Discrimination of Apples Using Near Infrared Spectroscopy and Sorting Discriminant Analysis

Abstract

Near infrared spectra of apples contain the most useful information of the soluble solids content and firmness of apples. A new feature extraction method, called sorting discriminant analysis, was proposed to use a sorting method based on principal component analysis and linear discriminant analysis to extract the features of near infrared spectra. The objective of this research was to make use of feature extraction methods, such as principal component analysis, linear discriminant analysis, discriminant partial least squares, and sorting discriminant analysis to extract information from near infrared spectra of the “Huaniu” apples and the “Fuji” apples. After feature extraction, the nearest neighbor classifier was used to classify the apples, and the classification results were compared to study that which feature extraction method performed best. The experimental results showed principal component analysis + linear discriminant analysis and sorting discriminant analysis could extract discriminant information from near infrared spectra of apples better than principal component analysis and discriminant partial least squares, and sorting discriminant analysis was the best one. Sorting discriminant analysis can not only compress the high-dimensional near infrared spectra to the low-dimensional data but also project near infrared spectra to a new feature space where the data can be classified easily and effectively, and sorting discriminant analysis is superior to principal component analysis + linear discriminant analysis in most cases.

Keywords:

• Apple
• Near infrared spectroscopy
• Principal component analysis
• Linear discriminant analysis
• Discriminant partial least squares

INTRODUCTION

The apple is one of the four famous fruits in the world, and China is the country with the largest amount of apple production in the world. China leads the world in the production and the planting area of the apple. Postharvest processing, quality evaluation, and non-destructive testing of the apple are the important issues in the agricultural products processing area.^[1] The apple quality includes external quality (such as color, size, shape, and surface defects) and internal quality (such as sugar content, acidity, flavor, and vitamin). Both external quality and internal quality are very important in evaluating the quality of apples.

To evaluate the internal quality of apples, researchers focused on the measurement of the soluble solids content (SSC) and firmness with non-destructive methods, such as near infrared (NIR) spectroscopy,^[2] multispectral image,^[3] and laser light.^[4] Among the non-destructive methods applied to the apple, NIR spectroscopy is probably the most widely used. Liu et al. used Fourier-transform near-infrared (FT-NIR) diffuse reflectance spectroscopy to study the effects of four distances between the light source/detection probe on the prediction of apple’s sugar content with a coefficient determination of 0.8436 and a standard error of prediction (SEP) of 0.773.^[5] Fan et al. examined firmness and SSC of Red Fuji apples by Vis/NIR transmittance and validation models for SSC and firmness had a R² of 0.9532 and 0.8136, as well as, SEP of 0.3838 and 0.5344, respectively.^[6] The feasibility of direct standardization technique was studied to transfer a partial least square (PLS) calibration model developed on a FT-NIR spectrophotometer to a diode array (DA) spectrophotometer, for the prediction of the SSC in apples with root mean squared error of prediction (RMSEP) of 0.85°Brix.^[7] NIR spectroscopy was used to construct NIR prediction models for SSC and firmness based on a large dataset of apples from different seasons, origins, cultivars, and storage conditions. The RMSEP for predictions of the SSC was in the range 0.6–0.8°Brix.^[8] Zou et al. studied the feasibility of rapidly measuring intact apple SSC to establish relationships between the FT-NIR measurements and the SSC of the “Fuji” apples based on different methods, and compared the prediction performance of calibration models with different PLS methods and to find out the best model using 44 variables and 9 factors presented the best result (RMSECV = 0.3126, RMSEC = 0.1907, r_c = 0.9635, RMSEP = 0.4140, r_p = 0.9361).^[9] NIR spectroscopy and linear discriminant analysis (LDA)were used to discriminate apples on the basis of storage time. Average correct classification was higher than 93% in validation and close to 100% in calibration.^[10] NIR spectroscopy coupled with multivariate data analysis was performed to quantify SSC, total acid and polyphenol content of Golden Delicious (GD) and Pink Lady (PL) apples.^[11] Prediction accuracy of polyphenolcontent could be increased by 8.3 and 15% for PL and GD apples, respectively.^[11]

To evaluate the internal quality of apple by measuring SSC belongs to quantitative analysis of apples. This method must measure the sugar content and acidity by physical and chemical analyses to establish the mathematical model having a reciprocal relationship between SSC and NIR spectra. If the number of apple samples is large, the workload for quantitative analysis of apples is very heavy. On the other hand, quality evaluation of apples can be finished by qualitative analysis of apple using NIR spectroscopy. For example, the apples can be classified or graded according to the level of quality without the help of physical and chemical analyses. Because many fruits and vegetables available to people vary in composition for both nutrients and phytochemicals, classification of fruits and vegetables is important to researchers who attempt to assess relationships among diet, health, and disease.^[12] Some researchers studied the grading and classification of fruits using NIR spectroscopy and images (or machine vision). Rocha et al. approached the multi-class classification as a set of binary problems in such a way one could assemble together diverse features and classifier approached custom tailored to parts of the problem.^[13] The introduced fusion approach was validated using an image data set collected from the local fruits and vegetables distribution center and made public and it reduced the classification error in up to 15 percentage points with respect to the baseline.^[13] Ohali built a working model of a date fruit grading and sorting system including both: the hardware and the software.^[14] The hardware included the conveyer, camera control and helm control systems. The software system analyzed the fruit image and classifies them. The maximum accuracy of the system was 80% which was attained by a back-propagation neural network classifier. Carlomagno et al.^[15] described an experimental study on NIR transmittance spectrometry for sorting peaches according to their degree of ripeness. Blasco et al.^[16] presented a computer vision system that was developed for the recognition and classification of the most common external defects in citrus.^[16] The system combined spectral information about the defects with morphological estimations of them in order to classify the fruits in categories. Riquelme et al. proposed a procedure that enabled the identification of sound olives as well as a variety of defects based on three discriminant analyses.^[17] This methodology for the classification of olives made use of color features of the fruit together with several morphological characteristics of external defects, which enhanced the final performance. Kondo described an orange grading system, an eggplant grading system, a leek preprocessing and grading system, and a robotic grading system, because these grading systems were different types of product shapes and properties that made different processing in their grading procedures.^[18] Simultaneously, he also discussed the traceability systems accompanied with the grading systems.

This work tried to discriminate three kinds of apples (the 60 “Huaniu” apples, the 60 Grade I “Fuji” apples, and the 60 Grade II “Fuji” apples). In order to finish this task, a sorting discriminant analysis (SDA) was proposed to extract the features of NIR spectra in order to obtain the best classification results compared to principal component analysis (PCA), LDA, and discriminant partial least squares (DPLS). After feature extraction, the nearest neighbor classifier (NNC) was used to classify the apples, and the classification results were compared to study that which feature extraction method performed best.

MATERIALS AND METHODS

Apple Samples

The apples consisted of 60 “Huaniu” apples and 120 “Fuji” apples for this work, and were purchased at the local markets. They were stored for three days to equilibrate at 23 ± 3°C and 60–70% relative humidity (RH) before being examined by the NIR spectrometer. The “Fuji” apples were harvested in Shandong, China, and the “Huaniu” apples came from Gansu, China. The 120 “Fuji” apples were divided into first grade (Grade I) and second grade (Grade II; each grade having 60 apples), and the 60 “Huaniu” apples were collected as first grade (according to the Chinese national standard GB10651-89, apples are divided into three grades: special grade, first grade, second grade). So there were two types of apples: the “Huaniu” apples and the “Fuji” apples, and two grades of apples in the same type of the “Fuji” apples, i.e., three kinds of apples. There were 30 apples from every kind of apples as training samples and the other 30 apples as test samples in the following experiments.

NIR Spectra Measurement

The NIR spectra of apples were acquired in the reflectance mode using the Antaris II FT-NIR spectrophotometer (Thermo Electron Co., USA) equipped with a NIR fiber-optic probe. The FT-NIR spectrometer has a spectral range of 10,000–4000cm^–1 with a 3.856 cm^–1 sampling interval.^[19,20] The result analysis software (Antaris II System, Thermo Electron Co., USA) was used to acquire the NIR spectra. Each spectrum was collected as a 1557 dimensional datum, and it was recorded as log (1/R), where R = relative reflectance, by averaging 32 scans number. Three separate spectral measurements around the equator of the apple were made on the samples without any obvious surface defects.^[10] Three reflectance spectra were averaged to obtain a mean spectrum for the further study. Because NIR spectrophotometer is sensitive to the change of outer temperature and humidity in acquiring the NIR spectra, it was operated at the temperature of 23 ± 3°C, and at the RH of 60–70% during all experiments.

PCA

Matlab 7.11 (MathWorks, Natick, MA, USA) was used to perform PCA, LDA, SDA, and the nearest neighbor classifier (NNC) programs under Windows XP. PCA is aimed to extract the feature from high-dimensional data, and it can transform the high-dimensional data into the lower-dimensional data.^[21] Given a d-dimensional (d = 1557 in this work) vector representation of each spectrum, PCA can be used to project the vector onto p (p < d) directions corresponding to the maximum-variance directions in the original space. Given a set of the NIR spectra , k = 1,2,3, …, N, , PCA finds the eigenvectors v_k and the corresponding eigenvalues by solving the eigen equation: ,where is the covariance matrix. To transform the d-dimensional x_k to the p-dimensional y_k, the equation is calculated, where the columns of W are the eigenvectors v_k, and the W represents the linear transformation that maps the original d-dimensional space onto the p-dimensional feature subspace.^[22]

LDA

LDA,^[23] also known as Fisher discriminant analysis (FDA), is a valuable feature extraction method for classification because: (1) LDA can extract discriminating information from data, whereas PCA extracts information relevant to compression; (2) LDA creates a linear combination of the extracted features which can provide the largest mean differences between the classes. The objective of LDA is to find a project matrix W that maximizes the ratio of the determinant of the between-class scatter matrix S_b to the determinant of the within-class scatter matrix S_w:

(1)

The between-class scatter matrix S_b and the within-class scatter matrix S_w are given as follows:

(2)

(3)

where, c is the number of classes; N_i (i = 1, 2, …, c) is the number of samples in the ith class; x_ij is the jth sample in the ith class; m_i and m are the mean vectors of the ith class samples and all samples, respectively. If S_w is non-singular, Eq. (1) can be solved as an eigenvalue problem.

(4)

The largest eigenvalue of Eq. (4) is the value of Eq. (1). w is the eigenvector corresponding to the eigenvalue . For c-class classification problem, the optimal dimensionality of feature space is c-1.^[24]

DPLS

DPLS, also known as PLSs discriminant analysis (PLSDA), is a high-dimension reduction technique and feature extraction method for maximizing covariance between predictor block X and predicts block Y for each component, where the predicted variables are dummy variables (1 or 0) where “1” indicates an in-class member while “0” indicates a non-class member.^[25] DPLS is commonly used to compute a lower-dimensional representation between these two blocks by means of score vectors. Its classical form is based on the non-linear iterative partial least squares (NIPALS) algorithm.^[26]

SDA

In this study, a SDA was proposed based on PCA and LDA. SDA includes three steps:

The first step is the dimension of the original data is reduced by PCA, and the coordinate value of every data is obtained by projecting the original data to the new space composed by the full set of principal components.

The second step is after NIR spectra are performed by PCA, the eigenvectors are sorted according to the following equations:

(5)

(6)

where, J(v_k) is Fisher’s ratio of the eigenvector v_k obtained by PCA. The larger value of J(v_k) represents the more discriminant information contained in eigenvector v_k. The bigger eigenvalue represents the more information of NIR spectra in eigenvector v_k. According to Eq. (5), SDA attaches importance to both discriminant information and data information because it combines PCA and LDA. and mean that normalization, which is a pre-processing method,^[27] was used to process J(v_k) and λ_k, respectively. Here, the normalization of λ_k is,

(7)

and the normalization of J(v_k) is,

(8)

where, and are the minimum and the maximum of eigenvalue, respectively; and are the minimum and the maximum of Fisher’s ratio of the eigenvectors, respectively. If the > , the eigenvector v_k is considered to contain the more discriminant information than the eigenvector v_j. Based on this method, the eigenvectors from PCA are sorted according to Eq. (5). The compressed data are obtained by projecting the original data to the sorted eigenvectors.

The third step is the compressed data are projected to the discriminant vectors from LDA for classifier; that is to say, LDA extracts the discriminant information from the compressed data for further classification.

Theoretically, the bigger value of corresponds to the better classification ability of the associated eigenvector v_k. On the other hand, the bigger value of eigenvalue corresponds to more information contained in the projected data on its eigenvector. Therefore, both the value of J(v_k) and eigenvalue are considered to find the eigenvectors that could well extract the discriminant information from the NIR spectra.

NNC

The NNC is a simple but effective scheme, and it has been used to classify the fruits.^[15,28] The classification criterion in NNC is based on the nearest distance between two samples of different classes. Given a test sample x_i of the prediction set, NNC searches the nearest training sample x that is the closest in distance to the test sample x_i, and classifies x_i to the class which the nearest training sample x belongs to. The similarity or distance between two samples is measured in NNC, and the most commonly used measure is Euclidean distance: .

The NIR spectra were analyzed using a two-stage approach. In the first stage, the training samples and test samples were compressed to a low-dimensional data by PCA with the different number of principal components. The second stage was aimed at discriminating apples with NNC. In most instances, the fewer principal components were expected to express the data samples for PCA is a dimension reduction technique. Most of the information in data concentrated on the first k principal components which represented the proportion of the total data variance. The proportion was computed as follows:

(9)

By using Eq. (9), the number of principal components, i.e., k, could be obtained when the proportion was given, for example, .

PCA+LDA and NNC

LDA has been successfully used as a dimension reduction technique in apple classification^[29] and discrimination of pork storage time,^[20] etc. However, if LDA was directly used to deal with NIR spectra, it would encounter the difficulty of computation. One spectrum in this work was 1557 dimensions, and, therefore, scatter matrices were 1557 × 1557 = 2.4 M. First, it was computationally challenging to compute eigenvalues with the big matrices. Second, those big matrices were almost always singular when the dimension of samples greatly exceeded the number of samples. This was called a small sample size problem.^[30] To solve this problem, first the dimension of NIR spectra was reduced by PCA, and second, LDA was performed to extract the discriminating information from the dimension-reduced spectra by PCA, and finally NNC was used to classify the apples.

RESULTS AND DISCUSSION

NIR Spectra

Figure 1 showed the average NIR reflectance spectra of the “Fuji” apples and the “Huaniu” apples. Since the spectral data contained considerable noise when the absorb wave number was below 10,000 cm^–1 and above 4000 cm^–1, the wave numbers between 10,000 and 4000 cm^–1 were used in this work. These absorbance spectra overlapped heavily, especially the spectra between Grade I and Grade II of the “Fuji” apples. The peaks stayed at about 6900 and 5200 cm^–1 where the log (1/R) values of the “Huaniu” apples were sometimes bigger than those of the “Fuji” apples. Because it was difficult to discriminate the three kinds of apples just from the overlapping spectra, it was necessary to use feature extraction methods, such as PCA, LDA, SDA, and DPLS, to distinguish the kind of apples.

FIGURE 1 The average NIR spectra of apples.

Classification of Apples by DPLS

DPLS based on NIPALS was used to classify the apples in this work. The tolerance of convergence which is the upper limit in DPLS was set to = 11, 10, 9, 8, and 7%, respectively. Table 1 showed the classification results obtained for the “Fuji” and “Huaniu” apples. From Table 1, the best classification accuracy was 74.44% with tolerance = 9% and seven components.

TABLE 1 Classification accuracies for apples using DPLS

Tolerance	11%	10%	9%	8%	7%
Classification accuracies	71.11%	72.22%	74.44%	56.67%	64.44%
Number of components	2	4	7	11	13

Classification of Apples Using PCA and NNC

The test samples were compressed to three-dimensional data by PCA. The scores plot of principal component 1 (PC1) and principal component 2 (PC2) were illustrated in Fig. 2a, and PC1 and PC2 explained 99.14% of the total variance in the NIR spectra. The symbols of the “o”, “·” and “*” in Fig. 2a denoted the two-dimensional data from Grade II and Grade I of the “Fuji” apples (marked as Fuji I and Fuji II in Fig. 2) and the “Huaniu” apples, respectively. Some test samples overlapped between different classes, and made it difficult to discriminate among different classes of apples for the classifier. Figure 2b showed the scores plot of three principal components (PC1, PC2, and PC3) which explained 99.78% of the total variance when the test samples were transformed into three-dimensional data by PCA. Classification accuracies for apples using PCA with NNC were shown in Table 2. The NIR spectra were compressed to the low-dimensional data from 2 to 87 dimensions for classification using PCA and NNC, and the classification accuracies were the same values as 72.22%.

TABLE 2 Classification accuracies for apples using PCA, PCA+LDA, and SDA with NNC

The number of eigenvectors	The classification accuracies (%)
	PCA	PCA+LDA	SDA
2	72.22	74.44	74.44
5	72.22	74.44	71.11
10	72.22	74.44	81.11
15	72.22	87.78	84.44
20	72.22	91.11	92.22
25	72.22	92.22	90.00
35	72.22	90.00	91.11
40	72.22	92.22	93.33
45	72.22	91.11	92.22
50	72.22	91.11	95.56
55	72.22	93.33	94.44
59	72.22	93.33	96.67
65	72.22	94.44	95.56
68	72.22	93.33	96.67
72	72.22	93.33	96.67
78	72.22	94.44	95.56
85	72.22	94.44	95.56
87	72.22	95.56	95.56

Classification of Apples by PCA+LDA and NNC

The NIR spectra were reduced from 1557 dimensions to 50 dimensions by PCA, and the 50 dimensional test data were extracted features by LDA to the two-dimensional data for classification using PCA+LDA and NNC. Figure 2c displayed the scores plot of the discriminant vector 1 (DV1) and the discriminant vector 2 (DV2). The data from the “Fuji” apples and the “Huaniu” apples in Fig. 2c were separated better than those in Fig. 2a. The overlapping numbers of Grade II and Grade I of the “Fuji” apples in Fig. 2c were fewer than those in Fig. 2a. As was shown in Table 2, the NIR spectra were compressed by PCA to 2~87 (N – c =90-3, N: the number of training data, and c: the number of classes) dimensional data, and the compressed data were transformed by LDA to the two-dimensional data to be classified by NNC. Normally, when the dimensionality of the data compressed by PCA is higher, there is more discriminant information to be extracted by LDA, and the classification accuracy is higher. For example, PCA compressed the NIR data to ten dimensional data, and LDA transformed them to the two-dimensional data, and the classification accuracy with NNC was 74.44%. If PCA compressed the NIR data to 20 dimensional data and other things being equal them, the classification accuracy was 91.11%. As a result, the classification accuracies of PCA+LDA and NNC were better than those of PCA and NNC in Table 2.

FIGURE 2 Scores plot of: (a) PC1 and PC2; (b) PC1, PC2, and PC3; (c) DV1 and DV2.

Classification of Apples Using SDA and NNC

First, the NIR spectra were performed by PCA, and the 1557 dimensional data were compressed to 2~87 dimensional data. The 2~87 eigenvectors were computed by normalize J(v_k) whose values were displayed in Fig. 3a. As the k increased, the value of J(v_k) decreased. That is to say, the discriminant information mainly existed in the first few eigenvectors. g(v_k) was shown in Fig. 3b. The 2~87 dimensional data by PCA were sorted according to the sorted eigenvectors, and they were reduced to two-dimensional (c – 1 = 2) data by LDA, and finally were classified by NNC. The classification results of SDA with the different number of principal components were shown in Table 2, and they were better than those of PCA+LDA in most cases. For example, when NIR spectra was transformed to 50-dimensional data, the classification accuracy of PCA+LDA was 91.11% and that of SDA was 95.56%.

FIGURE 3 The values of: (a) the normalized J(v_k); (b) g(v_k).

The NIR spectra were reduced to 68 dimensional data by PCA, and the reduced data were sorted according to Eq. (5). The sorted data were extracted to the two-dimensional data, and scores plot of the sorting discriminant vector 1 (SDV1) and the sorting discriminant vector 2 (SDV2) were displayed in Fig. 4. In this case the three kinds of apples could be separated well in Fig. 4, so the classification accuracy of SDA was 96.67% which was the best accuracy compared to PCA, DPLS, and PCA+LDA.

FIGURE 4 Scores plot of SDV1 and SDV2.

From the above experiments, SDA and NNC can be a simple, effective, and highly-accurate classification model for the discrimination of apples. There are some other classification models developed by other researchers. PCA and artificial neural network (ANN) coupled with NIR were used to classify apple varieties with the accuracy of 100%.^[31] However, ANN is a complex classifier and it has problems such as local minima trapping, overfitting, and weight interference.^[32] Moving window partial least-squares discriminant analysis (MWPLSDA) was used to select useful wavelength intervals to build PLSDA model for classification of apples.^[14] MWPLSDA and PLSDA cannot extract the discriminant information from NIR spectra like LDA or SDA, so the performance of SDA and NNC is better than MWPLSDA. LDA was applied to FT-NIR spectral data to classify the apples on the basis of storage time.^[10] As was discussed in section “PCA+LDA and NNC”, LDA has small sample size problem while SDA has not this problem.

CONCLUSION

In this research, four kinds of feature extraction methods, such as PCA, PCA+LDA, DPLS, and SDA, were performed experiments to extract features from NIR spectra. SDA was proposed to use a sorting method based on PCA and LDA. Different from PCA and PCA+LDA, SDA takes into account not only original data reduction but also discriminant information retaining during launching PCA. The experimental results showed LDA and SDA could extract discriminant information from the NIR spectra of apples better than PCA and DPLS, and SDA was the best one. PCA is a good tool for NIR spectra to reduce dimension, but it is not a good tool for classifying apple samples. PCA+LDA is better than PCA in classifying apple samples because PCA+LDA extracts the discriminant information while PCA does not. SDA is superior to PCA+LDA because SDA sorts the eigenvalues considering the importance of original data information and discriminant information while PCA+LDA just thinks of the original data information in PCA stage.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for their constructive advice. We thank Dr. Qin Ouyang (School of Food & Biological Engineering, Jiangsu University) for giving us help in collecting NIR spectra of apples.

FUNDING

The authors acknowledge financial support of the project funded by the priority academic program development of Jiangsu Higher Education Institutions, National Science Foundation of China (No. 31471413), China Postdoctoral Science Foundation funded project (No. 20090460078), Nature Science Foundation of Anhui Provincial Colleges (No. KJ2012Z302), Anhui Provincial College Foundation for Young Talent (No. 2012SQRL251), and the key project of Education Department of Sichuan Province (No. 12ZA070).

Additional information

Funding

The authors acknowledge financial support of the project funded by the priority academic program development of Jiangsu Higher Education Institutions, National Science Foundation of China (No. 31471413), China Postdoctoral Science Foundation funded project (No. 20090460078), Nature Science Foundation of Anhui Provincial Colleges (No. KJ2012Z302), Anhui Provincial College Foundation for Young Talent (No. 2012SQRL251), and the key project of Education Department of Sichuan Province (No. 12ZA070).