https://libpls.net/publication/PLS_basic_2001.pdf

PLS-regression: a basic tool of chemometrics

Kernel methods provide a powerful and unified framework for pattern discovery, motivating algorithms that can act on general types of data (e.g. strings, vectors or text) and look for general types of relations (e.g. rankings, classifications, regressions, clusters). The application areas range from neural networks and pattern recognition to machine learning and data mining. This book, developed from lectures and tutorials, fulfils two major roles: firstly it provides practitioners with a large toolkit of algorithms, kernels and solutions ready to use for standard pattern discovery problems in fields such as bioinformatics, text analysis, image analysis. Secondly it provides an easy introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.

/pdf/kernel-methods-for-pattern-analysis-3ta60xrj0i.pdf

Kernel Methods for Pattern Analysis

Many individual companies and some industries monitor customer satisfaction on a continual basis, but Sweden is the first country to do so on a national level. The annual Customer Satisfaction Baro...

A National Customer Satisfaction Barometer: The Swedish Experience:

Economic Control of Quality of Manufactured Product.

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 emphasize group structure? Using PLS in this manner has heurestic support owing to the relationship between PLS and canonical correlation analysis (CCA) and the relationship, in turn, between CCA and linear discriminant analysis (LDA). This paper replaces the heuristics with a formal statistical explanation. As a consequence, it will become clear that PLS is to be preferred over PCA when discrimination is the goal and dimension reduction is needed. Copyright © 2003 John Wiley & Sons, Ltd.

Partial Least Squares for Discrimination

In 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 decompositions of the data matrices involved

PLS regression methods

Variable and subset selection in PLS regression

We present here an algorithmic approach to modelling data that includes principal component analysis (PCA) and partial least squares (PLS). In fact, the numerical algorithm presented can carry out PCA or PLS. The algorithm for linear analysis and extensions to non-linear analysis applies to both PCA and PLS. The algorithm allows for combination of PCA and PLS types of models and therefore extends modelling to new types of models that involve combination of regression models and ‘selection of variation’ models, which is the idea of PCA-type models. The fact that the algorithm carries out both PCA and PLS shows that PCA and PLS are based on the same theory. This theory is based on the H-principle of mathematical modelling. The algorithm allows tests for outliers, sensitivity analysis and tests of submodels. These aspects of the algorithm are treated in detail. We compute various measures of sizes, e.g. of components, of the covariance matrix, of its inverse, etc. that show how much the algorithm has selected at each step. The analysis is illustrated by data from practice.

A combined theory for PCA and PLS

Prediction Methods in Science and Technology.: Vol 1. Basic theory

We treat here an extension of linear PLS regression to include regression on quadratic PLS components. The quadratic regression can be viewed as a natural extention of linear PLS regression to quadratic PLS according to the H-principle of mathematical modelling. The numerical implementation is treated in detail. It is shown that this approach can be used for models with large numbers of variables. Some modelling strategies are discussed depending on the purpose of the modelling. Applications of this approach are treated.

Agnar Höskuldsson

Papers

PLS regression methods

Variable and subset selection in PLS regression

A combined theory for PCA and PLS

Prediction Methods in Science and Technology.: Vol 1. Basic theory

Quadratic PLS regression