Dimensionality Reduction of High-Dimensional Highly Correlated Multivariate Grapevine Dataset

Abstract

Viticulturists traditionally have a keen interest in studying the relationship between the biochemistry of grapevines' leaves/petioles and their associated spectral reflectance in order to understand the fruit ripening rate, water status, nutrient levels, and disease 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 vineyard nutrient status; this constitutes a high dimensional dataset with a covariance matrix that is ill-conditioned. The identification of the variables (wavelength bands) that contribute useful information for nutrient assessment and prediction, plays a pivotal role in multivariate statistical modeling. In recent years, researchers have successfully developed many continuous, nearly unbiased, sparse and accurate variable selection methods to overcome this problem. This paper compares four regularized and one functional regression methods: Elastic Net, Multi-Step Adaptive Elastic Net, Minimax Concave Penalty, iterative Sure Independence Screening, and Functional Data Analysis for wavelength variable selection. Thereafter, the predictive performance of these regularized sparse models is enhanced using the stepwise regression. This comparative study of regression methods using a high-dimensional and highly correlated grapevine hyperspectral dataset revealed that the performance of Elastic Net for variable selection yields the best predictive ability.

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“…Variables with high correlations to other variables and a high variance inflation factor (VIF) when performing a multiple linear regression were identified as candidates to be removed. In order to account for multicollinearity and reduce the dimensionality of the dataset, both penalized and stepwise regression models were investigated (Jha et al, 2017).…”