Principal component analysis

Abdi, Hervé; Williams, Lynne J.

doi:10.1002/wics.101

Cited by 11,104Statistical Methods and ApplicationsAdvanced Statistical Methods and ModelsSpectroscopy and Chemometric Analyses

Principal component analysis

Abdi, Hervé, Williams, Lynne J.·2010·WIREs Computational Statistics

DOI 10.1002/wics.101

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Abstract

Abstract Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter‐correlated quantitative dependent 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, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross‐validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen‐decomposition of positive semi‐definite matrices and upon the singular value decomposition (SVD) of rectangular matrices. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction

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Two techniques [9,18] employ the principal component analysis [53] to filter out irrelevant attributes.
“Two techniques [9,18] employ the principal component analysis [53] to filter out irrelevant attributes.”
From A Systematic Review of Data Quality in CPS and IoT for Industry 4.0 (2023) · cites this paper as [53]
PCA may not always be suitable for all datasets or analysis goals, and its effectiveness depends on the underlying structure of the data.
“However, it is important to note that PCA may not always be suitable for all datasets or analysis goals, and its effectiveness depends on the underlying structure of the data [17] [56].”
From Comparative Analysis of Intrusion Detection Systems and Machine Learning Based Model Analysis through Decision Tree (2023) · cites this paper as [17]

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Authors: Abdi, H., & Williams, L. J.
Affiliations: The University of Texas at Dallas (US)
University of Toronto (CA)
Corresponding author: Abdi, Hervé
ORCID: Abdi, Hervé
Williams, Lynne J.
Venue: WIREs Computational Statistics
Publisher: Wiley
Published: 2010-07
Volume: 2
Issue: 4
Pages: 433-459
ISSN: 1939-0068 (ISSN-L)
1939-5108
DOI: 10.1002/wics.101
OpenAlex: W2128728535
Cited by: 11,104
References: 72
Citations by year: 2026: 1223 · 2025: 1515 · 2024: 1198 · 2023: 1227 · 2022: 1105 · 2021: 967 · 2020: 795 · 2019: 650 · 2018: 630 · 2017: 466 · 2016: 374 · 2015: 307 · 2014: 299 · 2013: 201 · 2012: 103
FWCI: 93.40
Type: journal article
Language: en
Open access: closed
Licence: onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations: Wiley Interdisciplinary Reviews Computational Statistics (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
Keywords: principal component analysis, dimensionality reduction, multivariate analysis, correspondence analysis, multiple factor analysis, singular value decomposition, eigenvalue decomposition, bootstrapping, jackknife, cross-validation, orthogonal components, data visualization

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