The samples with obviously incomplete or wrong data are eliminated, whether NIR spectra or SSC, thus obtaining a total of 122 samples. Then samples were divided into the training set and test set by the SPXY algorithm (Galvao et al., 2005), with 70% of the samples as the training set and 30% as the test set. The principle of the Kennard stone algorithm (KS) algorithm is to calculate the Euclidean distance among all samples: select two samples with the maximum Euclidean distance into the training set, then carry out the iterative calculation, select the samples with the maximum and minimum Euclidean distance into the training set until the number of samples required by the training set is reached. SPXY algorithm is based on the KS algorithm, and it furthermore involves the chemical values and spectra among samples when calculating Euclidean distance, which makes the training set more representative, and makes the generalization ability of the established prediction model better.

The random frog (RF) algorithm (Li et al., 2012) was used to obtain the corresponding number of characteristic wavelengths of NIR spectral data, which has the features of conceptually simplicity, and fewer parameters to be trained in algorithm implementation, strong global search and optimization ability, etc. The principles of the algorithm are as follows. Each sample in a population is regarded as a frog. Then the whole population is divided into m sub-groups with the scale of n. In each sub-group, the frogs with the best and worst fitness are used to produce a new child frog, which can be viewed as a jump of the best frog. If the fitness of the child frog is better than the parent with the worst fitness, replace the worst parent with the child, otherwise, randomly generate a new child, which can be viewed as the best frog's jumping again. If the fitness of the new child frog is still worse than the worst parent, then randomly generate another new child to replace the parent with the worst fitness. The evolutionary strategy of the random frog algorithm is like frogs jumping toward the optimal solution so that the algorithm gradually converges to the optimal solution.

The more specific steps of this algorithm are as follows: First, initialize parameters. Second, randomly generate an initial frog group and calculate the fitness of each frog. Third, arrange the frogs in descending order according to the value of fitness, and record the local optimal solution P_x. Then divide the F frogs from the initial group into sub-groups, namely, allocate F frogs into m sub-groups with the scale of n. Fourth, do a local search process, i.e., do the process described above in each sub-group. As a result, sub-groups do the fourth process, redivide the frog group, do the same operation as the first round, and record the global optimal solution P_x. Fifth, verify the calculation stop condition. If the convergence conditions of the algorithm are reached, the RF algorithm ends. If the global optimal solution has not been significantly improved, the execution of the algorithm should also be stopped.

To validate the performance of the RF algorithm in this task, the other common wavelength selection namely the competitive adaptive reweighted sampling algorithm (CARS) is used for comparison with the RF algorithm.

The AdaBoost classifier (Freund et al., 1999) is selected for modeling. Boosting is an important integrated learning technology, which can enhance weak classifiers with poor prediction performance into strong classifications with good prediction performance in a cascade way. The core of its adaptability is that the wrong samples of the previous basic classifier will be strengthened, and all the weighted samples will be used to train the next basic classifier again. At the same time, a new weak classifier is added in each round until a predetermined small enough error rate or a predetermined maximum number of iterations is reached.

Specifically, the entire AdaBoost iterative algorithm consists of three steps: First, initialize the weight distribution of training data. If there are n samples, each training sample is given the same weight of 1/n at the beginning. Second, train weak classifiers. In the specific training process, if a sample point has been accurately classified, its weight will be reduced in the construction of the next training set; On the contrary, if a sample point is not accurately classified, its weight will be improved. Then, the weight updated sample set is used to train the next classifier, and the whole training process goes on in this way, iteratively. Third, combine the trained weak classifiers into strong classifiers. After the training process of each weak classifier, increase the weight of the weak classifier with a small classification error rate to make it play a greater decisive role in the final classification function while doing the opposite operation for the weak classifier with a large classification error rate.

To compare the performance of various classifiers, we choose AdaBoost, k-Nearest Neighbor (KNN), Bayes classifier, and LS-SVM to explore the best-performing classification model. In the current study, we use Matlab and Weka to establish the models.

To verify the efficiency of the classification system, evaluation indicators viz. confusion matrix, accuracy, precision, recall, F₁, micro-measures, and macro-measures are considered.

1) Confusion matrix: Assume that “Positive” means the positive samples and that “Negative” means the negative samples. Meanwhile, “True” represents that the prediction is right while “False” represents that the prediction is wrong. As a result, “TP” and “TN” mean that the positive sample is classified as “Positive” and that the negative sample is labeled as “Negative”, respectively. “FP” and “FN” represent that the negative sample is labeled as “Positive” and that the positive sample is classified as “False.” The four indicators make up the confusion matrix.

2) Accuracy: It is a ratio that is used to estimate the classification ability of a model within the range from 0 to 1. Generally speaking, the larger accuracy is, the better the classification is. It can be calculated by the following equation:

3) Precision: Precision is only used to evaluate the classification ability of the positive samples within the range from 0 to 1. It is obvious that the larger precision is, the more effective the system is. It is computed by:

4) Recall: It is a ratio from 0 to 1. Obviously, the more it is close to 1, the better the system is. The calculation equation is:

5) F₁: It is a harmonic mean of recall and precision. In this study, we consider the weight of recall and precision the same, which means attaching the weight of 0.5 to either of them. It is calculated by:

6) Receiver Operating Characteristic (ROC) Curve and Area Under Curve (AUC): The abscissa of the ROC curve is the false positive rate (FPR) while the ordinate is the true positive rate (TPR), where FPR=FPTN+FP and TPR=YPTN+FN. Generally speaking, the closer the ROC curve is to the upper left corner of the image, the better the performance of the binary classifier. AUC is the area under the ROC curve and it is generally within the range of (0.5, 1). When the closer the ROC curve is to the upper left corner, the greater the value of AUC.

The NIR spectra in different picking times are shown in Figure 1. The trend of the citrus spectra collected each time is similar. There is an obvious absorption trough near 1,080, 1,300, 1,700, and 2,200 nm, respectively. According to the principles of NIR spectroscopy, due to the fact that the sample will selectively absorb NIR waves with different frequencies, the NIR wave which passes through the sample will become weaker in some wavelength ranges, and the transmitted NIR wave will carry the information of organic component and structure. Therefore, it can be inferred that these absorption troughs can probably be the most informative areas, which can be reflected in the characteristic wavelength selection.

Our reason for using fruits with different picking periods for modeling is to increase the coverage of the SSC, allowing a larger range of variation in the spectral data and ultimately increasing the model robustness. We performed the statistical tests on the obtained spectral data and SSC and found significant differences between spectral data and SSC for non-adjacent picking periods (p < 0.05) and no significant differences for adjacent picking periods (p > 0.05). This is in accordance with expectations. Because, as the fruit ripens, the SSC will certainly increase and the spectral differences will increase.

As mentioned above, the characteristic wavelength selection can accelerate the computation speed and reduce computation cost to a degree. RF algorithm is chosen to generate characteristic wavelengths with the numbers 10, 50, 100, 200, 250, 275, and 300, respectively, which is displayed in Figure 2. It is easy to find that the larger the number of characteristic wavelengths is, the smaller the cutoff probability is. The cutoff probability indicates the threshold value for screening the required number of informative wavelengths. The wavelength numbers, 10, 50, 100, 200, 250, 275, and 300, respectively correspond to the cutoff probabilities, 0.0471, 0.0260, 0.0225, 0.0222, 0.0091, 0.0060, and 0.0047. The cutoff probability generally decreases as the number of informative wavelengths increases (Figure 2). Meanwhile, it is true with what has been inferred in the above section that the absorption troughs can be the most informative, most of the retaining wavelengths gather in the areas inferred before viz. 1,080, 1,300, 1,700, and 2,200 nm. This probably has a relationship with the functional groups viz. —OH, —CH, —NH.

In addition, the classification models based on CARS selected wavelengths are established, and their performance is not as good as the RF-based models. For example, when ten characteristic wavelengths are selected, the RF-based model gives a better performance than the model based on CARS, with the accuracy of 60.9, 69.6, 65.2, and 62.2% vs. 52.78, 52.78, 58.33, and 47.22% for AdaBoost, KNN, Bayes, and LS-SVM modeling methods, respectively. Overall, CARS does not perform as well as RF for the informative wavelength selection.

The spectral properties of plants are mainly determined by their internal structure. For the current study, the obtained spectra are the result of the interaction of the incident light with the chemical composition and physical structure of Citrus. For Miyagawa Satsuma, its structure can be divided into exocarp (oil cell layer), mesocarp (white cortex), endocarp, fruit, and fruit stem from outside to inside. Among them, the surface of the soluble dietary fiber of mandarin pulp is not smooth, the strips and gaps are intertwined, and there are raised particles; the surface of the soluble dietary fiber of mandarin peel is larger, but the surface depressions are mixed with a few spherical particles. There is a strong interaction between the two molecules.

As an important indicator for evaluating fruit sweetness, SSC is mainly composed of soluble sugars (including sucrose, fructose, and glucose). In the NIR region, the stretching and deformation vibration absorption peaks of O−H bonds in soluble sugars are located around 1,440 and 2,080 nm, and there are three absorption peaks of soluble solids at 980, 1,169, and 1,485 nm (Musingarabwi et al., 2016). The water content has a great influence on the absorption of the plant spectrum. Under the condition of multi-layer leaves, the water absorption bands at 1,100 and 960 nm have a great influence on spectral reflectance. Absorption leads to a decrease in reflectance and an increase in absorbance, and peaks of reflectance (i.e., peaks and valleys of absorbance) appear at 1,600 and 2,200 nm (Ma et al., 2017).

The wavelengths selected by RF include three characteristic wavelengths near the absorption peaks of soluble solids at 980 nm, 1,169 nm, and 1,485 nm, and two characteristic wavelengths near the absorption peaks of stretching and deformation vibrations of O−H bonds in soluble sugars at 1,440 nm and 2,080 nm, and a characteristic wavelength near the strong absorption peak of water at 1,400 nm. This analysis explains why the model based on the RF selected wavelengths performs better.

The research holds the opinion that consumers are more concerned about whether the Miyagawa Satsuma is sweet or not, but not the concrete value of sweetness. Referring to Figure 3, the dichotomous map or histogram of 122 Miyagawa Satsuma citruses' SSC, the distribution of this figure is roughly similar to the normal distribution, whose mean of all citruses' SSC is 9.06 Brix and the SD is 0.93 Brix. To carry out our belief, 9 Brix was taken as the boundary after asking an expert in agriculture for advice. As a consequence, the citruses with SSC more than or equal to 9 Brix are considered to be sweet and the others are not sweet for the following classification modeling.

Figure 4 shows the comparison of NIR spectra of sweet and unsweet fruit samples. As shown in Figure 4, the large overlap between the spectral curves of the sweet and unsweet samples indicates that the model will not perform as expected if the model is constructed based on original spectra. Therefore, we need to select the informative wavelengths specific to SSC classification, and then combine them with pattern recognition methods for modeling.

As mentioned before, AdaBoost, KNN, Bayes, and LS-SVM are adopted to establish classification models. The performance comparison of different classifiers under different characteristic wavelengths is shown in Table 1. The conclusion can be drawn that when the number of characteristic wavelengths is 275, the classification model established by the AdaBoost classifier performs best (bold in the table), with accuracy, precision, recall, and F₁-score 78.3%, 80.5%, 78.3%, 0.780, respectively.

From the perspective of the number of characteristic wavelengths, when the number is 10, the best performer is the KNN classifier, with accuracy, precision, recall, and F₁-score 69.6%, 69.8%, 69.6%, and 0.696. When the number is 50, LS-SVM performs best according to the accuracy of 67.6%, precision of 57.1%, recall of 100%, and F₁-score 0.727. When the number is 100, Adaboost performs best while the best performer belongs to Bayes when the number is 200. As for the number 250, the results of AdaBoost are as good as Bayes. Finally, AdaBoost still stands out among four classifiers when under the condition of 300 characteristic wavelengths. From Table 1, it can be found that when the number of characteristic wavelengths is either too small or too large, the performance of every different classifier is not as good as the situation when the number is proper, from the perspective of four classifiers.

Compared to the results of original wavelengths number 1,556 without any procession, the best results of AdaBoost, KNN, and LS-SVM happen when they are through characteristic wavelengths selection, however, except Bayes. But after weighing the wavelength reduction and performance, it is reasonable to think that characteristic wavelength selection also works for Bayes.

The ROC of positive and negative samples of the test set is shown in Figure 5. It can be seen that the ROC curves of positive and negative samples are all close to the upper left corner, and the total AUC is 0.841, indicating that the model has good robustness and can adapt flexibly to the uneven distribution of positive and negative samples in actual situations.

Too many spectral features bring information redundancy, and too few spectral features bring information loss. Based on the experimental results, for this classification task, the optimal number of spectral features is 275. Compared to the other modeling methods, the AdaBoost method achieves the best performance at 275 wavelength numbers. This is because AdaBoost combines multiple weak classifiers in a reasonable way to make one strong classifier. The other three methods used in this paper just give one separate model.