A modification of canonical variates analysis to handle highly collinear multivariate data

Abstract

A modification of the standard Canonical Variates Analysis (CVA) method to cope with collinear high-dimensional data is developed. The method utilizes Partial Least Squares regression as an engine for solving an eigenvector problem involving singular covariance matrices. Three data sets are analyzed to demonstrate the properties of the method: a two-group problem with near infrared spectroscopic data consisting of 60 samples and 376 variables, a multi-group problem with fluorescence spectroscopic data (1023 variables) consisting of 83 samples from six groups and a three-group problem with physical-chemical data (10 variables) consisting of 41 samples from three groups. It is demonstrated that the modified CVA method forces the discriminative information into the first canonical variates as expected. The weight vectors found in the modified CVA method possess the same properties as weight vectors of the standard CVA method. By combination of the suggested method with, for example, Linear Discriminant Analysis (LDA) as a classifier, an operational tool for classification and discrimination of collinear data is obtained.

A physiochemical theory on the applicability of soft mathematical models—experimentally interpreted

“…Spectra were evaluated from chemical assignments in the literature [20]. Spectra on barley samples were classified by Extended Canonical Variates Analysis (ECVA) [21] and ß-glucan predicted by Partial Least Squares regression (PLSR) [22] and interval i-PLSR [23].…”

A new holistic exploratory approach to Systems Biology by Near Infrared Spectroscopy evaluated by chemometrics and data inspection

“…However, this is now possible by the newly developed extended canonical variates analysis (ECVA) developed by Nørgaard et al [53]. ECVA forces discrimination into the first canonical variates and uses the PLSR method as an engine for solving the eigenvector problem involving singular covariance matrices.…”

Trends in the application of chemometrics to foodomics studies

“…Recently, SIMCA was applied to detect adulteration of hazelnut paste with almond paste or chickpea flour based on NIR spectroscopy (LÓPEZ et al, 2014), authentication of geographical origin of honey (LATORRE et al, 2013), and for the discrimination of fresh and frozen beef burger products from beef offal adulteration using IR spectroscopy (ZHAO et al, 2014). NØRGAARD et al, 2006) has been developed as a modifi cation of Canonical Variates Analysis (CVA). CVA (CAMPBELL & ATCHLEY, 1981) aims to estimate directions in space that maximize the differences between the groups according to well-defi ned optimization criterion, which is fi nding a direction that maximizes difference between projected mean values of each group relative to projected variance within groups.…”

“…In this way, canonical variates are calculated in the original high-dimensional space making it possible to deal with such data. Application of linear discriminant analysis (LDA) to the canonical variates allows the discriminative directions to be estimated directly in the original multidimensional space (NØRGAARD et al, 2006). The number of canonical directions is always one less than the number of classes in the dataset.…”

“…ECVA provides plots easily interpretable, similar to PLS-DA loadings and scores, canonical weights, and variates explain the patterns related to variables and observations, respectively, in each canonical direction. Additionally, ECVA has been shown to be an effi cient classifi cation method for more than two class problems (NØRGAARD et al, 2006).…”