The chemometrics version of PLS was developed around 25 years ago to cope with and utilize the rapidly increasing volumes of data produced in chemical laboratories. Since then, the first simple two-block PLS has been extended to deal with non-linear relationships, drift in processes (adaptive PLS), dynamics, and with the situation with very many variables (hierarchical models). Starting from a ...

Partial least squares (PLS) is one of the most common regression algorithms in chemistry, relating input–output samples (x i , y i) by a linear multivariate model. In this paper we analyze the PLS algorithm under a specific probabilistic model for the relation between x and y. Following Beer's law, we assume a linear mixture model in which each data sample (x, y) is a random realization from a ...

We compare a number of data-rich prediction methods that are widely used in macroeconomic forecasting with a lesser known alternative: partial least squares (PLS) regression. In this method, linear, orthogonal combinations of a large number of predictor variables are constructed such that the covariance between a target variable and these common components is maximized. We show theoretically th...

Partial Least Squares (PLS) methods are particularly suited to the analysis of relationships between measures of brain activity and of behavior or experimental design. In neuroimaging, PLS refers to two related methods: (1) symmetric PLS or Partial Least Squares Correlation (PLSC), and (2) asymmetric PLS or Partial Least Squares Regression (PLSR). The most popular (by far) version of PLS for ne...

Plasmin (PLS) and urokinase-type plasminogen activator (UPA) are ubiquitous proteases that regulate the extracellular environment. Although they are secreted in inactive forms, they can activate each other through proteolytic cleavage. This mutual interplay creates the potential for complex dynamics, which we investigated using mathematical modeling and in vitro experiments. We constructed ordi...

Use of the partial least squares (PLS) method has been on the rise among e-collaboration researchers. It has also seen increasing use in a wide variety of fields of research. This includes most business-related disciplines, as well as the social and health sciences. The use of the PLS method has been primarily in the context of PLS-based structural equation modeling (SEM). This article discusse...

In this paper we propose a new approach to study the properties of the Partial Least Squares (PLS) estimator. This approach relies on the link between PLS and discrete orthogonal polynomials. Indeed many important PLS objects can be expressed in terms of some specific discrete orthogonal polynomials, called the residual polynomials. Based on the explicit analytical expression we have stated for...

Partial 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 emphas...

Methods of multiblock bilinear factorizations have increased in popularity in chemistry and biology as recent increases in the availability of information-rich spectroscopic platforms has made collecting multiple spectroscopic observations per sample a practicable possibility. Of the existing multiblock methods, consensus PCA (CPCA-W) and multiblock PLS (MB-PLS) have been shown to bear desirabl...

Typically, flow volumes are visualized by defining their boundary as iso-surface of a level set function. Grid-based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particlebased methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advanta...