# Interpretable Machine Learning for Legume Yield Prediction Using Satellite Remote Sensing Data
## 3 Results
### SHAP-Based Interpretation of XGBoost Feature Contributions  
To understand the general patterns of feature influence on crop yield predictions made by the ML model showing the best performance, namely XGBoost, this section focuses on global interpretability using SHAP values. As this model is an ensemble of decision trees, TreeSHAP can accurately identify the most influential features driving predictions. To this end, a SHAP summary plot is provided in Figure 4, which shows the most influential features by summarizing the mean absolute SHAP values. The higher the SHAP value the greater the contribution of that feature to increasing the ML model's prediction. In short, \(EVI\) was found to be the most important feature, displaying the highest mean absolute SHAP value of approximately 0.32, followed by \(NDVI\) with a mean absolute SHAP value of 0.22. This plot highlights also the importance of the green (\(B03\)) and short-wave infrared (\(B12\)) spectral bands among the most influential features for crop yield prediction. VIs, like \(GRVI\) and \(SBI\), also demonstrated remarkable importance. Other indices, including \(MSAVI\), \(WI\), and \(NDWI\) in descending order of mean absolute SHAP value, showed moderate contributions. The sum of the four other features (\(OSAVI\), \(SAVI\), \(SR\), and \(WDRVI\)) has a combined mean absolute SHAP value of 0.02. This signifies that the individual contributions of these features are relatively small in comparison to the top nine features. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(MAE\) & \(MSE\) & \(RMS\) & \(R^{2}\) \\ \hline DT & 0.3297 & 0.1970 & 0.4438 & 0.6393 \\ XGBoost & **0.2399** & 0.1149 & 0.3389 & **0.8756** \\ RF & 0.2900 & 0.1661 & 0.4076 & 0.6959 \\ SVR & 0.2404 & 0.1129 & 0.3360 & 0.7933 \\ KNN & 0.2624 & 0.1646 & 0.4057 & 0.6987 \\ MLPR & 0.2467 & **0.1125** & **0.3354** & 0.8141 \\ \hline \hline \end{tabular}  
* DT: Decision Tree; KNN: K-Nearest Neighbors; MLPR: Multi-Layer Perceptron Regressor; RF: Random Forest; SVR: Support Vector Regressor; XGBoost; Extreme Gradient Boosting.  
\end{table} 
Table 1: Evaluation metrics of the utilized machine learning models; the best values in each column are highlighted in bold. In order to get more information about not only the feature's importance but also the distribution of how much that feature influences each prediction, a beeswarm plot is provided in Figure 5. This helps towards determining whether characteristics consistently affect predictions in a positive or negative way across samples. The horizontal positioning of each dot, representing a distinct data point, indicates the SHAP value, which shows the extent to which that attribute increased or decreased the model's prediction for that particular instance. While features with narrower distributions often have a more uniform but lesser influence, those with wider distributions appear to have a larger and more varied impact on crop yield estimates. Furthermore, the concentration of data points with comparable levels of influence is shown when dots cluster vertically around a specific SHAP value. Focusing on Figure 5, high values of both \(EVI\) and \(NDVI\) (red circles) exhibited a positive correlation with lupin yield (pushing the prediction higher). In contrast, low values (blue circles) are associated with negative SHAP values (pushing the prediction lower). This pattern is consistent with the known agronomic roles of \(EVI\) and \(NDVI\) as indicators of vegetation vigor, canopy density, and chlorophyll content, which are key drivers of biomass accumulation in legumes [8; 44]. The observed positive relationship reinforces the interpretation that increased vegetative development during the mid-season is strongly linked to enhanced yield potential. On the other hand, high values of the green and short-wave infrared spectral bands demonstrate an almost negative correlation with the predicted crop yield. Consequently, higher reflectance in these portions of the spectrum tends to decrease the model's prediction of crop yield.