Spectral Index Optimization and Machine Learning for Hyperspectral Inversion of Maize Nitrogen Content

Abstract

Hyperspectral remote sensing provides a powerful tool for crop nutrient monitoring and precision fertilization, yet its application is hindered by high-dimensional redundancy and inter-band collinearity. This study aimed to improve maize nitrogen estimation by constructing three types of two-dimensional full-band spectral indices—Difference Index (DI), Simple Ratio Index (SRI), and Normalized Difference Index (NDI)—combined with spectral preprocessing methods (raw spectra (RAW), first-order derivative (FD), and second-order derivative (SD)). To optimize feature selection, three strategies were evaluated: Grey Relational Analysis (GRA), Pearson Correlation Coefficient (PCC), and Variable Importance in Projection (VIP). These indices were then integrated into machine learning models, including Backpropagation Neural Network (BP), Random Forest (RF), and Support Vector Regression (SVR). Results revealed that spectral index optimization substantially enhanced model performance. NDI consistently demonstrated robustness, achieving the highest grey relational degree (0.9077) under second-derivative preprocessing and improving BP model predictions. PCC-selected features showed superior adaptability in the RF model, yielding the highest test accuracy under raw spectral input (R² = 0.769, RMSE = 0.0018). VIP proved most effective for SVR, with the optimal SD–VIP–SVR combination attaining the best predictive performance (test R² = 0.7593, RMSE = 0.0024). Compared with full-spectrum input, spectral index optimization effectively reduced collinearity and overfitting, improving both reliability and generalization. Spectral index optimization significantly improved inversion accuracy. Among the tested pipelines, RAW-PCC-RF demonstrated robust stability across datasets, while SD-VIP-SVR achieved the highest overall validation accuracy (R² = 0.7593, RMSE = 0.0024). These results highlight the complementary roles of stability and accuracy in defining the optimal pipeline for maize nitrogen inversion. This study highlights the pivotal role of spectral index optimization in hyperspectral inversion of maize nitrogen content. The proposed framework provides a reliable methodological basis for non-destructive nitrogen monitoring, with broad implications for precision agriculture and sustainable nutrient management.

1. Introduction

In the context of sustainable modern agriculture, achieving precise crop nutrient monitoring and scientific fertilization management has become a critical pathway to enhancing agricultural efficiency, ensuring food security, and reducing environmental pollution [1]. Nitrogen is widely recognized as the most essential macronutrient for maize growth, acting as a structural component of proteins, chlorophyll, and nucleic acids [2], and directly regulating photosynthesis, biomass accumulation, and yield formation. It directly influences photosynthetic efficiency, dry matter accumulation, and final yield formation through participation in key enzymatic reactions, such as photophosphorylation and nitrate assimilation, as well as the regulation of plant hormone synthesis and metabolism [3]. Maize exhibits high sensitivity to nitrogen supply, and excessive nitrogen application not only leads to resource waste but also contributes to groundwater nitrate pollution and increased greenhouse gas emissions [4]. Therefore, developing non-destructive, efficient, and accurate monitoring approaches for maize nitrogen content is urgently needed to advance green agriculture [5,6].

Traditional destructive sampling methods for biochemical content inversion are time-consuming, labor-intensive [7], and limited in spatial coverage, making them unsuitable for real-time, large-scale field monitoring. Conventional remote sensing technologies, due to their low spectral resolution, fail to capture fine spectral features within narrow wavelength ranges, resulting in limited accuracy for biochemical parameter inversion [8]. Previous studies have confirmed that maize leaves exhibit distinct absorption peaks in the blue (approximately 430 nm) and red (approximately 660 nm) spectral regions, high reflectance in the green band (approximately 550 nm) [9], and elevated reflectance in the near-infrared region (700–1300 nm) influenced by internal leaf structure [10]. Specifically, the 690–700 nm band is highly sensitive to stress-induced chlorophyll content changes, and the 760–790 nm range effectively reflects plant water stress [11], and the 730 nm and 960 nm bands are closely associated with plant water absorption bands [12]. Hyperspectral technology, with its hundreds to thousands of continuous narrow bands, can sensitively capture subtle spectral differences in crop leaves across the visible to near-infrared spectrum, establishing a strong correlation between spectral signals and biochemical content [13], thus providing reliable technical support for accurate maize nitrogen content inversion [14,15,16].

However, hyperspectral data suffer from high information volume, significant band redundancy, and strong collinearity among variables, which constrain their application in high-precision inversion of crop physiological parameters. Li et al. (2023) found that redundant information and high collinearity in hyperspectral data limit the effectiveness and accuracy of model simulations [17]. To address this, researchers commonly employ feature selection or extraction techniques to reduce spectral data dimensionality, extracting the most representative spectral features for target variables. Zhang et al. (2019) noted that while short-wave infrared (SWIR) bands can enhance the accuracy of water and nitrogen content inversion in high-throughput remote sensing phenotyping, selecting a limited set of high-quality band combinations through appropriate dimensionality reduction significantly improves model stability and efficiency [18,19]. Among various dimensionality reduction methods, spectral indices are widely used due to their dual functionality in feature construction and selection. For instance, classic vegetation indices like NDVI and EVI enhance spectral contrast relationships through physical or mathematical formulations [20], extracting highly sensitive feature combinations in subsequent selections. Compared to conventional feature algorithms, spectral indices offer advantages such as multi-band synergy, high information utilization, and clear physical significance [21,22].

Spectral indices have evolved rapidly. Although classic indices are widely applied in crop monitoring, their reliance on fixed sensitive bands makes them susceptible to background interference under varying environmental conditions, limiting model generalization. With advancing research, spectral index construction has moved beyond traditional optical property constraints, adopting band-by-band combinatorial approaches. Chen et al. demonstrated that such methods can significantly improve accuracy under specific regional and sample conditions but often face the “curse of dimensionality” [23], creating a trade-off between computational efficiency and result stability. Consequently, selecting optimal band combinations through scientific methods to achieve spectral index optimization has become a core component in enhancing the predictive capability for crop physiological parameters. Most current studies rely solely on the Pearson Correlation Coefficient (PCC) for spectral index selection. While PCC is simple and effective for measuring linear correlations, it fails to capture nonlinear relationships between spectral indices and nitrogen content [24], often resulting in insufficiently representative selected indices. Alternative feature selection methods, such as Grey Relational Analysis (GRA) and Variable Importance in Projection (VIP), have not been widely applied in spectral index optimization [25]. Additionally, neglecting the compatibility between spectral index optimization methods and modeling algorithms [26], as well as failing to tailor index selection strategies to the characteristics of different machine learning models, limits the predictive potential of spectral indices, ultimately affecting model inversion accuracy and generalization [27,28]. To ensure consistent evaluation, we also predefined a single selection rule for determining the overall optimal pipeline: the configuration achieving the highest R² on the independent validation set, with RMSE used as the secondary criterion. The detailed implementation is described in the Methods section.

To address these gaps, this study proposes a comprehensive framework for maize nitrogen estimation that integrates full-band index construction, preprocessing methods (RAW, FD, SD), and multiple feature selection strategies (GRA, PCC, VIP). The optimized indices are then coupled with three representative machine learning models—Backpropagation Neural Network (BP), Random Forest (RF), and Support Vector Regression (SVR)—to evaluate their predictive performance and stability. Specifically, we aim to: (i) compare the adaptability of different indices and selection methods, (ii) identify the optimal selection–modeling combination for nitrogen inversion, and (iii) provide methodological insights for non-destructive nitrogen monitoring to support precision agriculture [29].

2. Materials and Methods

2.1. Study Site and Experimental Design

The study was conducted at the Dryland Agriculture Experimental Station in Yuzhong County (104°09′ E, 35°56′ N; altitude 1749 m, Figure 1), Gansu province, China, which is situated in a typical semi-arid climatic zone. The site has an average annual evaporation of 1450 mm, mean annual precipitation of 327 mm (mainly concentrated from July to September), mean annual temperature of 7.6 °C, accumulated temperature ≥0 °C is 3244 °C, accumulated temperature ≥10 °C is 2479 °C, and annual sunshine duration ranging from 1626 to 2666 h.

A field experiment was conducted to investigate the effects of varying plant densities (42,000, 63,000, and 84,000 plants ha⁻¹) and nitrogen application rates (0, 80, 160, and 240 kg N ha⁻¹) on maize growth. Plant densities were achieved by adjusting row spacing, combined with four nitrogen levels, resulting in 12 treatment combinations. Each treatment was replicated three times, yielding a total of 36 plots. A 2-m buffer zone was established around the experimental area, and 1-m isolation strips between adjacent plots. Maize was sown on 25 April 2024 and harvested on 27 September 2024. Irrigation was scheduled based on reference crop evapotranspiration (ET₀), while other management practices followed local recommendations.

2.2. Data Collection

Hyperspectral data were collected on 5 July, 11 July, 16 August, and 22 August 2024. Canopy spectral reflectance of maize was measured using a FieldSpec 4 spectroradiometer (Analytical Spectral Devices, Inc., Boulder, CO, USA) covering the 350–2500 nm range. The sampling interval was 1.4 nm for 350–1000 nm and 2 nm for 1001–2500 nm. The spectral resolution was 3 nm at 700 nm, 10 nm at 1400 nm, and 10 nm at 2100 nm [30]. The instrument automatically interpolated the sampled data to 1 nm intervals for output. The fiber optic cable length was 1.5 m, with a field-of-view angle of 25°. Measurements were taken under clear, windless conditions between 11:00 and 14:00, ensuring the fiber optic probe was oriented vertically downward and positioned approximately 1 m above the canopy top. For each plot, three representative quadrats were selected to reflect the plot’s growth status. Ten spectral curves were recorded per quadrat, and the average was used as the spectral reflectance for that quadrat [31], resulting in a total of 144 datasets. A standard whiteboard calibration was performed prior to each sample measurement. Destructive sampling was conducted synchronously within the hyperspectral measurement quadrats to determine maize canopy nitrogen content. Data processing and analysis were conducted using ViewSpecPro Version6.2 (ASD Inc., Boulder, CO, USA) for spectral data inspection and calibration, and MATLAB R2023b (MathWorks, Natick, MA, USA) for spectral index construction, feature selection, and model implementation.

2.3. Spectral Data Preprocessing

Raw spectra comprehensively record the absorption and scattering information generated by the interaction between samples and light. However, they inevitably include interferences such as instrumental background noise and baseline drift, which introduce uncertainty into subsequent analyses. To minimize errors and enhance the signal-to-noise ratio of spectral data, preprocessing of the raw spectra is essential. Existing spectral preprocessing techniques are diverse and can be categorized into four main types based on their characteristics: baseline correction [32], scatter correction [33], smoothing, and proportional scaling (

Table 1. Preprocessing methods of spectral data.

Preprocessing Method [35]	Category	Abbreviation	Main Function
RAW	Raw reflectance	RAW	Original spectral data without any processing
Standardization	Min–Max scaling	MMS	Scales values into the range [0, 1]
	Z-score scaling	Z-Score	Standardizes data to zero mean and unit variance
	Normalization	Normalize	Normalizes samples to eliminate scale differences
Smoothing	Moving average	MovingAvg	Reduces noise and smooths spectral curves
	Savitzky–Golay smoothing [36]	SG	Smooths spectra while preserving curve shape
Scatter correction	Multiplicative scatter correction	MSC	Corrects scattering and particle size effects
	Standard normal variate	SNV	Reduces variability caused by scatter differences
Derivative transform	First derivative	FD	Enhances slope changes and highlights spectral inflection points
	Second derivative	SD	Strengthens spectral features and improves resolution
Baseline correction	Detrend	Detrend	Removes baseline drift and background trends

) [34]. The final preprocessing method was determined according to the correlation between spectral information features and nitrogen content, with raw spectra (RAW), first-order derivative (FD), and second-order derivative (SD) were selected as the three preprocessing approaches.

2.4. Spectral Index Construction and Selection Methods

To fully exploit the spectral features in hyperspectral data that are most sensitive to variations in maize nitrogen content, this study selected three types of two-dimensional spectral indices based on a full-band combination strategy: Normalized Difference Index (NDI), Simple Ratio Index (SRI), and Difference Index (DI) [37,38,39,40,41,42]. The specific formulas are given in Equations (1)–(3). Subsequently, three representative feature optimization methods were employed for feature selection and comparative analysis, thereby yielding effective input variables for subsequent modeling.

$$ND{I}_{i,j}={\displaystyle \frac{R_i-R_j}{R_i+R_j}}$$

(1)

$$D{I}_{i,j}=R_i-R_j$$

(2)

$$SR{I}_{i,j}={\displaystyle \frac{R_i}{R_j}}$$

(3)

where R_i and R_j represent the reflectance at wavelengths i and j, respectively.

Hyperspectral data exhibit high dimensionality and strong inter-band correlations. Direct use in modeling can easily lead to overfitting and compromise model stability; therefore, feature optimization is essential. This study employed three methods—Grey Relational Analysis (GRA), Pearson Correlation Coefficient (PCC), and Variable Importance in Projection (VIP)—to screen the constructed spectral indices, identifying sensitive band features that are highly correlated with maize nitrogen content.

(1) Grey Relational Analysis (GRA)

Grey Relational Analysis (GRA), based on grey system theory, measures the degree of association between variables by comparing the geometric similarity between the reference sequence and comparison sequences. It is particularly suitable for analyzing small samples and non-normally distributed data [43]. The calculation formula is:

$$\xi i(k)={\displaystyle \frac{\frac{min}{i}\frac{min}{k}\left|X_0(k)-X_i(k)\right|+\rho \frac{max}{i}\frac{min}{k}\left|X_0(k)-X_i(k)\right|}{\left|X_0(k)-X_i(k)\right|+\rho \frac{max}{i}\frac{min}{k}\left|X_0(k)-X_i(k)\right|}}$$

(4)

where ξi(k) represents the correlation coefficient of sequence X_i at time k, X₀(k) is the reference sequence, and ρ is the resolution coefficient (typically set to 0.5). The mean value of the correlation coefficients is the grey relational degree, which is used to measure the correlation between the spectral index and nitrogen content.

(2) Pearson Correlation Coefficient (PCC)

The Pearson Correlation Coefficient (PCC) is used to measure the linear correlation between spectral indices and nitrogen content, with larger absolute values indicating stronger correlations [44]. The calculation formula is:

$$r={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(X_i-\overline{X}\right)}^2}\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}}$$

(5)

where r is the Pearson correlation coefficient, ranging from [−1, 1], with absolute values closer to 1 indicating stronger correlation; X_i and Y_i represent the values of the two variables for the i observation sample; $\overline{X}$ and $\overline{Y}$ are the means of the two variables; and n is the number of samples.

(3) Variable Importance in Projection (VIP)

The Variable Importance in Projection (VIP) score, based on the Partial Least Squares Regression (PLSR) model, is used to comprehensively evaluate the contribution of each variable to model interpretation and prediction. It performs exceptionally well in handling multicollinearity and high-dimensional feature data [45]. The calculation formula is:

$$VI{P}_j=\sqrt{{\displaystyle \frac{p\cdot {{\displaystyle \sum }}_{a=1}^A\left(SS{Y}_a\cdot \frac{w_{ja}^2}{\parallel w_a{\parallel }^2}\right)}{{{\displaystyle \sum }}_{a=1}^{A}SS{Y}_a}}}$$

(6)

where VIPj represents the VIP value of the j-th variable, p is the total number of independent variables, w_ja denotes the weight of variable j in the a-th latent variable, ‖wa‖ is the Euclidean norm of the weight vector, and SSYa is the sum of squares explained by latent variable a for the dependent variable. Generally, a variable is considered an important feature when VIP > 1.

2.5. Model Construction

To comprehensively evaluate the adaptability and predictive capability of different feature selection strategies in spectral inversion modeling, the top-ranked spectral indices (based on scores) were selected using GRA, PCC, and VIP as input variables, with maize plant nitrogen content serving as the dependent variable. Three typical regression models were constructed: Backpropagation Neural Network [46] (BP), Random Forest [47] (RF), and Support Vector Regression (SVR). Each model offers distinct advantages, making them suitable for nonlinear regression, high-dimensional multivariate inputs, and small-sample modeling scenarios, with strong generalization ability and robustness.The methodological workflow of the entire process (including spectral index construction, feature selection, and model construction) is illustrated in Figure 2, which is the methodological workflow diagram for this study.

During the model performance evaluation phase, the R² (Formula (6)) was used to measure the model’s ability to explain the variance in PNC, where a value closer to 1 signifies a better model fit. The (RMSE, Formula (7)) quantified the average magnitude of the deviation between predicted and observed values, with lower values indicating higher prediction accuracy. We predefined the optimal pipeline as the configuration achieving the highest R² on the independent validation set, with RMSE as a secondary criterion. In addition, to ensure practical interpretability, we also report robust pipelines that show stable performance across preprocessing scenarios and datasets.

$$R^2={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^{\mathrm{n}}({\widehat{y}}_i-\overline{y})}}{{\displaystyle {\sum }_{i=1}^n(y_i-\overline{y})}}}$$

(7)

$$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{({\widehat{y}}_i-y_i)}^2}}{n}}}$$

(8)

3. Results

3.1. Spectral Preprocessing

The maximum correlation coefficients between preprocessing methods and nitrogen content are shown in Figure 3. FD and SD were selected as superior methods, with RAW as the control. Figure 4 shows the spectra. The RAW curve (Figure 4a) captures canopy reflectance and nitrogen-related features, especially in the red edge (700–750 nm) and NIR (800–1000 nm), but is affected by baseline drift and noise.

FD (Figure 4b) emphasizes slope changes, improving the discrimination of absorption boundaries, particularly between red and red edge (550–750 nm). SD (Figure 4c) highlights curvature and inflection points, performing well under noisy conditions and overlapping peaks, especially in the NIR and SWIR regions (1350–1450 nm). In summary, RAW preserves full reflectance, FD enhances gradients, and SD extracts subtle features. All three datasets were used in subsequent index construction and modeling. As observed in the figures, the RAW spectrum retains complete reflectance information, making it suitable for constructing and interpreting traditional spectral indices. The FD spectrum enhances gradient information, facilitating the extraction of change boundaries, while the SD spectrum excels in amplifying subtle features and mitigating overlapping interference. To improve model adaptability and feature extraction capability, subsequent analyses in this study will involve constructing and screening spectral indices, as well as modeling, using all three datasets.

3.2. Results of Spectral Index Construction and Selection

The maximum correlation values between the spectral indices extracted from Figure 5, Figure 6 and Figure 7 (a–i) and nitrogen content, along with their corresponding wavelength positions, are presented in

Table 2. Optimal wavelength positions and performance metrics (GRA degree, Pearson correlation coefficient, and VIP score) of spectral indices with respect to nitrogen content.

Feature Selection Strategies	Processing Method	DI Optimal Wavelength Position (i, j)/nm	Max(ξ/r/Score)	SRI Optimal Wavelength Position (i, j)/nm	Max(ξ/r/Score)	NDI Optimal Wavelength Position (i, j)/nm	Max(ξ/r/Score)
GRA	RAW	(718, 1726)	0.8717	(702, 1801)	0.8851	(700, 1801)	0.8947
	FD	(685, 1507)	0.8809	(746, 1126)	0.8876	(679, 1639)	0.9037
	SD	(646, 612)	0.8923	(750, 1155)	0.8939	(547, 551)	0.9077
PCC	RAW	(493, 492)	0.7510	(1743, 707)	0.7797	(1743, 707)	0.7771
	FD	(1566, 684)	0.7949	(1333, 734)	0.8228	(1566, 683)	0.7991
	SD	(646, 612)	0.8112	(547,551)	0.8313	(551, 547)	0.8295
VIP	RAW	(1344, 725)	1	(1595, 1596)	1	(1595, 1596)	1
	FD	(714, 705)	1	(1094, 671)	1	(1296, 1071)	1
	SD	(1153, 721)	1	(1778, 2398)	1	(2121, 473)	1

. All three feature selection methods identified highly correlated bands but differed in performance. With GRA, NDI achieved the highest grey relational degree: ξ_max = 0.8947 (RAW, 700–1801 nm), 0.9037 (FD, 679–1639 nm), and 0.9077 (SD, 547–551 nm). PCC favored SRI, with r_max = 0.8313 (547–551 nm), highlighting sensitivity to red edge and visible regions. VIP selected bands mainly in the red edge and NIR (1595–1596 nm, 1153–721 nm, 1778–2398 nm), enhancing model explanatory power. Overall, GRA emphasized NDI, PCC highlighted SRI, and VIP identified red edge/NIR synergy, confirming the red edge as the key region for nitrogen retrieval.

3.3. Model Prediction Results and Analysis

The scatter plots of observed versus predicted values for the Backpropagation neural network (BPNN) model are shown in Figure 8. The SD-GRA combination achieved the best validation accuracy (R² = 0.613, RMSE = 0.0030), outperforming RAW-PCC (0.577), FD-VIP (0.524), and ALL (0.490). The ALL input caused overfitting and gave the poorest validation performance. Ranking: SD-GRA > RAW-PCC > FD-VIP > ALL.

The scatter plots for the Random Forest (RF) model are shown in Figure 9. RAW-PCC and ALL-PCC performed best (R² = 0.743 and 0.695, RMSE = 0.002–0.003), confirming RF’s robustness with high-dimensional data. FD-PCC and SD-PCC were weaker in validation. Ranking: RAW-PCC > ALL-PCC > FD-PCC > SD-PCC.

The scatter plots for the Support Vector Regression (SVR) model are shown in Figure 10. RAW and ALL combinations under PCC and VIP achieved high validation R² (>0.72) with RMSE ≈ 0.002. The RAW-VIP combination was optimal (R² = 0.729, RMSE = 0.002). Ranking: RAW-VIP > ALL-VIP > FD-VIP > SD-VIP.

Within each model family, SD-GRA performed best for BP, RAW-PCC for RF, and RAW-VIP for SVR. A comprehensive evaluation indicated that SD-VIP-SVR achieved the highest overall validation accuracy, whereas RAW-PCC-RF provided stable and robust performance across preprocessing scenarios (

Table 3. Summarizes the variables used in each modeling method and the corresponding R² values with 95% confidence intervals.

Input Variable	Model Method	Train			Test
		R2	95% CI	RMSE	R2	95% CI	RMSE
GRA-RAW-DBI	BPNN	0.6034	[0.4292, 0.7382]	0.0031	0.5774	[0.2852, 0.7823]	0.0032
	RF	0.6046	[0.4306, 0.7391]	0.0032	0.6223	[0.3409, 0.8087]	0.0030
	SVR	0.5250	[0.3377, 0.6795]	0.0035	0.6972	[0.4441, 0.8507]	0.0027
GRA-FD-DBI	BPNN	0.6693	[0.5117, 0.7854]	0.0029	0.5237	[0.2247, 0.7493]	0.0034
	RF	0.7178	[0.5757, 0.8191]	0.0027	0.5257	[0.2268, 0.7506]	0.0033
	SVR	0.6470	[0.4832, 0.7696]	0.0030	0.5966	[0.3085, 0.7937]	0.0031
GRA-SD-DBI	BPNN	0.7387	[0.6041, 0.8333]	0.0026	0.6134	[0.3295, 0.8036]	0.0030
	RF	0.7526	[0.6232, 0.8427]	0.0025	0.6808	[0.4204, 0.8417]	0.0027
	SVR	0.7454	[0.6133, 0.8378]	0.0025	0.7593	[0.5397, 0.8838]	0.0024
GRA-ALL-DBI	BPNN	0.6227	[0.4427, 0.7580]	0.0031	0.4901	[0.1479, 0.7553]	0.0035
	RF	0.7900	[0.6685, 0.8710]	0.0023	0.6716	[0.3602, 0.8542]	0.0028
	SVR	0.7652	[0.6328, 0.8549]	0.0024	0.6813	[0.3741, 0.8590]	0.0027
PCC-RAW-DBI	BPNN	0.5031	[0.3135, 0.6626]	0.0036	0.7432	[0.5140, 0.8753]	0.0025
	RF	0.5959	[0.4201, 0.7327]	0.0032	0.6564	[0.3863, 0.8281]	0.0028
	SVR	0.5661	[0.3847, 0.7107]	0.0033	0.7366	[0.5037, 0.8719]	0.0025
PCC-FD-DBI	BPNN	0.6668	[0.5085, 0.7837]	0.0029	0.5116	[0.2120, 0.7417]	0.0034
	RF	0.7156	[0.5727, 0.8176]	0.0027	0.5991	[0.3116, 0.7952]	0.0031
	SVR	0.6598	[0.4995, 0.7787]	0.0029	0.6866	[0.4287, 0.8449]	0.0027
PCC-SD-DBI	BPNN	0.6925	[0.5420, 0.8016]	0.0028	0.5755	[0.2830, 0.7812]	0.0032
	RF	0.7526	[0.6232, 0.8427]	0.0025	0.6181	[0.3355, 0.8063]	0.0030
	SVR	0.7480	[0.6169, 0.8396]	0.0025	0.6765	[0.4143, 0.8393]	0.0028
PCC-ALL-DBI	BPNN	0.7713	[0.6415, 0.8588]	0.7713	0.6950	[0.3944, 0.8658]	0.0027
	RF	0.7798	[0.6537, 0.8644]	0.0024	0.6422	[0.3195, 0.8393]	0.0029
	SVR	0.7579	[0.6225, 0.8501]	0.0025	0.6703	[0.3583, 0.8536]	0.0028
VIP-RAW-DBI	BPNN	0.3971	[0.2053, 0.5766]	0.0039	0.4694	[0.1702, 0.7142]	0.0035
	RF	0.3846	[0.1936, 0.5660]	0.0040	0.2584	[0.0253, 0.5543]	0.0042
	SVR	0.2727	[0.0994, 0.4648]	0.0043	0.4844	[0.1846, 0.7241]	0.0035
VIP-FD-DBI	BPNN	0.1715	[0.0344, 0.3604]	0.0046	0.3575	[0.0795, 0.6350]	0.0039
	RF	0.4672	[0.2752, 0.6343]	0.0037	0.2771	[0.0335, 0.5705]	0.0041
	SVR	0.3748	[0.1846, 0.5576]	0.0040	0.3613	[0.0821, 0.6379]	0.0039
VIP-SD-DBI	BPNN	0.4826	[0.2914, 0.6465]	0.0036	0.3387	[0.0672, 0.6206]	0.0039
	RF	0.5353	[0.3493, 0.6874]	0.0034	0.4957	[0.1957, 0.7315]	0.0034
	SVR	0.5250	[0.3377, 0.6795]	0.0035	0.5512	[0.2549, 0.7664]	0.0033
VIP-ALL-DBI	BPNN	0.6321	[0.4545, 0.7647]	0.0027	0.5882	[0.2512, 0.8109]	0.0031
	RF	0.6665	[0.4985, 0.7886]	0.0029	0.6519	[0.3326, 0.8443]	0.0029
	SVR	0.5643	[0.3721, 0.7160]	0.0033	0.4306	[0.0981, 0.7187]	0.0037

). Thus, SD-VIP-SVR can be regarded as the overall optimal pipeline, and RAW-PCC-RF as a robust and practical alternative for field applications.

4. Discussion

4.1. Impact of Spectral Index Types and Feature Selection Methods on Inversion Accuracy

Spectral index optimization proved decisive for maize nitrogen inversion, in line with evidence from wheat, rice, and soybean studies highlighting the red-edge region as critical for nitrogen retrieval [48,49,50]. In our work, NDI consistently outperformed SRI and DI across preprocessing scenarios, supporting Nikova et al.’s finding that normalized indices can reduce illumination and soil background interference via difference–sum operations [51]. Its improved performance after derivative preprocessing further suggests enhanced sensitivity to subtle chlorophyll and leaf structure variations, echoing results from cross-crop research [52,53,54]. Moreover, our results reinforce the physiological basis that nitrogen content strongly affects canopy chlorophyll concentration and leaf mesophyll scattering, which are most effectively captured by normalized indices in the 700–750 nm red-edge and 800–1000 nm NIR regions. Similar spectral–physiological linkages have been reported in rice and wheat, where derivative-enhanced NDIs captured subtle nitrogen-induced changes in pigment gradients and canopy internal multiple scattering.

In feature selection, PCC, GRA, and VIP displayed complementary advantages. PCC worked well with RF/SVR under RAW conditions, but has limitations with nonlinear relationships [55]. GRA captured trend similarity but was sensitive to noise under high dimensionality. VIP, built on the PLSR foundation, successfully identified cross-band contributions, and when paired with SVR, achieved the highest accuracy (R² = 0.7593, RMSE = 0.0024), consistent with recent studies integrating hyperspectral and machine learning frameworks [56].

4.2. Applicability of Optimal Selection-Modeling Combinations

Our adaptability analysis showed PCC + RF (RAW) and VIP + SVR (SD) outperform most reported pipelines, even exceeding PCA + SVR benchmarks [57]. Mechanistically, RF’s ensemble learning mitigates PCC’s linear limitations, making it well-suited for field-scale monitoring, while VIP + SVR leverages nonlinear mapping to support precision fertilization applications, a pattern echoed in soybean and rice work using hyperspectral–ML approaches [58,59,60]. These findings also imply that integrating derivative preprocessing with nonlinear learning can better capture canopy spectral plasticity under variable illumination and background conditions. However, this study is constrained to maize in a single region and season. Broader multi-season, multi-crop validation is needed to assess robustness and transferability. Future work should combine deep learning and multi-source hyperspectral data (UAV, satellite) to enhance stability and expand applicability [61,62,63].

5. Conclusions

This study underscores the critical role of spectral index optimization in hyperspectral inversion of maize nitrogen content. Among the constructed indices—Normalized Difference Index (NDI), Simple Ratio Index (SRI), and Difference Index (DI)—NDI exhibited superior performance across preprocessing methods, consistent with earlier findings that normalized structures mitigate illumination and soil background effects [64,65]. Under original spectrum (RAW) conditions, the optimal NDI (700, 1801 nm) achieved a grey relational degree of 0.8947. After second-derivative (SD) preprocessing, the grey relational degree increased to 0.9077 (547, 551 nm), highlighting the advantage of normalized structures combined with derivative operations in enhancing nitrogen-sensitive features [66]. The three feature selection methods—Grey Relational Analysis (GRA), Pearson Correlation Coefficient (PCC), and Variable Importance in Projection (VIP)—demonstrated distinct adaptability but collectively improved modeling accuracy [67,68]. VIP excelled in Support Vector Regression (SVR) (SD preprocessing: test set R² = 0.7593, RMSE = 0.0024); PCC showed the highest stability in Random Forest (RF) (RAW conditions: test set R² = 0.6564, RMSE = 0.0028); and GRA was advantageous in BP neural networks with derivative features (SD preprocessing: test set R² = 0.6134, RMSE = 0.0030). Overall, the SD-VIP-SVR combination achieved the highest inversion accuracy, representing the optimal model in this study. Spectral index optimization significantly enhances model reliability and generalization compared to full-spectrum input [69], serving as a key component and innovative contribution to hyperspectral technology applications in crop nitrogen monitoring. In addition, the optimized spectral–machine learning framework proposed in this study can be further applied to identify optimal nitrogen application rates, providing scientific guidance for precision fertilization and promoting sustainable nutrient management in agricultural production. Future studies should validate this pipeline across multiple seasons and crops to assess its broader applicability in precision fertilization systems [70].