AbstractPartial least squares (PLS) was not originally designed as a tool for
statistical discrimination. In spite of this, applied scientists routinely use
PLS for classification and there is substantial empirical evidence to suggest
that it performs well in that role. The interesting question is: why can a
procedure that is principally designed for overdetermined regression problems
locate and e... hiện toàn bộ
AbstractA generic preprocessing method for multivariate data, called orthogonal
projections to latent structures (O‐PLS), is described. O‐PLS removes variation
from X (descriptor variables) that is not correlated to Y (property variables,
e.g. yield, cost or toxicity). In mathematical terms this is equivalent to
removing systematic variation in X that is orthogonal to Y. In an earlier paper,
Wold ... hiện toàn bộ
AbstractIn this paper we develop the mathematical and statistical structure of
PLS regression. We show the PLS regression algorithm and how it can be
interpreted in model building. The basic mathematical principles that lie behind
two block PLS are depicted. We also show the statistical aspects of the PLS
method when it is used for model building. Finally we show the structure of the
PLS decomposi... hiện toàn bộ
Max Bylesjö, Mattias Rantalainen, Olivier Cloarec, Jeremy K. Nicholson, Elaine Holmes, Johan Trygg
AbstractThe characteristics of the OPLS method have been investigated for the
purpose of discriminant analysis (OPLS‐DA). We demonstrate how class‐orthogonal
variation can be exploited to augment classification performance in cases where
the individual classes exhibit divergence in within‐class variation, in analogy
with soft independent modelling of class analogy (SIMCA) classification. The
predi... hiện toàn bộ
AbstractA new diagnostic called the core consistency diagnostic (CORCONDIA) is
suggested for determining the proper number of components for multiway models.
It applies especially to the parallel factor analysis (PARAFAC) model, but also
to other models that can be considered as restricted Tucker3 models. It is based
on scrutinizing the ‘appropriateness’ of the structural model based on the data
a... hiện toàn bộ
Partial least squares discriminant analysis (PLS‐DA) has been available for
nearly 20 years yet is poorly understood by most users. By simple examples, it
is shown graphically and algebraically that for two equal class sizes, PLS‐DA
using one partial least squares (PLS) component provides equivalent
classification results to Euclidean distance to centroids, and by using all
nonzero components to l... hiện toàn bộ
AbstractThis report describes significance testing for PLS and OPLS® (orthogonal
PLS) models. The testing is applicable to single‐Y cases and is based on ANOVA
of the cross‐validated residuals (CV‐ANOVA). Two variants of the CV‐ANOVA are
introduced. The first is based on the cross‐validated predictive residuals of
the PLS or OPLS model while the second works with the cross‐validated predictive
sco... hiện toàn bộ
AbstractThis paper presents a dedicated investigation and practical description
of how to apply PARAFAC modeling to complicated fluorescence excitation–emission
measurements. The steps involved in finding the optimal PARAFAC model are
described in detail based on the characteristics of fluorescence data. These
steps include choosing the right number of components, handling problems with
missing va... hiện toàn bộ
Mireia Farrés, Stefan Platikanov, Stefan Tsakovski, Romà Tauler
This study compares the application of two variable selection methods in partial
least squares regression (PLSR), the variable importance in projection (VIP)
method and the selectivity ratio (SR) method. For this purpose, three different
data sets were analysed: (a) physiochemical water quality parameters related to
sensorial data, (b) gas chromatography–mass spectrometry (GC‐MS) chemical
(organic... hiện toàn bộ