Chlorophyll content was measured based on the absorbance of the supernatant dimethyl-formamide extract (Table 1). The mean values of chlorophyll content per leaf area (μg cm⁻²) were 53.77 and 74.92 on 10 May, 47.07 and 46.25 on 12 July, and 111.93 and 95.32 on 26 July for 0% and 85% shading, respectively (Table 1). The difference in chlorophyll content was only significant between the treatments on 10 May, although a Tukey–Kramer test showed that shading was not effective for increasing the chlorophyll content of second picking leaves. In fact, this treatment prevented increases in chlorophyll content and merely resulted in an increased difference (albeit not significantly so). Figure 1 shows the chlorophyll/carotenoid ratios calculated for the different picking dates and shade treatments. While ratios ranged from 2.71 to 3.91 for the unshaded samples picked on 10 May, they were greater than 4.00 for all other samples (barring some irregular values).

Figure 2 shows the mean reflectance for each date and treatment. A comparison of leaves from the first picking (10 May) showed that shading pushed the reflectance near to the green peak and lower at the red edge inflection point (REIP). Further, the reflectance of the 0% and 85% shaded samples separated completely at certain wavelengths (e.g., 725 nm). However, these tendencies were not observed during subsequent pickings. Reflectance values at some wavelengths were required to separate the samples of the two treatments. Thus, reflectance values at 400, 414, 427, 437, 515, 692, and 780 nm and at 539, 698, and 752 nm were differentiated using a stepwise linear discriminant analysis for measurements obtained on 12 and 26 July, respectively.

The correlation coefficients between the reflectance and chlorophyll content (Figure 3) revealed two troughs: one near the green peak (R = −0.70 at 552 nm for shaded leaves on 10 May; R = −0.75 at 535 nm for non-shaded leaves on 10 May; R = −0.74 at 553 nm for shaded leaves on 12 July; R = −0.71 at 555 nm for non-shaded leaves on 12 July; R = −0.70 at 550 nm for shaded leaves on 26 July; R = −0.38 at 551 nm for non-shaded leaves on 26 July) and the other near the REIP (R = −0.85 at 718 nm for shaded leaves on 10 May; R = −0.70 at 707 nm for non-shaded leaves on 10 May; R = −0.88 at 720 nm for shaded leaves on 12 July; R = −0.91 at 720 nm for non-shaded leaves on 12 July; R = −0.91 at 735 nm for shaded leaves on 26 July; R = −0.74 at 726 nm for non-shaded leaves on 26 July). With the exception of non-shaded leaves collected on 10 May, the reflectance near the REIP showed higher absolute values of correlation coefficients than those near the green peak. Furthermore, no clear correlation existed between reflectance near the green peak and chlorophyll content when all measurements were combined.

The first derivative spectra confirmed a positive correlation between the REIP and wavelengths that are slightly longer than at the green peak (between 550 and 650 nm) and a negative correlation between wavelengths that are slightly shorter than at the green peak (between 500 and 550 nm) and the start of the red edge domain. The highest positive correlations were confirmed at 576 (R = 0.92), 633 (R = 0.93), 644 (R = 0.99), 735 (R = 0.97), 562 (R = 0.96), and 755 nm (R = 0.91) and the highest negative correlations were confirmed at 533 (R = −0.91), 525 (R = −0.92), 515 (R = −0.96), 702 (R = −0.98), 526 (R = −0.97) and 702 nm (R = −0.90) for shaded leaves on 10 May, non-shaded leaves on 10 May, shaded leaves on 12 July, non-shaded leaves on 12 July, shaded leaves on 26 July, and non-shaded leaves on 26 July, respectively.

The optimal values of hyperparameters are shown in Figure 4. When the original reflectance was used, the mean values for combinations of hyperparameters were (ntree, mtry, nodesize, nodedepth, nsplit) = (513, 11, 4, 30, 10) for RF, (C, ϭ) = (2¹⁸, 2⁻¹⁰) for SVM, (number of hidden layers, unit size of first layer, unit size of second layer, unit size of third layer, unit size of the fourth layer, unit size of the fifth layer, unit size of the sixth layer, batch size, learning rate, number of epochs, rate of drop out, weight decay) = (4, 41, 45, 41, 43, 44, 39, 13, 0.006919, 100, 0.157386, 0.005528) for DBN, and (Cr, Kp) = (2¹⁵, 2¹) for KELM, while (ntree, mtry, nodesize, nodedepth, nsplit) = (519, 13, 4, 30, 11) for RF, (C, ϭ) = (2²⁰, 2⁻¹²) for SVM, (number of hidden layers, unit size of first layer, unit size of second layer, unit size of third layer, unit size of fourth layer, unit size of fifth layer, unit size of sixth layer, batch size, learning rate, number of epochs, rate of drop out, weight decay) = (4, 43, 46, 46, 44, 43, 41, 11, 0.006685, 104, 0.157487, 0.005637) for DBN, and (Cr, Kp) = (2¹⁷, 2⁻⁶) for KELM.

Figure 5 shows the relationships between estimated and measured chlorophyll contents, the statistics of RPD (ratio of performance to deviation) and RMSE values calculated using regression models based on machine learning algorithms are shown in Table 2, and the performances of regression models based on machine learning algorithms are shown in Figure 6 and Figure 7. For RF and KELM, derivative spectra values were effective for estimating chlorophyll content rather than reflectance values, while the other two algorithms had smaller RMSEs when reflectance was used. For all algorithms, the mean values of RPD were greater than 1.4 (Category B) when original reflectance values were applied, which indicates that all resulting regression models were acceptable for estimating chlorophyll content. Mean RPD values were greater than 2.0 (Category A) when derivative spectra values were used. For all 100 repeats, DBN and KELM displayed RPD values of greater than 1.4 when reflectance data were used. When derivative spectra values were used, KELM was still acceptable for all 100 repeats; however, DBN occasionally produced RPD values below 1.4 (four instances).

The DSAs (data-based sensitivity analyses) showed similar patterns of importance among the different algorithms (Figure 8). The highest importance values were confirmed at 701–750 nm for SVM and at 751–800 nm for RF, DBN, and KELM when first derivative spectra were used. The reflectance at 701–750 nm still had the greatest influence on chlorophyll content estimation; however, its importance was mostly unclear, except when using the RF technique and near the green peak for SVM and KELM.

In higher plants like tea trees, chlorophyll pigment consists of chlorophyll a and chlorophyll b. Concentrations relate closely to primary production because these pigments absorb sunlight and use their energy to synthesize carbohydrates using CO₂ and H₂O [49]. While carotenoids are also involved in photoprotection and light collection during photosynthesis [50], they also help to protect unsaturated fatty acids, phospholipids, and galactolipids from oxidative damage [51]. Some previous studies showed that the chlorophyll a/b ratio increases linearly, and the ratio is positively correlated with the amount of the core complex of photosystem II [52,53]. On the other hand, carotenoids are also involved in photoprotection and light collection in photosynthesis [54], and they also help to protect unsaturated fatty acids, phospholipids, and galactolipids from damage [51]. Based on these features of photosynthetic pigments, the total chlorophyll/carotenoid ratio or chlorophyll a/carotenoid ratio have been used as good indicators for evaluating environmental stress in plants [8,22,55]. Generally, shaded leaves contain more photosynthetic pigments than leaves in sunlight, because such leaves increase their chlorophyll a content to allow themselves to harvest more light and nitrogen [56]. Thus, light stress increases the chlorophyll/carotenoid ratio. In this study, an experiment was conducted in a greenhouse, an environment that may stress tea trees over and above shade treatment.

Previous studies have evaluated the performance of random forest (RF) regression and reported that it possessed better results than stepwise regression and support vector machine (SVM), linear regression, and radiative transfer modelling [57] for estimating vegetation properties [58]. However, more suitable algorithms were found and kernel-based extreme learning machine (KELM) generally performed the best (49 and 57 out of 100 repetitions for reflectance and first derivative spectra, respectively) for estimating the chlorophyll content when assessed using the ratio of performance to deviation (RPD) values. Although SVM’s robustness has been reported in some studies [59,60,61], and it performed best in 20 and 37 of the repeats, it also showed the worst performance in 28 and 33 repetitions for the reflectance and first derivative spectra, respectively. These results strongly suggest that SVM is not a stable method. KELM and SVM are both kernel-based algorithms, and poor selection of kernel function parameters may negatively affect their accuracies [62]. Indeed, the variance of the kernel function parameters of KELM was apparently smaller than that of SVM. The selected the kernel bandwidth (σ) values (of the SVM-based approach) ranged from 2⁻⁴⁰ to 2⁵⁰ and from 2⁻⁵⁰ to 2⁴⁹, while the kernel parameter (Kp) ranged from 2⁻⁸ to 2²⁴ and from 2⁻¹⁰ to 2¹⁰ for reflectance and first derivative spectra, respectively. Furthermore, ELM has fewer optimisation constraints [63], which has been shown to be an advantage in regression applications [64]. Although deep belief nets (DBN) has also been reported to have great performance [65] and it performed best in repetitions 30 and 6, its poor performance was also recognised. DBN had the maximum number of hyperparameters of the four algorithms examined in this study since a total of twelve hyperparameters (unit sizes of six layers, batch size, learning rate, number of epochs, rate of drop out and weight decay) had to be optimised. The relatively small training data set may have prevented the method from producing sufficient results for tuning its measured chlorophyll content for both reflectance and first derivative spectra. Further, the order of KELM, DBN, and SVM was the same for both the reflectance and first derivative spectra, although the similarity with the measured chlorophyll content decreased. The use of reflectance was more effective for this purpose due to its ability to recognise patterns, and the first derivative spectra were noisier than the original reflectance data (Figure 3), which might have prevented the machine learning algorithms from producing robust results. However, the models based on RF changed dramatically, and there was a clear advantage for using first derivative spectra. Generally, importance is focused on a small number of variables in RF-based models [6]. Its performance may be improved if the variables highly correlated with chlorophyll content are selected and if the effects from noisy variables (e.g., first derivative values from 400 to 500 nm and longer than 800 nm) are negligible.

High correlation coefficients were confirmed between the measured values and estimated values from KELM or DBN, and irregular values were not confirmed for any data or treatment (Figure 4). On the contrary, RF-based methods produced less stressed samples (i.e., non-shaded samples on 10 May and 12 July). In this study, most of the samples were affected by shading treatments or the greenhouse, and this result implies that RF is unsuitable for imbalanced data caused by the small sample size of lower stressed measurements. SVM also had a similar feature, and its estimated values were almost constant in some combinations of training data, even though a stratified random sampling approach was applied (Figure 4). Generally, models based on KELM performed best for both reflectance and first derivative spectra for each treatment (open or shaded tea trees; Figure 6). However, those based on DBN performed best for the shaded samples collected on 10 May and for the unshaded samples collected on 26 July when reflectance was used. DBN tended to estimate the chlorophyll content with greater error since the sample sizes and standard deviations calculated from the chlorophyll content were small. If either of these issues is removed, DBN may, however, constitute the better option. It performed relatively well for the shaded samples collected on 26 July, which was the smallest sample collected.

Derivative spectra have been applied for quantifying the leaf chlorophyll content, and its great potential has been shown [21,44,45,66,67]. However, the first derivative spectra were only advantageous for the RF-based method since the accuracies of the other algorithms were reduced, or the differences in accuracy were small. Furthermore, although RF performed better for the shaded samples when reflectance data were used, this tendency was obscure for the first derivative spectra for all observations. RF was effective in certain bands because the importance concentrated on some specific bands (Figure 8). However, it is usually difficult to calculate first derivative spectra from the hyperspectral data obtained from satellite- or air-borne remote sensing, whose bandwidths are wider than those from FielSpec 4, limiting the applicability of this algorithm.

Our experiments were performed on six tea trees in a greenhouse at the Institute of Fruit Tree and Tea Science, National Agriculture and Food Research Organization, Shimada, Japan. Three trees were placed under a Dio Chemicals shading net #1800 (80%–85% shading, Dio Chemicals Ltd., Japan), while the remaining three trees were cultivated under 0% shading (unshaded; Figure 9), for the periods from 19 April to 10 May and 14 June to 12 July for the first and second flushes of leaves, respectively. After the first two pickings (sampled on 10 May and 12 July), all shade nets were removed, and the last samples were collected on 26 July. The numbers of samples are shown in Table 1.

New shoots were sampled from each tree on each sampling day, and reflectance and chlorophyll contents were measured from them. The numbers of samples collected differed between the two treatments since one tree and several leaves died before sampling.

An ASD FieldSpec4 unit (Analytical Spectral Devices, USA) was used to obtain reflectance data from leaf clippings. This device has three detectors: visible and near-infrared (VNIR), short wave infra-red (SWIR) 1, and SWIR 2. The splice correction function of ViewSpec Pro Software (Analytical Spectral Devices) was applied to correct differences in the spectral drifts (at 1000 and 1800 nm) caused by inherent variation in detector sensitivities. The first derivative spectra were also calculated from these reflectance spectra. After measuring reflectance, leaf discs (8 mm in diameter) were prepared and soaked in dimethyl–formamide to measure pigment concentrations using dual-beam scanning ultraviolet-visible spectrophotometers (UV-1280, Shimadzu, Japan). To quantify chlorophyll a, b and carotenoid contents (in μg ml⁻¹) from the dimethyl–formamide extracts, the following calculations [68] were applied, and the results are expressed in μg cm⁻²:(1)Car=(1000A480−1.12Chla−34.07Chlb)/245 (2)Chla=12A663.8−3.11A646.8 (3)Chlb=20.78A646.8−4.88A663.8 where A is the absorbance, and the subscripts represent the wavelength (nm).

For modelling, all measurements were divided into three groups (a training dataset (50%), a validation dataset (25%) and a test data dataset (25%)) using a stratified sampling approach [69] that was repeated a hundred times to obtain robust results.

When applying machine learning algorithms, it is necessary to select wavelengths that are effective for removing non-informative variables to obtain better and simpler prediction models [70]. The genetic algorithm (GA)-based approach is an adaptive heuristic search algorithm based on the concept of natural selection and survival of the fittest among individuals over consecutive generations. It was used to estimate the chlorophyll content because of its high performance in both regression and classification [70,71,72,73]. In this approach, each of five generations was composed of a population of character strings (i.e., combinations of narrow wavebands) analogous to a chromosome, from which the best waveband combination was finally selected after a process of evolution using R version 3.5.3 [74]. The regression models were then created using the selected bands and different supervised learning methods: RF, SVM, DBN, and KELM. For optimising the hyperparameters of these machine learning algorithms, Bayesian optimisation was applied with the Gaussian process [37,39] using R version 3.5.3 [74] and the “rBayesianoptimization” package [75].

The root-mean-square error (RMSE, Equation (4)) and the ratio of performance to deviation (RPD, Equation (5)) [89] were applied to evaluate each method’s estimation accuracy using R version 3.5.3 [74]. Each method was classified into three categories according to RPD values: Category A (RPD > 2.0), Category B (1.4 ≤ RPD ≤ 2.0) and Category C (RPD < 1.4). The models categorised as A or B were assumed to have the potential to estimate chlorophyll content [90]:(4)RMSE=1n∑i=0n(yi^−yi)2 (5)RPD=SD/RMSE where SD is the standard deviation of the real chlorophyll content, which was calculated from the measurements from the HPLC in the test data, n is the number of samples, yi is the real chlorophyll content, and yi^ is the estimated chlorophyll content.

Although RF generates important measures for variables, other algorithms are generally more difficult to implement. Since few studies have attempted cross-algorithm comparisons, a sensitivity analysis of selected narrow-bands of the machine learning algorithm-based regression models using data-based sensitivity analysis (DSA) was conducted. This analysis performs a black-box use of the fitted models with their machine learning algorithms by querying the fitted models with sensitivity samples and recording their responses [91].