Improving the Estimation of Apple Leaf Photosynthetic Pigment Content Using Fractional Derivatives and Machine Learning

Abstract

As a key functional trait, leaf photosynthetic pigment content (LPPC) plays an important role in the health status monitoring and yield estimation of apples. Hyperspectral features including vegetation indices (VIs) and derivatives are widely used in retrieving vegetation biophysical parameters. The fractional derivative spectral method shows great potential in retrieving LPPC. However, the performance of fractional derivatives and machine learning (ML) for retrieving apple LPPC still needs to be explored. The objective of this study is to test the capacity of using fractional derivative and ML methods to retrieve apple LPPC. Here, the hyperspectral data in the 400–2500 nm domains was used to calculate the fractional derivative order of 0.2–2, and then the sensitive bands were screened through feature dimensionality reduction to train ML to build the LPPC estimation model. Additionally, VIs-based ML methods and empirical regression models were developed to compare with the fractional derivative methods. The results showed that fractional derivative-driven ML methods have higher accuracy than the ML methods driven by the original spectra or vegetation index. The results also showed that the ML methods perform better than empirical regression models. Specifically, the best estimates of chlorophyll content and carotenoid content were achieved using support vector regression (SVR) at the derivative order of 0.2 (R2 = 0.78) and 0.4 (R2 = 0.75), respectively. The fractional derivative maintained a good universality in retrieving the LPPC of multiple phenological periods. Therefore, this study highlights that the fractional derivative and ML improved the estimation of apple LPPC.

SPECTRAL VEGETATION INDEXES AS INDICATORS OF LEAF PIGMENT CONTENT IN APPLE (Malus domestica Borkh.)

“…Полученные результаты показали, что для бесконтактного определения содержания пигментов в листьях яблони можно использовать простые вегетационные индексы, но они должны быть адаптированы для конкретного сорта. Качество результатов при этом вполне сопоставимо с таковым, полученным на основе методов машинного обучения (19) или методов, основанных на использовании нейронных сетей (20). При этом в отличие от сложных методов, предлагаемые нами подходы более просты в использовании.…”

“…Причем во многих публикациях акцент сделан на разработке новых методов извлечения информации о содержании пигментов в растениях. Так, для листьев яблони в Китае (19,20) (22), каротиноиды -методом фон Ветштейна (23).…”

Combining Fractional Derivatives and Machine Learning: A Review

“…Cheng et al predicted the photosynthetic pigments in apple leaves using fractional derivatives to augment the data and range of machine learning algorithms, i.e., support vector machines, k-nearest neighbor, random forest, and neural networks [38]. In [39], it is shown that a similar approach using a different algorithm, XGBoost, can be used to estimate the moisture content of agricultural soil.…”

Combining Fractional Derivatives and Supervised Machine Learning: A Review

“…Cheng et al predict the photosynthetic pigments in apple leaves using fractional derivatives to augment the data and range of machine learning algorithms, i.e., support vector machines, k nearest neighbor, random forest, and neural networks, [37]. In [38], it is shown that a similar approach though using a different algorithm, XGBoost, can be used to estimate agricultural soil moisture content.…”