2.02 - Principal Component Analysis: Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice

Abstract

Principal component analysis (PCA) is the most fundamental, general purpose multivariate data analysis method used in chemometrics. A geometrical projection analogy is used to introduce derivation of bilinear data models, focusing on scores, loadings, residuals, and data rank reduction. This is followed by a presentation and comparison of three alternative algebraic formulations for components analysis as well as algorithms for their calculations. The general history of PCA (and factor analysis) in mathematics and statistics is introduced, including contributions from chemometrics. An example on how to work with PCA in practice and its power for data structure visualization end the chapter.

Keywords

data structure; effective rank; eigenvector–eigenvalue extraction; latent variables; loadings; NIPALS algorithm; principal component analysis; projection; residuals; scores; singular-value decomposition; visualization

Published in

Title: Comprehensive Chemometrics : Chemical and Biochemical Data Analysis
Publisher: Elsevier

SLU Authors

• Geladi, Paul

  • Department of Forest Biomaterials and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1016/B978-0-444-64165-6.05002-3
• ISBN: 978-0-444-64165-6
• eISBN: 978-0-444-64166-3

Permanent link to this page (URI)

https://res.slu.se/id/publ/129879