Analysis of two partial-least-squares algorithms for multivariate calibration
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Summary
Two algorithms for multivariate calibration are analysed in terms of standard linear regression theory and the matrix inversion problem of linear regression is shown to be solved by transformations to a bidiagonal form in PLS1 and to a triangular form inPLS2.
- Type
- article
- Published
- 1987-08-01
- Cited by
- 340
- References
- 19
- OpenAlex
- https://openalex.org/W1979612645
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:119534578
Keywords
Partial least squares regression, Mathematics, Multivariate statistics, Chemometrics, Calibration
References
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- Generalized Inverse of Matrices and Its Applications
- Partial least-squares regression: a tutorial
- ON THE STRUCTURE OF PARTIAL LEAST SQUARES REGRESSION
- The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses
- Methods of conjugate gradients for solving linear systems
- A Note on the Use of Principal Components in Regression
- Multivariate Calibration
- Multivariate Calibration by Data Compression
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- Model Selection Techniques for Kernel-Based Regression Analysis Using Information Complexity Measure and Genetic Algorithms
- A Two Step Model for Linear Prediction, with Connections to PLS
- Optimized scaling. A novel approach to linear calibration with closed data sets
- Multiplex screening using enzyme inhibition, fluorescence detection and chemometrics
- Apprentissage dans les espaces de grande dimension : application à la caractérisation des tumeurs noires de la peau à partir d'images
- Multivariate statistical process control of chemical processes
- L'évaluation du risque et de la performance des Hedge Funds
- Learning comprehensible models for analysis and predictions in scientific databases
- Quantification of Prediction Uncertainty for Principal Components Regression and Partial Least Squares Regression
- Nær- infrarød deteksjon av avgasser fra fremtidig brenselcelle- konsept.
- Statistical molecular design of peptoid libraries
- Principal covariates regression: Part I. Theory
- Validity of business excellence models : a conceptual and empirical analysis : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Technology at Massey University, Palmerston North, New Zealand
- Control no destructivo e in situ de productos y procesos en la industria del cerdo ibérico usando sensores espectrales de infrarrojo cercano
- Assigning environmental variables to observed biological changes
- White, grey and black multicomponent systems: A classification of mixture problems and methods for their quantitative analysis
- Working with collinearity in epidemiology : development of collinearity diagnostics, identifying latent constructs in exploratory research and dealing with perfectly collinear variables in regression
- Improvements to PLS methodology
- Multivariate calibration as an identification method and its relationship to the extended Kalman filter
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