Yanrui Zhou

The feasibility of quantifying the soluble solids content of intact apples was investigated by visible and near infrared (vis–NIR) transmittance spectroscopy combined with the least squares support vector machines (LS-SVM) method. The spectra were pretreated by Savitzky-Golay smoothing, first and second derivatives, standard normal variate transformation, and multiplicative scatter correction. The regression models were developed by LS-SVM and partial least squares (PLS). The accuracy of the LS-SVM and PLS models was compared. 

Apples are a very popular fruit in people's daily lives because of their delicious taste and nutritional value. Soluble solids content (SSC) is one of the most important evaluation criteria affecting the consumers' appreciation for selection. However, the traditional measurement methods have many disadvantages, such as long analysis time, high costs, and complications. 

Visible–near infrared (vis–NIR) spectroscopy is a rapid, reliable, and nondestructive approach for the measurement of SSC in several fruits. Many researchers have reported using nondestructive techniques to assess the SSC value of fruits. In 2004, Chauchard and colleagues (1) showed that the least squares support vector machines (LS-SVM) method was more accurate in prediction than partial least square (PLS) and multiple linear regression (MLR) for predicting the total acidity in fresh grapes. In 2006, Zude and colleagues (2) applied acoustic impulse resonance frequency sensors and miniaturized vis–NIR spectrometers to predict fruit flesh firmness and SSC when the fruit was still on the tree as well as its shelf life. As a result, SSC prediction of freshly harvested apples had a standard error of cross validation (SECV) of 1.29 °Bx. In 2009, Fan and colleagues (3) investigated fruit orientation in the examination of SSC in red Fuji apples by vis–NIR transmittance spectroscopy and concluded that the best fruit orientation was when the stem–calyx axis was vertical and the fruit surface was illuminated from the upper side. Also in 2009, Paz and colleagues (4) performed a comparative study which was made of the performance of different spectrophotometers as part of some research into the potential of NIR reflectance spectroscopy as a nondestructive method for predicting soluble solids content. Many publications have proven that multivariate calibration methods in NIR spectroscopy for estimating varieties of fruit properties are a good alternative (5,6). Although linear models such as multiple linear regression (MLR), principal component regression (PCR), and PLS are widely used in the prediction of fruit quality, nonlinear calibration methods often have better performance, especially in improving the robustness of NIR spectroscopy. Support vector machines (SVM) is a powerful methodology for solving problems in nonlinear classification, function estimation, and density estimation. LS-SVM is an improved method of standard SVM put forward by Suykens and Vande in 1999 and Suykens and colleagues in 2002. It transformed the quadratic programing problem of a standard SVM demand solution to a linear problem by using the least square value function and equality constraints and increased the training speed and restraining precision. Some researchers have applied LS-SVM to regression models. Kovalenko and colleagues (7) determined amino acid composition of soybeans and concluded that the performance of LS-SVM was better than that of artificial neural networks (ANN). Sun and colleagues (8) reported that LS-SVM models were better than PLS models with correlation coefficient (

) and root mean square error of prediction (RMSEP) of (0.88, 0.80 °Bx) and (0.82, 1.01 °Bx) for portable and on-line measurement mode, respectively. Liu and colleagues (9) developed an NIR spectrometry regression model by LS-SVM, and the results showed that portable NIR combined with LS-SVM was a feasible method to predict Brix values of intact pears nondestructively. Also, Liu and colleagues (10) investigated the performance of NIR spectrometers with LS-SVM in determining acetic, tartaric, and formic acids, and the pH of fruit vinegars. The results indicated that NIR spectroscopy (7800–4000 cm

) combined with LS-SVM could be utilized as a precision method for the determination of organic acids and pH of fruit vinegars. In addition, Liu and colleagues (11) applied principal component analysis (PCA) combined with partial least-squares discriminant (DPLS) and LS-SVM to realize the rapid identification of different varieties of pears. Both of those two models had preferable results, that the rate of identification is 100%. Nie and colleagues (12) investigated the performance of vis–NIR spectroscopy as a rapid and nondestructive technique to determine the boiling time of yardlong beans. Pissard and colleagues (13) determined the vitamin C, polyphenol, and sugar contents in apples by NIR spectroscopy combined with the LS-SVM method. 

The objectives of this study were to investigate the feasibility of using vis–NIR spectroscopy combined with the LS-SVM method to predict the SSC of intact apples nondestructively and to compare the accuracy of the LS-SVM and PLS models. 

A total of 160 Fuji apples were obtained from a local fruit supermarket near Nanchang, Jiangxi province in China. The apple samples were stored at 20 °C constant temperature and 60% relative humidity for 24 h before vis–NIR spectra measurement. After that, three separate signs were made on the equator of each apple with the locations 120° apart, avoiding any obvious surface defects (such as bruises or scars).  

NIR diffuse reflectance spectra in the 200–1100 nm region were obtained with NIR spectrometry equipment that consisted of four light sources that could be used both in the visible and near infrared region, 350–1650 nm (type reference: 41850SP, 12 V, 50 W, halogen, Osram lamps), a spectrometer, a fiber-optics probe (74-UV, Ocean Optics), an optical fiber, a fruit holder or light collection fixture, a computer system with SpectraSuite software (Ocean Optics), and other accessories. The transmission mode was applied for this experiment. The four light sources were placed at a height of about 200 mm above the sample. The fiber spectrometer used in this experiment was a model QE65000 system from Ocean Optics. This spectrometer was equipped with a 1044 horizontal × 64 vertical element linear silicon charge-coupled device (CCD) detector with a wavelength range of 200–1100 nm. The probe of the spectrometer was placed under and close to the sample. The arrangement of the equipment is shown in Figures 1 and 2. As for the spectrometer parameter setting, integration time was 100 ms, smoothness was 15, and the average number was 1. Before the spectrum collection of individual apple samples, the dark current and the reference should be measured. In this process, air was used as the reference. The spectra of all individual fruit were measured at three positions that were signed around the equator, approximately 120° apart, and perpendicular to the stem–calyx axis. The spectra of the samples were calculated as an average of the three measurements.  

Figure 1: Schematic diagram of NIR acquisition device.			

To build the calibration and the validation models, the real quality parameters of individual fruit should be assessed. The SSC values of the apples were determined using a conventional destructive testing method. The SSC values of apples were determined immediately after vis–NIR spectroscopy measurements using a digital refractometer (PR-101α, ATGO). The measurement accuracy is ±0.1 °Bx, and the measurement range is 0–45.0 °Bx with automatic temperature compensation.  

Figure 2: Top view of light source and apple.			

Because PLS is already widely used in mathematical algorithms for multivariate linear regression, the theory of these methods will not be presented explicitly herein. The principle behind the PLS algorithm is to correlate the spectrum 

 and compress it in a set of new independent latent variables. The predictions ŷ are computed by the following equation:  

Where β(withcircumflex) is a (p×1) vector of regression coefficients; and 

The SVM method has been proven to be a useful approach for solving problems in nonlinear classification, function estimation, and density estimation. SVM is based on statistical learning theory related to the principle of structural risk minimization.  

LS-SVM is an optimized algorithm based on the standard support vector machine proposed by Suykens (14). LS-SVM has a good theoretical foundation in the statistical learning method and the capability of dealing with linear and nonlinear multivariate calibration (15,16). The details of the LS-SVM algorithm can be found in the literature (14). 

In LS-SVM function estimation, the standard framework is based on a primal-dual formulation (17). Suppose the training samples are {

 is an output parameter of sample number. In SVM, the data is nonlinearly mapped to form the input space to a high dimensional feature space using φ(

).The estimated function is introduced as  

 is the bias term. The following optimization problem is formulated:  

where γ is the regularization parameter which balances the model's complexity and the training errors, and 

This optimization problem can be solved in a dual space. To solve the problem, the following Lagrangian is defined:  

. The solution of the above equation can be obtained by partially differentiating with respect to ω, 

, the following linear system is obtained:  

The LS-SVM model can be defined as follows (14):  

The robustness of LS-SVM models is largely determined by the crucial elements of optimal input feature subset, proper kernel function, and optimum kernel parameters. To improve the training speed and reduce the training error, available latent variables (LVs) that were applied as inputs of LS-SVM models were necessary. 

The PLS method to determine LVs was used in the LV-SVM model to ensure that all variability was considered by the analysis. Commonly used kernel functions are linear_kernel, polynomial_kernel, and RBF_kernel. However, there is no systematic methodology for the selection of a kernel function. The optimal parameters of each kernel function are found from an intensive grid search and leave-one-out cross-validation and selected when resulting in smaller root mean square error of cross-validation (RMSECV). Grid search is a two-dimensional minimization procedure based on an exhaustive search in a limited range. In each iteration, one leaves one point, and fits a model on the other data points. The performance of the model is estimated based on the point left out. This procedure is repeated for each data point. The LS-SVM model was carried out using MATLAB (Mathworks) and free LS-SVM software for MATLAB (LS-SVM v1.5, Suykens, Leuven, Belgium). 

The standard error of calibration (SEC), the standard error of prediction (SEP), and the correlation coefficient (

) were used to measure the model's performance. The SEC, SEP, and 

are the measurement and prediction value of the samples, ӯ

 is the number of apples in the calibration set and the prediction set. The value 

All samples were randomly divided into calibration sets of 120 samples and prediction sets of 40 samples (18). No single sample was used in calibration and prediction sets at the same time. To ensure the adaptability of the calibration models, the samples with high and low SSC values were put in the calibration set, and the other sample selections inside each group were performed randomly. To compare the performance of different calibration models, the samples in the calibration and prediction sets were kept unchanged for all calibration models. The calibration and prediction set data are presented in Table I.  

Table I: Characteristics of calibration and prediction set			

Three transmittance spectra of each sample were averaged into one spectrum, and then the averaged spectrum was transformed into an absorbance spectrum using the log(1/

) relationship. Because of obvious scattering, noise could be observed at the beginning and the end of the spectral data. Thus, the first 300 nm and the last 69 nm data were eliminated to improve the measurement accuracy and speed, so the spectral analysis was based on 505–1031 nm wavelengths (3). To reduce spectral noise and enhance the useful information, several spectral pretreatment methods were applied. These methods included Savitzky-Golay smoothing (smoothing) with a window width of 5 points and 0 order polynomial to eliminate the random noise, Savitzky-Golay first derivative (1Der ) with a window width of 3 points and second order polynomial, and Savitzky-Golay second derivative (2Der) with a window width of 5 points and second order polynomial to remove baseline shifts and make superimposed peaks more obvious, standard normal variate transformation (SNV) to remove slope variation and correct scatter effects in spectra, and multiplicative scatter correction (MSC) to remove these effects by linearizing each spectra to the average spectra, respectively (19). In this paper, four combinations of pretreatment methods were used to preprocess the sample spectra: 1Der + MSC + smoothing; 1Der + SNV + smoothing; 2Der + MSC + smoothing; and 2Der + SNV + smoothing. All of these pretreatment methods were carried out using Unscrambler V8.0 software (CAMO AS). The original absorbance spectra and pretreatment spectra of the samples are shown in Figure 3.  

Figure 3: (a) The original absorbance spectra and preprocessed spectra by (b) 1Der + MSC + smoothing, (c) 1Der + SNV + smoothing, (d) 2Der + MSC + smoothing, and (e) 2Der  + SNV + smoothing.			

All of the combinations of different pretreatment methods had an effect on reducing the number of LVs for PLS models; the results are presented in Table II. In contrast, the combination of 1Der + MSC + smoothing had a better performance than others (

= 0.91, SEP = 0.51). Therefore, the combination of 1Der + MSC + smoothing was applied in this work.  

Table II: Statistical results of PLS models with different pretreatment methods  			

To improve the computational speed and training accuracy of the vis–NIR model, suitable LVs were selected as inputs for the LS-SVM model. The LVs that were selected could explain most of the spectral variances and represent the main information of the original spectra to the measured chemicals. We applied the PLS method to obtain the optimal input feature subset for LS-SVM. By means of PLS, the first 11 important LVs were regarded as the inputs of the LS-SVM model according to the smallest prediction residual error sum of squares (PRESS).

Therefore, the optimal number of LVs for the LS-SVM model could be achieved by the PLS method and the computational time of the LS-SVM model could be reduced at the same time. 

Articles

The feasibility of quantifying the soluble solids content of intact apples was investigated by visible and near infrared (vis–NIR) transmittance spectroscopy combined with the least squares support vector machines (LS-SVM) method. The spectra were pretreated by Savitzky-Golay smoothing, first and second derivatives, standard normal variate transformation, and multiplicative scatter correction.

Yanrui Zhou

Articles

Quantification of the Soluble Solids Content of Intact Apples by Vis–NIR Transmittance Spectroscopy and the LS-SVM Method