Principal component analysis - University of Texas at Dallas

OverviewPrincipal component analysisHerv eAbdi1 and Lynne J. Williams2 Principal component analysis (PCA) is a multivariate technique that analyzes a datatable in which observations are described by several inter-correlated quantitativedependent variables. Its goal is to extract the important information from the table,to represent it as a set of new orthogonal variables called Principal components, andto display the pattern of similarity of the observations and of the variables as pointsin maps. The quality of the PCA model can be evaluated using cross-validationtechniques such as the bootstrap and the jackknife. PCA can be generalizedascorrespondence analysis (CA) in order to handle qualitative variables and asmultiple factor analysis (MFA) in order to handle heterogeneous sets of , PCA depends upon the eigen-decomposition of positive semi-definite matrices and upon the singular value decomposition (SVD) of rectangularmatrices. 2010 John Wiley & Sons, Comp Stat2010 2 433 459 Principal component analysis (PCA) is probably themost popular multivariate statistical techniqueand it is used by almost all scientific disciplines.

Overview Principal component analysis HerveAbdi´ 1∗ and Lynne J. Williams2 Principalcomponentanalysis(PCA)isamultivariatetechniquethatanalyzesadata table in which ...

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