# Interpretable Machine Learning for Legume Yield Prediction Using Satellite Remote Sensing Data
## 4 Discussion  
The present study initially assessed the predictive performance of six distinct ML models, namely DT, XGBoost, RF, KNN, SVR, and MLPR in the context of crop yield prediction using remote sensing data. In brief, XGBoost demonstrated superior performance, achieving the highest \(R^{2}\) score (0.8756), and low errors, while MLPR and SVR had competitive, yet lower performance. This finding supports recent studies stressing the strength of gradient-boosted decision tree ensembles when dealing with high-dimensional, non-linear data, especially when combined with hyperparameter optimization techniques [72; 73; 74]. This strength was particularly advantageous in this analysis dealing with remote sensing data, where interactions between VIs and spectral bands are complex. In addition to predictive accuracy, SHAP analysis was used to enhance model interpretability in the best-performing ML model. SHAP can also address correlated features by distributing the importance (Shapley values) between them based on their marginal contributions across all possible coalitions of features [75]. This means that if two features are highly correlated and provide similar information to the model, SHAP will attribute the \"credit\" for their joint contribution in a fair, game-theoretic manner, rather than assigning all importance to just one of them. This leads to more reliable interpretations, especially in agriculture, where spectral bands and vegetation indices often exhibit strong interdependencies. In the current analysis, a high-level overview was accomplished concerning which variables consistently affect crop yield predictions, allowing us to reveal general agronomic patterns like the strong role of \(EVI\) and \(NDVI\). This is attributed to the fact that both indices serve as proxies for plant health, vigor, and photosynthetic activity. These are central physiological processes which directly influence biomass accumulation and yield formation. In the case of lupin, a leguminous crop that relies on effective canopy development and nitrogen fixation for optimal productivity, higher \(NDVI\) and \(EVI\) values typically reflect healthy, actively growing plants with dense foliage, adequate nutrient  
Figure 5: SHAP beeswarm plot illustrating how SHAP values are distributed across all features in the XGBoost model. status, and minimal stress. They integrate spectral responses from red and near-infrared bands (in the case of \(NDVI\)) or add blue band correction (in the case of \(EVI\)), enhancing sensitivity to chlorophyll content and structural canopy characteristics. As a consequence, their prominence in the model is not only statistically significant, but also agronomically meaningful. This observation qualitatively aligns with simple regression analyses, where crop yield models using \(NDVI\) often show an exponential increase with the latter [76; 77]. Moreover, [PERSON] et al. [78] highlighted that \(EVI\)-based models provided slightly more precise yield estimates compared to those based on \(NDVI\). Denser foliage is associated with higher values of \(EVI\) and \(NDVI\), which reflect greater photosynthetic activity and biomass accumulation, ultimately leading to higher yield. In contrast, the green spectral band (\(B03\)) exhibits a more complex response at high canopy densities. Reflectance saturation, where spectral indices or bands lose sensitivity at high biomass levels, is a well-recognized challenge in remote sensing of vegetation [79]. Thus, during the mid to late pod filling phase, the dense lupin canopy can lead to reflectance saturation or even a slight decrease in \(B03\). This phenomenon is primarily driven by increased self-shadowing and complex internal light scattering within the thick canopy, rather than photosynthetic absorption of green wavelengths. Consequently, lower \(B03\) values in this mature stage probably indicate a highly developed canopy, correlating with maximized yield.