Soil characterization via methods of functional data analysis

HA Statistics

Gilliland, Andrew John ; Scott, Marian

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: Soil characterization, functional data analysis, FDA, MIR spectroscopy, functional regression, functional principal components analysis.;   

Others  :  http://theses.gla.ac.uk/8267/1/2017gillilandmsc.pdf

来源: University of Glasgow

【 摘 要 】

Soil is a fundamental natural resource which is relied upon globally for its vital ecological and economic functions. It is important for many reasons including the production of food, support of wildlife and in supporting the mitigation of global warming. With an increasing world population, tremendous pressure is placed on the world’s natural resources. In order to keep up with the agricultural needs of a growing global population, soil management and monitoring practices need to be put in place. However, the standard procedures for monitoring soil quality are prohibitively expensive and slow, with an additional hazard to the environment through use of harmful chemicals. Thus, there has been a widespread interest into the use of diffuse reflectance spectroscopy for the prediction of physical and chemical properties in the soil. This method of recording soil data is cost-effective, rapid, requires minimal sample preparation and does not involve the use of hazardous chemicals. Currently, multivariate analyses such as partial least squares regression are routinely used to predict a wide range of soil properties from spectral data obtained from a mid- and near-infrared diffuse reflectance spectroscopy of soil samples. Whilst this method has been shown to successfully predict a multitude of soil quantities, methods of functional data analysis provide an alternate way of studying continuous data, recognising that it is sometimes more natural, and often fruitful, to view a collection of data points as observed realisations of random functions. In this thesis, the main focus is to compare standard multivariate techniques of analysing soil spectra to methods of functional data analysis. Chapter 1 provides an introduction to the importance of soil monitoring, mid-infrared spectroscopy, a description of the data and the objectives of the thesis. Following this, Chapter 2 demonstrates the performances of principal component analysis, linear discriminant analysis and support vector machines in investigating the variability of the soil spectra across the mid-infrared range. These multivariate methods are assessed on their ability to distinguish differences between groups of spectra based on various grouping variables. In Chapter 3, functional data analysis is introduced and methods of functional principal component analysis and functional hypothesis testing are implemented. Functional principal component analysis is applied to identify regions of the spectra which contain the principal modes of variation which could be pertinent to explaining differences between samples of different land-uses or sampling sites. Functional hypothesis tests are used to directly test for differences between groups of spectra and pointwise permutation F-tests are used to locate regions of the spectra where these group differences are prominent. Chapter 4 introduces functional linear regression as an alternative to the industry standard of partial least squares regression for relating the spectra to the physical wet chemistry properties of the soil. In this chapter, it is of interest to identify physical soil properties which can be successfully predicted by functional and partial least squares regression; and what the achievable performances of these predictions are. Comparisons between the two approaches are made and the advantages of each approach are considered. Finally, Chapter 5 provides a summary of the work presented and discusses the limitations and remaining challenges for the use of functional data analysis for the characterization of soil.