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Dimensionality Reduction of High-Dimensional Highly Correlated Multivariate Grapevine Dataset

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Document pages: 16 pages

Abstract: Viticulturists traditionallyhave a keen interest in studying the relationship between the biochemistry ofgrapevines’ leaves petioles and their associated spectral reflectance in orderto understand the fruit ripening rate, water status, nutrient levels, anddisease risk. In this paper, we implement imaging spectroscopy (hyperspectral)reflectance data, for the reflective 330 - 2510 nm wavelength region (986 total spectral bands), to assess vineyardnutrient status; this constitutes a high dimensional dataset with a covariancematrix that is ill-conditioned. The identification of the variables (wavelengthbands) that contribute useful information for nutrient assessment andprediction, plays a pivotal role in multivariate statistical modeling. In recent years, researchers have successfullydeveloped many continuous, nearly unbiased, sparse and accurate variableselection methods to overcome this problem. This paper compares fourregularized and one functional regression methods: Elastic Net, Multi-Step Adaptive Elastic Net, Minimax Concave Penalty, iterative SureIndependence Screening, and Functional Data Analysis for wavelength variableselection. Thereafter, the predictive performance of these regularized sparsemodels is enhanced using the stepwise regression. This comparative study ofregression methods using a high-dimensional and highly correlated grapevine hyperspectral dataset revealed that theperformance of Elastic Net for variable selection yields the best predictiveability.

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