Rademacher Complexity-Guided Genetic Programming for Interpretable Spectral Index Discovery in UAV-Based Mistletoe Detection

From the Environmental and Remote Sensing community, the need for AI models that are accurate but also interpretable is increasing. However, usually Deep and Machine Learning techniques are uninterpretable. In this study, we propose to use Genetic Programming (GP) because of the readable nature of candidate solutions, like arithmetic expressions, for the detection of Phoradendron velutinum on five-band multispectral aerial images. Nevertheless, GP suffers from the bloat problem, which is the uncontrolled size growth of the candidate solutions, making them uninterpretable. With the aim of obtaining smaller, simpler, and interpretable solutions, we propose to test five GP simplification methods. The methods considered were Gws 25, Pruning 2%, and Gws 25 and Pruning 2% together. In addition, we proposed two novel approaches based on the Rademacher Complexity (RC) metric called Rademacher and Fit Rademacher. These strategies were evaluated over 30 independent runs with five-fold cross-validation on 250 images of 300 × 300 pixels. The folds group tiles by source frame, so the reported metrics are within-site estimates. The Fit Rademacher method achieved a 54% reduction in the average tree size (22 Fit Rademacher vs. 48 nodes Plain GP) and the highest Recall among all methods (0.566), trading precision and overall agreement for that gain: relative to Plain GP, its test κw falls from 0.448 to 0.402, its F1 from 0.499 to 0.399, and its precision from 0.498 to 0.307. Among the solutions found, GP-VRI (GP Velutinum Red Index) is a compact expression that was algebraically reduced from 25 to 14 nodes, that uses only the Red (650 nm) and Blue (450 nm) bands, and whose structure is biochemically plausible in light of the flavanone, carotenoid, and chlorophyll content reported for P. velutinum. A second solution, GP-VSDI (GP Velutinum Spectral Difference Index), was algebraically reduced from 28 to 24 nodes and uses the same two bands: the R−B difference appears twice in its denominator, while its numerator reduces to a constant factor where R≥2B, independently confirming that this band combination is the most informative for distinguishing P. velutinum from its background on this dataset. These results establish RC-guided GP simplification as a knowledge extraction mechanism in the remote sensing problem studied here, producing models compact enough to be inspected and assessed by domain experts, whose structure is physically consistent with the known spectral behavior of the target species. The methodological contribution is the pair of RC-guided operators; the detection framework and dataset are inherited from previous work.