The construction of a partial least squares biplot
Doctoral Thesis
2014
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University of Cape Town
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Abstract
In multivariate analysis, data matrices are often very large, which sometimes makes it difficult to describe their structure and to make a visual inspection of the relationship between their respective rows (samples) and columns (variables). For this reason, biplots, the joint graphical display of the rows and columns of a data matrix, can be useful tools for analysis. Since they were first introduced, biplots have been employed in a number of multivariate methods, such as Correspondence Analysis (CA), Principal Component Analysis (PCA), Canonical Variate Analysis (CVA) and Discriminant Analysis (DA), as a form of graphical display of data. Another possible employment is in Partial Least Squares (PLS). First introduced as a regression method, PLS is more flexible than multivariate regression, but better suited than Principal Component Regression (PCR) for the prediction of a set of response variables from a large set of predictor variables. Employing the biplot in PLS gave rise to the PLS biplot, a new addition to the biplot family. In the current study, this biplot was successfully applied to the sensory data to investigate the relationships between the sensory panel characteristics and the chemical quality measurements of sixteen olive oils. It was also applied to a large set of mineral sorting production data to investigate the relationships between the output variables and the process factors used to produce a final product. Furthermore, the PLS biplot was applied to a Binomialdistributed data concerning the diabetes testing of Indian women and to a Poisson-distributed data showing the diversity of arboreal marsupials (possum) in the Montane ash forest. After these applications, it is proposed that the PLS biplot is a useful graphical tool for displaying results from the (univariate) Partial Least Squares-Generalized Linear Model (PLS-GLM) analysis of a data set. With Partial Least Squares Regression (PLSR) being a valuable method for modelling high-dimensional data, especially in chemometrics, the PLS biplot was successfully applied to a cereal evaluation containing one hundred and forty five infrared spectra and six chemical properties, and a gene expression data with two thousand genes.
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Oyedele, O. 2014. The construction of a partial least squares biplot. University of Cape Town.