fatty acid of each peak
Fig. 1. Gas chromatogram of the mixture of sesame oil and soya oil (1:1) sample.
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Table 1 Statistical values of ␣-linolenic acid and linoleic acid content for both calibration and prediction set. Acid
Models
Sample no.
Range
Mean
Standard deviation
␣-Linolenic acid
Calibration Prediction All samples
78 77 155
0.000–0.276 0.000–0.275 0.000–0.276
0.033 0.034 0.033
0.044 0.044 0.044
Linoleic acid
Calibration Prediction All samples
78 77 155
0.058–0.702 0.055–0.716 0.055–0.716
0.373 0.371 0.372
0.140 0.141 0.140
was determined by comparing the graphs of the samples and of the standards (All fatty acid standards were purchased from Sigma Co. Ltd.). The peak positions of fatty acids and C19:0 (internal standard from Sigma Co. Ltd.) were shown in Fig. 1. It can be seen that all the fatty acids and the internal standard were separated completely and the peak form was good under the adopted chromatography conditions. Both the standard curves of ␣-linolenic acid and linoleic acid correlated predominantly. The correlation coefficient of the standard curves exceeds 0.99. Statistical values of ␣-linolenic acid and linoleic acid content for both calibration and prediction sets are shown in Table 1. The content value of ␣-linolenic acid and linoleic acid was the ratio of fatty acid to oil (w/w).
yˆ are computed by the equations: yˆ = Xb + e
where X is a n × p matrix containing p spectral responses of n samples, b(1,p) is the vector of PLS regression coefficients and e(n,1) is vector of errors that cannot be explained by the model. In UVE-PLS method, a PLS regression coefficient matrix b = [b1 ,. . .bp ] is calculated through a leave-one-out validation [17–19], then the reliability of each variable (wavelength) can be quantitatively measured by its stability, the stability of variable j can be calculated as: sj =
2.3. Theory of wavelet transform (WT) WT is a powerful tool to compress analytical data [15]. Raw data are transformed into the wavelet domain by WT, and the information contained in the raw data can be represented by the wavelet coefficients. Wavelet is defined as the dilation and translation of the basis function ϕ(t) i.e., 1 t− ϕa,b (t) = √ ϕ( ), a a
(a, b ∈ R, a = / 0)
(1)
where a and b are dilation and translation parameters, j respectively. If a and b are discretized with a = a0 and j
b = kb0 a0 ϕj,k (t) =
(j, k ∈ Z, a0 = / 0), respectively, Eq. (1) becomes:
−j/2 −j a0 ϕ(a0 t
− kb0 )
k∈Z
(3)
where cj,k is the approximate coefficient (low-frequency component) of the signal at the decomposition level of j and dj,k the detained coefficient (high-frequency component). The original signal c0,n can be reconstructed by these coefficients. The reconstruction formula is as follows: cj+1,k =
n
cj,n hk−2n +
(6)
std (ˇj )
where mean(ˇj ) and std(ˇj ) are the mean and standard deviation of the regression coefficients of variable j. To determine the uninformative variables, an artificial random variable matrix, with a range of approximately 10−10 (noise level), is appended to the dataset, and their C values, which is stability of random noise matrix, are
computed. If cjdataset < max(cjrandom ) the jth experimental vari-
able is considered to be uninformative, and is eliminated from the experimental dataset. There are some variants of UVE, like ␣-UVE. The cutoff threshold is generally defined by: cutoff = ˛ × max(abs(cjrandom ))
(2)
n∈Z
mean (ˇj )
where ˛ is 0.7 in this study.
The wavelet defined by Eq. (2) is called discrete wavelet (Dwavelet transform), where a0 = 2 and b0 = 1 are generally used. Mallat [16] proposed an efficient algorithm to perform Dwavelet transform by assuming the discrete signal fn = c0,n , where n is the signal number. The Mallat algorithm is as follows.
⎧ cj,k = cj+1,n h, ⎪ ⎨ n ∈Z ⎪ dj+1,n g , ⎩ dj,k =
(5)
dj,n gk−2n
k∈Z
(4)
n
2.4. Uninformative variable elimination by partial least squares In PLS model, there are some of the variables that can be noisy and/or do not contain information relevant for modeling Y. Eliminating these variables from the explanatory part of data can improve the model. In linear least squares models, the predictions
2.5. Calibration model and prediction evaluation PLS analysis is a widely utilized for multivariate regression method in spectroscopic analysis [20]. PLS considers simultaneously the spectral data matrix (X) and the target chemical properties matrix (Y). PLS uses the chemical concentration information during the decomposition process, this causes spectra containing higher constituent concentrations to be weighted more heavily than those with low concentrations [21]. To prevent overfitting problems, full cross-validation was used to determine the optimal number of latent variables (LVs) by root-mean-square error of cross-validation (RMSECV), which is defined as:
RMSECV =
1 o p (ci − ci )2 n n
1/2 (7)
i=1
where, cio is the reference value of sample I in the calibration set, p ci is the concentration predicted by the model, and n is the size of the calibration set. In this study, PLS was used to establish calibration model. Different inputs, namely, variables selected by WT-UVE and only compressed wavelet coefficients, and the full spectral variables, were inputted into PLS. The performances of different established PLS models were compared by coefficient of determination (r2 ) and root mean square error of prediction (RMSEP). Generally, a good model should have higher r2 and lower RMSEP values.
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Fig. 2. Near-infrared transmission spectra (1282–2500 cm−1 ) of typical edible oil sample.
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Fig. 3. Wavelet approximate coefficients by Db1 at scale 5.
3. Results and discussion 3.1. Transmission spectra of edible oils The original spectra transmission spectra of typical edible oil sample at NIR region are shown in Fig. 2. Peaks at 1726 and 1765 nm were assigned to 2 × C–H stretching vibration of CH2 . Weak peaks at 2140 and 2190 nm were assigned to =C–H stretching + C=C stretching of HC=CH. Peak at 2310 nm was assigned to C–H stretching +C–H deformation of CH2 . Peak at 2347 nm was assigned to CH2 symmetric stretching + =CH2 deformation of HC=CHCH2 . Weak peak at 2380 nm was assigned to 3 × O–H deformation vibration of ROH. However, we did not know which peaks were related to ␣-linolenic or linoleic acid and which peaks attribute to prediction model. Moreover, when there were many samples, their spectral curves were overlapped. Their absorbed peaks were hard to be identified and analyzed. It was important to perform feature selection in multivariable analysis. 3.2. Full-spectrum PLS models PLS models were developed to determine ␣-linolenic and linoleic acid content in edible oils. Full-spectra in NIR were inputted into PLS model. Twenty LVs were calculated and variously used in the different PLS models. The best LV numbers were eight and nine for ␣-linolenic and linoleic acid, respectively. The prediction results for prediction set generated by the PLS models based on fullspectra are shown in Table 2. The r2 and RMSEP for prediction set were 0.8748 and 0.0337 for ␣-linolenic prediction, and 0.8336 and 0.0576 for linoleic prediction. Thus, good ␣-linolenic and linoleic acid content determination performance was achieved by NIR spectra. Although it was hard to determine ␣-linolenic and linoleic acid content from spectra by naked eyes, the PLS can extract useful information from NIR spectra to establish the calibration model and did a good prediction of ␣-linolenic and linoleic acid content in edible oils.
Fig. 4. Stability distributions of 42 wavelet approximate coefficients for ␣-linolenic (a) and linoleic (b) acid. The two red lines indicated the lower and upper cutoff.
However, there are 1314 variables in the full NIR spectra, thousands of variables caused the PLS process complex and timeconsuming. The training time using PLS increased with the square of the number of training samples and linearly with the number
Table 2 Results of prediction set for ␣-linolenic and linoleic acid content determination in edible oils by PLS models. Acid
Variable selection method
Variable numbers
PCs
Coefficient of determination
RESEP
␣-Linolenic
None WT WT-UVE
1314 42 27
8 12 15
0.8748 0.9124 0.9345
0.0337 0.0134 0.0123
Linoleic
None WT WT-UVE
1314 42 19
9 12 15
0.8336 0.8737 0.9054
0.0576 0.0506 0.0437
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3.4. Further variable selection by UVE UVE was further conducted to improve prediction results and eliminate the uninformative variables. In the process of UVE, the useful variables in the compressed wavelet coefficients selected by UVE are used by the PLS model. Fig. 4 shows the stability corresponding to each compressed wavelet coefficient for ␣-linolenic and linoleic acid by UVE, respectively. Two horizontal lines show the lower and upper cutoff determined with ˛ = 0.7. The coefficients whose stability is within the cutoff lines will be treated as uninformative and be eliminated, and those which lie out of cutoff lines were retained as informative information. Finally, 19 and 27 coefficients were retained for ␣-linolenic and linoleic acid, respectively. To evaluate the effect of the selection WT-UVE, the spectra reconstructed from the retained 19 and 27 wavelet coefficients of ␣linolenic and linoleic acid are shown in Fig. 5. The red curve shows the original spectrum of sample (one of the calibration data set for comparison). Because the Db1 (Haar wavelet function) was used, compared with the original spectra, the reconstructed spectrum was like a bar-plot, where the bar region represent the wavelength selected by WT-UVE, but the flat regions whose ordinate values is zero represent the unselected wavelengths which might no contribution to calibration model, and the retained wavelengths might attribute a spectra region to a specific chemical structure. In Fig. 5, the retained coefficients of ␣-linolenic and linoleic acid were similar. This is because the molecular structures of ␣-linolenic and linoleic acid are similar. Although it is difficult to attribute a spectral region to a specific chemical structure, it can be found that there are some differences among the retained regions of the
Fig. 5. Reconstructed spectra with the retained coefficients of ␣-linolenic (a) and linoleic (b) acid after WT-UVE variable eliminate. The original spectrum of sample one of the calibration data set for comparison.
of variables (dimension of spectra) [22]. Thus we proposed WT to firstly compress spectral data. 3.3. Wavelet transform analysis WT has been proved to be a highly efficient technology for data compression. After being processed by WT, the useful information is mainly concentrated on low frequency regions (the larger scale) [15,23]. There are several parameters that will affect on efficiency of WT, such as wavelet filter, decomposition scale and compression ratio. However, a systematic comparison of the performance of WT using different parameters is beyond the scope of our work. So, the simplest “db1” or Haar wavelet filter and decomposition scale 5 were adopted in further calculation. The 42 compressed wavelet approximate coefficients are shown in Fig. 3, compared with Fig. 2, the contour of compressed spectra was similar to the original spectra, and most of noise was eliminated. The obtained 42 wavelet coefficients were inputted into PLS. When LV number was 12 and 12, best ␣-linolenic and linoleic acid results were obtained, respectively. The results for prediction set generated by the PLS models based on wavelet coefficients are shown in Table 2. The r2 and RMSEP for prediction set were 0.9124 and 0.0134 for ␣-linolenic prediction, and 0.8737 and 0.0506 for linoleic prediction. The prediction results for both ␣-linolenic and linoleic acid were improved by WT, compared with results predicted based on full-spectrum. Moreover, the numbers of input variables were reduced from 1314 to 42 and PLS calibration model was simplified by WT.
Fig. 6. Relationship of predicted vs reference values of ␣-linolenic (a) and linoleic (b) acid in edible oils based on 19 and 27 wavelet approximate coefficients obtained by the WT-UVE-PLS model.
D. Wu et al. / Analytica Chimica Acta 634 (2009) 166–171
reconstructed spectra. The result shows that it is very important to perform variable selection in multivariable analysis by using the NIR spectrum. The retained coefficients were employed as inputs for PLS model. The performance of WT-UVE-PLS model was evaluated by the 77 unknown samples in the prediction set. The best calibration models of WT-UVE-PLS for ␣-linolenic and linoleic acid were obtained based on 15 and 15 LVs, respectively. Table 2 shows the prediction results of WT-UVE-PLS model. The predicted vs reference values of ␣-linolenic (a) and linoleic (b) acid in edible oils based on 19 and 27 wavelet approximate coefficients are shown in Fig. 6. In the figure, the solid line is the regression line corresponding to the ideal, unity correlation between the predicted and reference values. The results indicated a satisfying performance of using NIR spectroscopy and WT-UVE-PLS model to determine ␣-linolenic and linoleic acid in edible oils. For comparison, the results predicted by the conventional PLS model with full spectra data, PLS model with compressed wavelet coefficients (WT-PLS) and the WT-UVE-PLS model are shown in Table 2. Compared with the conventional PLS model with full spectra data, WT-PLS model not only speed up the calculation, but also improve prediction precision. Furthermore, after the compressed wavelet coefficients were processed by UVE, only 27 and 19 variables were detained for ␣-linolenic and linoleic acid, respectively. The predicted result was further improved by UVE. This is easily comprehended, because the information which was no contribution to calibration model in compressed wavelet coefficients was eliminated. All results demonstrated that WT-UVE method could obtain more parsimonious and efficient model to determine ␣linolenic and linoleic acid in edible oils. 4. Conclusion NIR spectroscopy technique was evaluated to determine ␣linolenic and linoleic acid in edible oils. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The good performance showed a potential application using WTUVE to select NIR effective variables. The overall results indicate that NIR spectroscopy combined with PLS could be applied as a
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precision and rapid method to determine ␣-linolenic and linoleic acid in edible oils. The results might be useful for the process and online monitoring of essential fatty acids in edible oils. Acknowledgements This study was supported by National Science and Technology Support Program (2006BAD10A0403, 2006BAD05A02) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, and the Natural Science Foundation of China (P.R.C.) (Project No. 30671213). References [1] B.M. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K.I. Theron, J. Lammertyn. Postharvest Biol. Technol. 46 (2007) 99. [2] H. Cen, Y. He, Trends Food Sci. Technol. 18 (2007) 72. [3] C. Pasquini, J. Braz. Chem. Soc. 14 (2003) 198. [4] E. De Pedro, A. Garrido, I. Bares, M. Casillas, I. Murria, Application of near infrared spectroscopy for quality control of Iberian pork industry, in: K.I. Hildrum, et al. (Eds.), Near infrared spectroscopy: bridging the gap between data analysis and NIR applications, Ellis Horwood, Chichester, UK, 1992, p. 145. [5] I. González-Martıˇın, C. González-Pérez, N. Alvarez-Garcıˇıa, J.M. GonzálezCabrera, Meat Sci. 69 (2005) 243. [6] I. González-Martıˇın, C. González-Pérez, J. Hernández-Méndez, N. AlvarezGarcía, Meat Sci. 65 (2003) 713. [7] A. Dalle Zotte, P. Berzaghi, L.M. Jansson, I. Andrighetto, Anim. Feed Sci. Technol. 128 (2006) 108. [8] C.E. Realini, S.K. Duckett, W.R. Windham, Meat Sci. 68 (2004) 35. ˜ J.A. Ramírez, Isabel Díaz, Food Chem. 100 (2007) [9] M. Pla, P. Hernández, B. Arino, 165. [10] S. Armenta, S. Garrigues, M. de la Guardia, Anal. Chim. Acta 596 (2007) 330. [11] A.F. Costa Pereira, M.J. Coelho Pontes, F.F. Gambarra Neto, S.R. Bezerra Santos, R.K. Harrop Galvao, M.C. Ugulino Arau jo, Food Res. Int. 41 (2008) 341. [12] L.J. Bokobza, Near Infrared Spectrosc. 6 (1998) 3. [13] J.J. Workman Jr, Appl. Spectrosc. Rev. 31 (1996) 251. [14] W.S. Cai, Y.K. Li, X.G. Shao, Chemometrics Intell. Lab. Syst. 90 (2008) 188. [15] A.K.M. Leung, F.T. Chau, J.B. Gao, T.M. Shih, Chemometrics Intell. Lab. Syst. 43 (1998) 69. [16] S.G. Mallat, IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989) 674. [17] V. Center, D.L. Massart, O.E. de Noord, S. de Jong, B.M. Vandeginste, C. Sterna, Anal. Chem. 68 (1996) 3851. [18] S.F. Ye, D. Wang, S.G. Min, Chemometrics Intell. Lab. Syst. 91 (2008) 194. [19] Q.J. Han, H.L. Wu, C.B. Cai, L. Xu, R.Q. Yu, Anal. Chim. Acta 612 (2008) 121. [20] I.E. Frank, J.H. Kalivas, B.R. Kowalski, Anal. Chem. 55 (1983) 1800. [21] T. Naes, T. Isaksson, T. Fearn, T. Davies, Multivariate calibration and classification, NIR Publications, Chichester, UK, 2002. [22] F. Chauchard, R. Cogdill, S. Roussel, J.M. Rogera, V. Bellon-Maurel, Chemom. Intell. Lab. Syst. 71 (2004) 141. [23] X.G. Shao, A.K.M. Leung, F.T. Chau, Accounts Chem. Res. 36 (2003) 276.
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Analytica Chimica Acta journal homepage: www.elsevier.com/locate/aca
Determination of ␣-linolenic acid and linoleic acid in edible oils using near-infrared spectroscopy improved by wavelet transform and uninformative variable elimination Di Wu a,1 , Xiaojing Chen a,b,1 , Pinyan Shi a , Sihan Wang a , Fengqin Feng a,∗ , Yong He a,∗ a b
College of Biosystems Engineering and Food Science, Zhejiang University, 268 Kaixuan Road, Hangzhou 310029, China Department of Physics, Xiamen University, Xiamen 361005, China
a r t i c l e
i n f o
Article history: Received 15 October 2008 Received in revised form 4 December 2008 Accepted 10 December 2008 Available online 24 December 2008 Keywords: Near-infrared spectroscopy ␣-Linolenic acid and linoleic acid Edible oils Wavelet transform (WT) Uninformative variable elimination (UVE)
a b s t r a c t This paper proposes an analytical method for simultaneous near-infrared (NIR) spectrometric determination of ␣-linolenic and linoleic acid in eight types of edible vegetable oils and their blending. For this purpose, a combination of spectral wavelength selection by wavelet transform (WT) and elimination of uninformative variables (UVE) was proposed to obtain simple partial least square (PLS) models based on a small subset of wavelengths. WT was firstly utilized to compress full NIR spectra which contain 1413 redundant variables, and 42 wavelet approximate coefficients were obtained. UVE was then carried out to further select the informative variables. Finally, 27 and 19 wavelet approximate coefficients were selected by UVE for ␣-linolenic and linoleic acid, respectively. The selected variables were used as inputs of PLS model. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The coefficient of determination (r2 ) and root mean square error prediction set (RMSEP) for prediction set were 0.9345 and 0.0123 for ␣-linolenic acid prediction by WT-UVE-PLS model. The r2 and RMSEP were 0.9054, 0.0437 for linoleic acid prediction. The good performance showed a potential application using WT-UVE to select NIR effective variables. WT-UVE can both speed up the calculation and improve the predicted results. The results indicated that it was feasible to fast determine ␣-linolenic acid and linoleic acid content in edible oils using NIR spectroscopy. © 2008 Elsevier B.V. All rights reserved.
1. Introduction ␣-Linolenic acid, systematically named all-cis-9, 12, 15octadecatrienoic acid 18:3 (n−3), and linoleic acid, systematically named cis, cis-9, 12-octadecadienoic acid, 18:2 (n−6) are two kinds of essential fatty acids for human beings. The lack of ␣-linolenic acid and linoleic acid may cause lipid metabolic turbulence and forgettery, fatigue and immunity depression, especially will lead to cardiovascular diseases and cancer. The intellective development of infants will be greatly hindered if they could not have enough ␣-linolenic acid or linoleic acid. However, these two acids could not be synthesized in human body, and must be taken in from diet. Therefore, it is very important to know the contents of these two fatty acids in various edible oils.
∗ Corresponding authors. Tel.: +86 571 86971143; fax: +86 571 86971143. E-mail addresses: [email protected] (D. Wu), [email protected] (F. Feng), [email protected] (Y. He). 1 The first two authors contribute equally to this paper. 0003-2670/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2008.12.024
Usually, the contents of fatty acids are determined using GC or HPLC, but they are destructive, with high cost and could not satisfy the need for rapid analyzing of the fatty acids. Thus, a rapid online method to determine the content of ␣-linolenic acid and linoleic acid is badly needed. Nowadays, near-infrared (NIR) spectroscopy are widely employed as alternatives to wet chemistry procedures for qualitative and quantitative analysis in agriculture and food quality evaluation [1,2]. It is non-invasive, fast, and has a potential for the industrial online application. NIR spectroscopy can avoid the generation of harmful chemical residues because in most analyses no reagents or solvents are required. NIR spectrometers can be more easily deployed in industrial facilities without strict environmental control, compared with mid-infrared instruments [3]. In 1992, De Pedro et al. (1992) used NIR spectroscopy to predict the subcutaneous fat content of oleic, linoleic, palmitic and stearic acids in Iberian pork compared with those obtained by gas chromatography [4]. González-Martıˇın et al. used NIR spectroscopy to determine fatty acid composition in intramuscular fat of Iberian pork loin [5] and in the subcutaneous fat of Iberian breed swine [6]. The ability of Vis/NIR spectroscopy to accurately predict linolenic acid in animal products has been reported by other workers in the
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past [7,8]. Pla et al. predicted the fatty acid content in rabbit meat by NIR [9]. In their study, prediction of linoleic was excellent (r2 = 0.91) while prediction of a-linolenic FA (r2 = 0.59) needs more precision. In the study on quality evaluation of edible oils, Armenta et al. determined acidity and peroxide index in edible oils using NIR [10]. Costa Pereira et al. used NIR spectroscopy to determine acidity, refractive index and viscosity in four types of edible vegetable oils (corn, soya, canola and sunflower) [11]. However, few contributions can be found on the use of NIR for quantitative determination of essential fatty acids in edible oils. NIR spectrum comprises a complex overlapping of various combinations and overtones of fundamental vibrational transitions [3,12,13], which constitutes a significant challenge for multivariate calibration. However, with hundreds or thousands wavelengths as input variables and hundreds of samples, NIR spectral data are too complicated to be trained directly in the chemomtric models. The training procedure is time-consuming and not convenient to fulfill the high-speed features of spectroscopic techniques. Some wavelengths or wavelength bands in full spectral regions may contain useless or irrelevant information for calibration model like noise and background than relevant information to models, which can worsen the predictive ability of the whole model. The selection of variables would affect the quality of multivariate calibration models [14]. Better quantitative calibration model may be obtained by selecting characteristic information such as samplespecific or component-specific instead of the full-spectrum. The elimination of uninformation variables can predigest calibration modeling and improve prediction results in terms of accuracy and robustness. Characteristic wavelengths instead of full spectra as input variables for calibration model might obtain better quantitative results. In this work, a hybrid variable selection method, which combined wavelet transform (WT) and elimination of uninformative variables (UVE), was applied for NIR spectral variable selection. The aim of this study is the simultaneous evaluation of essential fatty acids in edible oils, such as ␣-Linolenic acid and linoleic acid, by means of a fast and clean methodology based on NIR spectrometry combined with chemometric analysis (spectral wavelengths selection by WT and elimination of uninformative variables, and content determination by partial least square (PLS)).
2. Materials and methods 2.1. Sample preparation and spectral measurement The edible oils which were used in the experiment included the grinding sesame oil (Haining Yufeng brewage Co. Ltd.), the benne oil (Henan Licheng ),the purified benne oil (Zhoushan vegetable oil Co. Ltd.), the purified olive oil (Fanyu Hexing oil Co. Ltd.), peanut oil (Shandong Luhua group Co. Ltd.), the camellia oil (Changshan Shanshen camellia oil Co. Ltd.), the soya oil (Shanghai Jiali industrial Co. Ltd.), the Hippophae rhamnoides L fruit oil and seed oil (Qinghai Kangpude biological product Co. Ltd.).There are one hundred and fifty-five samples which were prepared by mixing two (1:1) or three (1:1:1) different kinds of pure edible oils and the samples were all transparent homogeneous. The samples were randomly divided into two groups, seventy-eight of which were used to establish the model, and the remained seventy-seven were used for prediction. A FT-IR-4100 spectrometer (JASCO, Tokyo, Japan) was applied for the spectral scanning, and the resolution of the spectrometer was 4.0 cm−1 . Transmission mode was applied and only the nearinfrared spectroscopy region (1280–2500 nm) was used for further calibration analysis. The sample was dropped into the fixed liquid cell with a 1.0 mm light path length, and then the fixed liquid cell was placed in the sample holder, which was mounted in the sample compartment.
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2.2. GC analysis The fatty acid was analyzed by SP-GC (Shandong Ruihong chemical industrial instrument Co. Ltd.). The SP-GC system was equipped with a FID and a capillary column DB-23 (60 m × 0.250 mm × 0.25 m) bought from Agligent Corporation. The temperature of the injection port and detector were set at 320 ◦ C and 330 ◦ C, respectively. The oven temperature was programmed at 190 ◦ C for 15 min. All fatty acid ester in samples can be eluded out the column at this condition. The carrier gas was nitrogen and its flow rate was 50 mL min−1 . The data was collected and analyzed by chromatograph workstation N-2000 with dual pathways of intellect information engineering research center of Zhejiang University. The steps of sample preparation for GC analysis: saponification: 100 mg samples were weighed accurately, and were put in the flask of 50 mL, and then 4 mL internal standard C19:0 (1 mg mL−1 ), 4 mL NaOH in methanol (2%) and zeolite were added in sequence. The fixed flask was circum-flowed on the water bath (60 ◦ C) for 15 min until no oil drop were left. esterification: 5 mL boron trifluoridemethanol was added in the flask, continue to boil for 2 min, and then 3 mL Hexane was added and continue to boil for one more minute, stopped heating let the flask to cool down to room temperature. After taken down the flask, a little saturated sodium chloride solution was added with shaking, then continued to add saturated sodium chloride until the flask was full, taken 1 mL top clear solution into a test tube and removed the trace water by adding some Na2 SO4 removing sterol: The sep-pak filter column was washed by sherwood oil firstly, then the sample was loaded and filtered quickly, 2 mL sherwood oil was used to wash the sample test tube and transferred to the sep-pak column, and then about 3 mL 5% aether in sherwood oil was used to wash the column drop by drop and the filtrate was collected in a clean test tube. The sep-pak column was washed using 2 to 3 mL mixed solvent of chloroform and methanol (chloroform: methanol was 2:1) to remove the adsorbed sterol, and then washed several times by sherwood oil for next use. The filtrate in the clean test tube was dried by blowing with nitrogen gas, and then resolved with 0.1 mL N-hexane of chromatographic pure grade, 1 L sample was taken for GC analysis. C19:0 was used as internal standard. The quantity ratio of ␣linolenic acid and linoleic acid and C19:0 was based as X-axis, and the peak area ratio of ␣-linolenic acid and linoleic acid and C19:0 was based as Y-axis, respectively. The two standard curves were drawn .The content of ␣-linolenic acid and linoleic acid was determined by testing the peak area ratio of ␣-linolenic acid and linoleic acid and C19:0, respectively. Gas chromatogram of the mixture of sesame oil and soya oil (1:1) sample is shown as Fig. 1. The corresponding fatty acid of each peak
Fig. 1. Gas chromatogram of the mixture of sesame oil and soya oil (1:1) sample.
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Table 1 Statistical values of ␣-linolenic acid and linoleic acid content for both calibration and prediction set. Acid
Models
Sample no.
Range
Mean
Standard deviation
␣-Linolenic acid
Calibration Prediction All samples
78 77 155
0.000–0.276 0.000–0.275 0.000–0.276
0.033 0.034 0.033
0.044 0.044 0.044
Linoleic acid
Calibration Prediction All samples
78 77 155
0.058–0.702 0.055–0.716 0.055–0.716
0.373 0.371 0.372
0.140 0.141 0.140
was determined by comparing the graphs of the samples and of the standards (All fatty acid standards were purchased from Sigma Co. Ltd.). The peak positions of fatty acids and C19:0 (internal standard from Sigma Co. Ltd.) were shown in Fig. 1. It can be seen that all the fatty acids and the internal standard were separated completely and the peak form was good under the adopted chromatography conditions. Both the standard curves of ␣-linolenic acid and linoleic acid correlated predominantly. The correlation coefficient of the standard curves exceeds 0.99. Statistical values of ␣-linolenic acid and linoleic acid content for both calibration and prediction sets are shown in Table 1. The content value of ␣-linolenic acid and linoleic acid was the ratio of fatty acid to oil (w/w).
yˆ are computed by the equations: yˆ = Xb + e
where X is a n × p matrix containing p spectral responses of n samples, b(1,p) is the vector of PLS regression coefficients and e(n,1) is vector of errors that cannot be explained by the model. In UVE-PLS method, a PLS regression coefficient matrix b = [b1 ,. . .bp ] is calculated through a leave-one-out validation [17–19], then the reliability of each variable (wavelength) can be quantitatively measured by its stability, the stability of variable j can be calculated as: sj =
2.3. Theory of wavelet transform (WT) WT is a powerful tool to compress analytical data [15]. Raw data are transformed into the wavelet domain by WT, and the information contained in the raw data can be represented by the wavelet coefficients. Wavelet is defined as the dilation and translation of the basis function ϕ(t) i.e., 1 t− ϕa,b (t) = √ ϕ( ), a a
(a, b ∈ R, a = / 0)
(1)
where a and b are dilation and translation parameters, j respectively. If a and b are discretized with a = a0 and j
b = kb0 a0 ϕj,k (t) =
(j, k ∈ Z, a0 = / 0), respectively, Eq. (1) becomes:
−j/2 −j a0 ϕ(a0 t
− kb0 )
k∈Z
(3)
where cj,k is the approximate coefficient (low-frequency component) of the signal at the decomposition level of j and dj,k the detained coefficient (high-frequency component). The original signal c0,n can be reconstructed by these coefficients. The reconstruction formula is as follows: cj+1,k =
n
cj,n hk−2n +
(6)
std (ˇj )
where mean(ˇj ) and std(ˇj ) are the mean and standard deviation of the regression coefficients of variable j. To determine the uninformative variables, an artificial random variable matrix, with a range of approximately 10−10 (noise level), is appended to the dataset, and their C values, which is stability of random noise matrix, are
computed. If cjdataset < max(cjrandom ) the jth experimental vari-
able is considered to be uninformative, and is eliminated from the experimental dataset. There are some variants of UVE, like ␣-UVE. The cutoff threshold is generally defined by: cutoff = ˛ × max(abs(cjrandom ))
(2)
n∈Z
mean (ˇj )
where ˛ is 0.7 in this study.
The wavelet defined by Eq. (2) is called discrete wavelet (Dwavelet transform), where a0 = 2 and b0 = 1 are generally used. Mallat [16] proposed an efficient algorithm to perform Dwavelet transform by assuming the discrete signal fn = c0,n , where n is the signal number. The Mallat algorithm is as follows.
⎧ cj,k = cj+1,n h, ⎪ ⎨ n ∈Z ⎪ dj+1,n g , ⎩ dj,k =
(5)
dj,n gk−2n
k∈Z
(4)
n
2.4. Uninformative variable elimination by partial least squares In PLS model, there are some of the variables that can be noisy and/or do not contain information relevant for modeling Y. Eliminating these variables from the explanatory part of data can improve the model. In linear least squares models, the predictions
2.5. Calibration model and prediction evaluation PLS analysis is a widely utilized for multivariate regression method in spectroscopic analysis [20]. PLS considers simultaneously the spectral data matrix (X) and the target chemical properties matrix (Y). PLS uses the chemical concentration information during the decomposition process, this causes spectra containing higher constituent concentrations to be weighted more heavily than those with low concentrations [21]. To prevent overfitting problems, full cross-validation was used to determine the optimal number of latent variables (LVs) by root-mean-square error of cross-validation (RMSECV), which is defined as:
RMSECV =
1 o p (ci − ci )2 n n
1/2 (7)
i=1
where, cio is the reference value of sample I in the calibration set, p ci is the concentration predicted by the model, and n is the size of the calibration set. In this study, PLS was used to establish calibration model. Different inputs, namely, variables selected by WT-UVE and only compressed wavelet coefficients, and the full spectral variables, were inputted into PLS. The performances of different established PLS models were compared by coefficient of determination (r2 ) and root mean square error of prediction (RMSEP). Generally, a good model should have higher r2 and lower RMSEP values.
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Fig. 2. Near-infrared transmission spectra (1282–2500 cm−1 ) of typical edible oil sample.
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Fig. 3. Wavelet approximate coefficients by Db1 at scale 5.
3. Results and discussion 3.1. Transmission spectra of edible oils The original spectra transmission spectra of typical edible oil sample at NIR region are shown in Fig. 2. Peaks at 1726 and 1765 nm were assigned to 2 × C–H stretching vibration of CH2 . Weak peaks at 2140 and 2190 nm were assigned to =C–H stretching + C=C stretching of HC=CH. Peak at 2310 nm was assigned to C–H stretching +C–H deformation of CH2 . Peak at 2347 nm was assigned to CH2 symmetric stretching + =CH2 deformation of HC=CHCH2 . Weak peak at 2380 nm was assigned to 3 × O–H deformation vibration of ROH. However, we did not know which peaks were related to ␣-linolenic or linoleic acid and which peaks attribute to prediction model. Moreover, when there were many samples, their spectral curves were overlapped. Their absorbed peaks were hard to be identified and analyzed. It was important to perform feature selection in multivariable analysis. 3.2. Full-spectrum PLS models PLS models were developed to determine ␣-linolenic and linoleic acid content in edible oils. Full-spectra in NIR were inputted into PLS model. Twenty LVs were calculated and variously used in the different PLS models. The best LV numbers were eight and nine for ␣-linolenic and linoleic acid, respectively. The prediction results for prediction set generated by the PLS models based on fullspectra are shown in Table 2. The r2 and RMSEP for prediction set were 0.8748 and 0.0337 for ␣-linolenic prediction, and 0.8336 and 0.0576 for linoleic prediction. Thus, good ␣-linolenic and linoleic acid content determination performance was achieved by NIR spectra. Although it was hard to determine ␣-linolenic and linoleic acid content from spectra by naked eyes, the PLS can extract useful information from NIR spectra to establish the calibration model and did a good prediction of ␣-linolenic and linoleic acid content in edible oils.
Fig. 4. Stability distributions of 42 wavelet approximate coefficients for ␣-linolenic (a) and linoleic (b) acid. The two red lines indicated the lower and upper cutoff.
However, there are 1314 variables in the full NIR spectra, thousands of variables caused the PLS process complex and timeconsuming. The training time using PLS increased with the square of the number of training samples and linearly with the number
Table 2 Results of prediction set for ␣-linolenic and linoleic acid content determination in edible oils by PLS models. Acid
Variable selection method
Variable numbers
PCs
Coefficient of determination
RESEP
␣-Linolenic
None WT WT-UVE
1314 42 27
8 12 15
0.8748 0.9124 0.9345
0.0337 0.0134 0.0123
Linoleic
None WT WT-UVE
1314 42 19
9 12 15
0.8336 0.8737 0.9054
0.0576 0.0506 0.0437
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3.4. Further variable selection by UVE UVE was further conducted to improve prediction results and eliminate the uninformative variables. In the process of UVE, the useful variables in the compressed wavelet coefficients selected by UVE are used by the PLS model. Fig. 4 shows the stability corresponding to each compressed wavelet coefficient for ␣-linolenic and linoleic acid by UVE, respectively. Two horizontal lines show the lower and upper cutoff determined with ˛ = 0.7. The coefficients whose stability is within the cutoff lines will be treated as uninformative and be eliminated, and those which lie out of cutoff lines were retained as informative information. Finally, 19 and 27 coefficients were retained for ␣-linolenic and linoleic acid, respectively. To evaluate the effect of the selection WT-UVE, the spectra reconstructed from the retained 19 and 27 wavelet coefficients of ␣linolenic and linoleic acid are shown in Fig. 5. The red curve shows the original spectrum of sample (one of the calibration data set for comparison). Because the Db1 (Haar wavelet function) was used, compared with the original spectra, the reconstructed spectrum was like a bar-plot, where the bar region represent the wavelength selected by WT-UVE, but the flat regions whose ordinate values is zero represent the unselected wavelengths which might no contribution to calibration model, and the retained wavelengths might attribute a spectra region to a specific chemical structure. In Fig. 5, the retained coefficients of ␣-linolenic and linoleic acid were similar. This is because the molecular structures of ␣-linolenic and linoleic acid are similar. Although it is difficult to attribute a spectral region to a specific chemical structure, it can be found that there are some differences among the retained regions of the
Fig. 5. Reconstructed spectra with the retained coefficients of ␣-linolenic (a) and linoleic (b) acid after WT-UVE variable eliminate. The original spectrum of sample one of the calibration data set for comparison.
of variables (dimension of spectra) [22]. Thus we proposed WT to firstly compress spectral data. 3.3. Wavelet transform analysis WT has been proved to be a highly efficient technology for data compression. After being processed by WT, the useful information is mainly concentrated on low frequency regions (the larger scale) [15,23]. There are several parameters that will affect on efficiency of WT, such as wavelet filter, decomposition scale and compression ratio. However, a systematic comparison of the performance of WT using different parameters is beyond the scope of our work. So, the simplest “db1” or Haar wavelet filter and decomposition scale 5 were adopted in further calculation. The 42 compressed wavelet approximate coefficients are shown in Fig. 3, compared with Fig. 2, the contour of compressed spectra was similar to the original spectra, and most of noise was eliminated. The obtained 42 wavelet coefficients were inputted into PLS. When LV number was 12 and 12, best ␣-linolenic and linoleic acid results were obtained, respectively. The results for prediction set generated by the PLS models based on wavelet coefficients are shown in Table 2. The r2 and RMSEP for prediction set were 0.9124 and 0.0134 for ␣-linolenic prediction, and 0.8737 and 0.0506 for linoleic prediction. The prediction results for both ␣-linolenic and linoleic acid were improved by WT, compared with results predicted based on full-spectrum. Moreover, the numbers of input variables were reduced from 1314 to 42 and PLS calibration model was simplified by WT.
Fig. 6. Relationship of predicted vs reference values of ␣-linolenic (a) and linoleic (b) acid in edible oils based on 19 and 27 wavelet approximate coefficients obtained by the WT-UVE-PLS model.
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reconstructed spectra. The result shows that it is very important to perform variable selection in multivariable analysis by using the NIR spectrum. The retained coefficients were employed as inputs for PLS model. The performance of WT-UVE-PLS model was evaluated by the 77 unknown samples in the prediction set. The best calibration models of WT-UVE-PLS for ␣-linolenic and linoleic acid were obtained based on 15 and 15 LVs, respectively. Table 2 shows the prediction results of WT-UVE-PLS model. The predicted vs reference values of ␣-linolenic (a) and linoleic (b) acid in edible oils based on 19 and 27 wavelet approximate coefficients are shown in Fig. 6. In the figure, the solid line is the regression line corresponding to the ideal, unity correlation between the predicted and reference values. The results indicated a satisfying performance of using NIR spectroscopy and WT-UVE-PLS model to determine ␣-linolenic and linoleic acid in edible oils. For comparison, the results predicted by the conventional PLS model with full spectra data, PLS model with compressed wavelet coefficients (WT-PLS) and the WT-UVE-PLS model are shown in Table 2. Compared with the conventional PLS model with full spectra data, WT-PLS model not only speed up the calculation, but also improve prediction precision. Furthermore, after the compressed wavelet coefficients were processed by UVE, only 27 and 19 variables were detained for ␣-linolenic and linoleic acid, respectively. The predicted result was further improved by UVE. This is easily comprehended, because the information which was no contribution to calibration model in compressed wavelet coefficients was eliminated. All results demonstrated that WT-UVE method could obtain more parsimonious and efficient model to determine ␣linolenic and linoleic acid in edible oils. 4. Conclusion NIR spectroscopy technique was evaluated to determine ␣linolenic and linoleic acid in edible oils. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The good performance showed a potential application using WTUVE to select NIR effective variables. The overall results indicate that NIR spectroscopy combined with PLS could be applied as a
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precision and rapid method to determine ␣-linolenic and linoleic acid in edible oils. The results might be useful for the process and online monitoring of essential fatty acids in edible oils. Acknowledgements This study was supported by National Science and Technology Support Program (2006BAD10A0403, 2006BAD05A02) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, and the Natural Science Foundation of China (P.R.C.) (Project No. 30671213). References [1] B.M. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K.I. Theron, J. Lammertyn. Postharvest Biol. Technol. 46 (2007) 99. [2] H. Cen, Y. He, Trends Food Sci. Technol. 18 (2007) 72. [3] C. Pasquini, J. Braz. Chem. Soc. 14 (2003) 198. [4] E. De Pedro, A. Garrido, I. Bares, M. Casillas, I. Murria, Application of near infrared spectroscopy for quality control of Iberian pork industry, in: K.I. Hildrum, et al. (Eds.), Near infrared spectroscopy: bridging the gap between data analysis and NIR applications, Ellis Horwood, Chichester, UK, 1992, p. 145. [5] I. González-Martıˇın, C. González-Pérez, N. Alvarez-Garcıˇıa, J.M. GonzálezCabrera, Meat Sci. 69 (2005) 243. [6] I. González-Martıˇın, C. González-Pérez, J. Hernández-Méndez, N. AlvarezGarcía, Meat Sci. 65 (2003) 713. [7] A. Dalle Zotte, P. Berzaghi, L.M. Jansson, I. Andrighetto, Anim. Feed Sci. Technol. 128 (2006) 108. [8] C.E. Realini, S.K. Duckett, W.R. Windham, Meat Sci. 68 (2004) 35. ˜ J.A. Ramírez, Isabel Díaz, Food Chem. 100 (2007) [9] M. Pla, P. Hernández, B. Arino, 165. [10] S. Armenta, S. Garrigues, M. de la Guardia, Anal. Chim. Acta 596 (2007) 330. [11] A.F. Costa Pereira, M.J. Coelho Pontes, F.F. Gambarra Neto, S.R. Bezerra Santos, R.K. Harrop Galvao, M.C. Ugulino Arau jo, Food Res. Int. 41 (2008) 341. [12] L.J. Bokobza, Near Infrared Spectrosc. 6 (1998) 3. [13] J.J. Workman Jr, Appl. Spectrosc. Rev. 31 (1996) 251. [14] W.S. Cai, Y.K. Li, X.G. Shao, Chemometrics Intell. Lab. Syst. 90 (2008) 188. [15] A.K.M. Leung, F.T. Chau, J.B. Gao, T.M. Shih, Chemometrics Intell. Lab. Syst. 43 (1998) 69. [16] S.G. Mallat, IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989) 674. [17] V. Center, D.L. Massart, O.E. de Noord, S. de Jong, B.M. Vandeginste, C. Sterna, Anal. Chem. 68 (1996) 3851. [18] S.F. Ye, D. Wang, S.G. Min, Chemometrics Intell. Lab. Syst. 91 (2008) 194. [19] Q.J. Han, H.L. Wu, C.B. Cai, L. Xu, R.Q. Yu, Anal. Chim. Acta 612 (2008) 121. [20] I.E. Frank, J.H. Kalivas, B.R. Kowalski, Anal. Chem. 55 (1983) 1800. [21] T. Naes, T. Isaksson, T. Fearn, T. Davies, Multivariate calibration and classification, NIR Publications, Chichester, UK, 2002. [22] F. Chauchard, R. Cogdill, S. Roussel, J.M. Rogera, V. Bellon-Maurel, Chemom. Intell. Lab. Syst. 71 (2004) 141. [23] X.G. Shao, A.K.M. Leung, F.T. Chau, Accounts Chem. Res. 36 (2003) 276.