## 4 Results
### Sensitivity to Spectral Bands  
Variable and feature selection have been one of the most significant processes in ML, with the aim of improving model accuracy and accelerating model processing. With 10 spectral bands of Sentinel-2 available (B2, B3, B4, B5, B6, B7, B8, B8A, B11, B12), it may not be practical to evaluate the performance of all the possible band combinations. This process could be challenging, as the characteristics of different ML models are distinct, and thus it is challenging to conduct a comparison among the different models under a unified standard. For example, GPR, RF and GBRT could provide feature relevance (spectral bands relevance) information that enables insight into feature selection processes, however, the feature relevance results are subject to the model itself, in other words, we could obtain different feature selection schemes, and such information is practical with single ML model based applications. In addition, ANN and SVR are not able to deliver feature relevance information. [PERSON], [PERSON], and [PERSON] [77] proposed the distance correlation (dCor) to measure the dependence of random vectors. dCor ranges between 0 and 1, and dCor (\(\mathbf{X}\), \(\mathbf{Y}\)) = 0 only if \(\mathbf{X}\) and \(\mathbf{Y}\) are independent, which is effective in the feature selection processes [78; 79; 80]. To identify the optimal number of Sentinel-2 spectral bands required for cotton LAI retrieval using MLRAs, we used the distance correlation combined with the backward elimination method [81; 82]. We also performed 10 random repetitions of each model to assess the model's robustness with the spectral bands. Notably, the distance correlation is subject to the training dataset adopted in this study. Figure 8 displays the distance correlation among the 10 spectral bands and LAI. The ranking of the dCor values between the 10 spectral bands and LAI are identified as B12 > B3 > B4 > B2 > B5 > B11 > B8A > B7 > B8 > B6 (B12: 0.88631, B3: 0.88630, B4: 0.88016, B2: 0.87721, B5: 0.87400, B11: 0.87338, B8A: 0.80219, B7: 0.76812, B8: 0.76585, B6: 0.68998). The visible and SWIR bands occupied the top rankings, while differences among the red-edge bands were distinct. The sensitivity results of different ML models to spectral bands using dCor and the backward elimination method (iteratively removing the spectral band with the lowest dCor value until only one spectral band is left) are shown in Figure 9, similarly, the standard error is given at each spectral bands combination (filling area of each model), lower values of the filling area corresponds to smaller standard error, and consequently, more robust model performance. Differences exist among the sensitivity of the models with the reduction in spectral bands. A turning point occurred at 6 for ANN, the accuracy begins to increase with the reduction in spectral bands before 6, though with some fluctuations, and then, the accuracy begins to decrease dramatically until reaching approximately 3. Similar trends are found among all the models except for GPR, as there is a relatively strong fluctuation at 7. GPR has a stable performance after 4. SVR, GPR and RF are robust for the spectral bands according to the standard error. Overall, model accuracy decreases as the spectral bands decrease, although there are some fluctuations in the models, whereas ANN provides the best model accuracy among the spectral band reductions on average (\(\overline{R^{2}}\) = 0.881, \(\overline{RMSE}\) = 0.625 and \(\overline{MAE}\) = 0.480, calculated by all the 10 groups of spectral bands). Figure 7: Sensitivity of the ML models to the training sample size (with intervals of 10) in terms of \(R^{2}\), RMSE and MAE with standard error. (**a**) \(R^{2}\); (**b**) RMSE; (**c**) MAE. The minimum number of bands required for cotton LAI retrieval are recognized as 6 for ANN and SVR, 5 for RF and GBRT, and 8 for GPR, in other words, increasing of the spectral bands of Sentinel-2 does not significantly improves the model accuracy.