Comparison of multivariate models and variable selection algorithms for rapid analysis of the chemical composition of field crops

Figures & data

Table 1. The key parameters of genetic algorithm (GA) for the prediction of different crop constituents.

Constituents	Ct	Nt	Pt
Population size	64	64	64
Window width	1	1	1
Penalty slope	0.05	0.05	0.03
Mutation rate	0.005	0.01	0.005
Crossover	double	double	double
Max generations	100	100	100
Replicate runs	10	10	10
LVs	14	13	14
RMSECV (g kg^−1)	16.74	1.75	0.43

Note: Ct, total carbon; Nt, total nitrogen; Pt, total phosphorus; LVs, the optimal number of latent variables; RMSE_CV, root mean squared error of cross-validation.

Table 2. Descriptive statistics for the concentrations of total carbon (Ct), total nitrogen (Nt), and total phosphorus (Pt) (expressed on a dry matter basis, g kg⁻¹) of field crops in China for the calibration and validation subsets.

Constituents	nSample	nOut	Range	Mean	CV	Skewness	Kurtosis
Calibration
Ct	437	16	201.80–461.54	372.10	9.80	−1.85	5.98
Nt	437	13	2.41–21.58	8.60	37.63	0.81	0.56
Pt	437	15	0.29–4.23	1.08	55.29	1.45	3.28
logCt	437	16	5.31–6.13	5.91	1.89	−0.70	0.89
logNt	437	13	0.88–3.07	2.08	18.15	−0.15	−0.17
logPt	437	15	−1.24–1.44	−0.06	−160.11	0.04	−0.52
Validation
Ct	187	–	207.18–423.83	366.85	9.66	−2.07	6.47
Nt	187	–	3.10–18.75	8.03	31.53	0.83	1.37
Pt	187	–	0.30–3.63	1.07	51.37	1.41	3.29
logCt	187	–	5.33–6.04	5.90	1.88	−0.80	0.69
logNt	187	–	1.13–2.93	2.04	15.54	−0.22	0.30
logPt	187	–	−1.20–1.29	−0.04	−179.15	0.11	−0.53

Note: logCt, logNt, and logPt mean natural log-transformed Ct, Nt, and Pt, respectively; n_Sample, number of samples used for calibration or validation; n_Out, number of outliers discarded during calibration; CV, coefficient of variation (%).

Figure 1. Visible and near-infrared absorbance spectra of crop samples for total carbon prediction (n = 608).

Table 3. Statistical evaluation of different variable selection methods used to predict the crop constituents (expressed on a dry matter basis, g kg⁻¹) derived by PLSR and SVMR models for the calibration and validation subsets using visible and near-infrared (Vis–NIR) reflectance spectroscopy.

Model	Calibration				Validation
	nSample	Time	$R_{CV}^2$	RMSECV	$R_P^2$	RMSEP
Ct
FS-PLSR	415	–	0.86	13.48	0.84	14.02
FS-SVMR	415	–	0.90	11.58	0.87	13.39
CARS-SVMR	74	0.12	0.94	9.21	0.91	11.29
GA-SVMR	76	47.00	0.93	10.09	0.88	12.71
UVE-SVMR	134	0.68	0.91	10.75	0.87	13.02
VIP-SVMR	214	0.10	0.93	9.63	0.90	11.36
Nt
FS-PLSR	415	–	0.85	1.27	0.81	1.49
FS-SVMR	415	–	0.90	1.03	0.86	0.95
CARS-SVMR	34	0.12	0.92	0.94	0.90	0.83
GA-SVMR	82	47.50	0.89	1.06	0.86	0.97
UVE-SVMR	165	0.68	0.91	0.97	0.88	0.90
VIP-SVMR	99	0.10	0.91	0.95	0.87	0.92
Pt
FS-PLSR	415	–	0.65	0.35	0.58	0.46
FS-SVMR	415	–	0.72	0.33	0.70	0.31
CARS-SVMR	67	0.12	0.76	0.31	0.73	0.29
GA-SVMR	70	48.75	0.80	0.28	0.77	0.27
UVE-SVMR	147	0.68	0.80	0.27	0.76	0.28
VIP-SVMR	136	0.10	0.77	0.29	0.74	0.30

Note: Ct, total carbon; Nt, total nitrogen; Pt, total phosphorus; FS, full spectrum; PLSR, partial least squares regression; SVMR, support vector machine regression; CARS, competitive adaptive reweighted sampling; GA, genetic algorithm; UVE, uninformative variable elimination; VIP, variable importance for projection; n_Sample, number of spectral variables used in the model calibration; Time, computation time (minutes) required by variable selection algorithms; R², coefficient of determination; RMSE, root mean squared error (g kg⁻¹). The results for R² and RMSE from the cross-validation and independent validation are labelled with the subscripts of CV and P, respectively.

Figure 2. Scatter plots of the measured and Vis–NIR predicted total C from different calibration models: (a) FS-PLSR, (b) FS-SVMR, (c) CARS-SVMR, (d) GA-SVMR, (e) UVE-SVMR, and (f) VIP-SVMR. Predictions on the calibration set during cross-validation (black circles, black regression lines) and predictions on the independent validation set (blue squares, blue regression lines). The 1:1 line (dotted) is shown in each figure.

Figure 3 . Scatter plots of the measured and Vis–NIR predicted total N from different calibration models: (a) FS-PLSR, (b) FS-SVMR, (c) CARS-SVMR, (d) GA-SVMR, (e) UVE-SVMR, and (f) VIP-SVMR. Predictions on the calibration set during cross-validation (black circles, black regression lines) and predictions on the independent validation set (blue squares, blue regression lines). The 1:1 line (dotted) is shown in each figure.

Figure 4. Scatter plots of the measured and Vis–NIR predicted total P from different calibration models: (a) FS-PLSR, (b) FS-SVMR, (c) CARS-SVMR, (d) GA-SVMR, (e) UVE-SVMR, and (f) VIP-SVMR. Predictions on the calibration set during cross-validation (black circles, black regression lines) and predictions on the independent validation set (blue squares, blue regression lines). The 1:1 line (dotted) is shown in each figure.

Figure 5. The comparison of spectral variables (indicated by the black vertical lines) selected by CARS, GA, UVE, and VIP from the Vis–NIR spectra transformed by the combination of the first derivative and SNV.