Principal component analysis

A review and recent developments

Bibliographic Data

ID23337451
AuthorsIan T Jolliffe (College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK), Jorge Cadima (0000-0003-3226-0184, Secção de Matemática (DCEB), Instituto Superior de Agronomia, Universidade de Lisboa, Tapada da Ajuda, Lisboa 1340-017, Portugal, corresponding author)
Year2016
Volume374
Issue2065
Pages20150202
Publication date2016-04-13
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenuePhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (JOURNAL)
Journal identifiersISSN: 1364-503X • E-ISSN: 1471-2962
PublisherThe Royal Society (PUBLISHER • GB)
DOI10.1098/rsta.2015.0202
PMID26953178
OpenAlexW2295124130
LanguageEN
Citations received372
References cited35

Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.

A priori and a posteriori · Component (thermodynamics) · Curse of dimensionality · Data mining · Dimensionality reduction · Eigenvalues and eigenvectors · Interpretability · Machine learning · Principal (computer security) · Principal component analysis · Sparse PCA · Statistics · Uncorrelated · Variance (accounting) · Artificial Intelligence · Blind Source Separation Techniques · Computer Science · Mathematics · Remote-Sensing Image Classification · Spectroscopy and Chemometric Analyses

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