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

2009; Elsevier BV; Linguagem: Inglês

10.1016/b978-044452701-1.00043-0

K.H. Esbensen, P. Geladi,

Statistical and numerical algorithms

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.