Selection of components in principal component analysis: A comparison of methods
Computational Statistics & Data AnalysisPublished 1 June 1995
Louis Ferré
Citations144
SJR quartileQ1
SJR score0.89
SNIP1.38
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The numerous methods most often used to determine the number of relevant components in principal component analysis are presented and it is shown why unfortunately most of them fail.
Abstract
The problem of the choice of the relevant components in principal component analysis is presented as a model selection problem. In this context, we present the numerous methods most often used to determine the number of relevant components and we try to show why unfortunately most of them fail. Then these methods are compared on simulated data to study their behaviour.
Keywords
ChemistryMathematicsEngineering
Multivariate Behavioral ResearchThe Scree Test For The Number Of Factors
13,510 Citations1966Raymond B. Cattell
Journal of the Royal Statistical Society Series B (Statistical Methodology)Cross-Validatory Choice and Assessment of Statistical Predictions
10,527 Citations1974M. Stone
TechnometricsCross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
2,496 Citations1978Svante Wold
PsychometrikaDetermining the Number of Components from the Matrix of Partial Correlations
2,425 Citations1976Wayne F. Velicer
An alternative solution which employs a matrix of partial correlations is considered, which gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis.
TechnometricsThe Relationship Between Variable Selection and Data Agumentation and a Method for Prediction
1,361 Citations1974David M. Allen
It is shown that data augmentation provides a rather general formulation for the study of biased prediction techniques using multiple linear regression and a way to obtain predictors given a credible criterion of good prediction is proposed.
The Annals of Mathematical StatisticsAsymptotic Theory for Principal Component Analysis
1,153 Citations1963T. W. Anderson
Journal of the Royal Statistical Society Series C (Applied Statistics)Discarding Variables in a Principal Component Analysis. I: Artificial Data
899 Citations1972Ian T. Jolliffe
It is shown that several of the rejection methods, of differing types, each discard precisely those variables known to be redundant, for all but a few sets of data.
TechnometricsCross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
578 Citations1978Svante Wold
BiometrikaTESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES
343 Citations1956D. N. Lawley
TechnometricsThe Relationship between Variable Selection and Data Agumentation and a Method for Prediction
251 Citations1974David M. Allen
Journal of the American Statistical AssociationAn Analysis of a Two-Way Model with Interaction and No Replication
208 Citations1972Dallas E. Johnson, Franklin A. Graybill
Journal of the Royal Statistical Society Series B (Statistical Methodology)Some Notes on Ordered Random Intervals
103 Citations1956David Barton, F. N. David
TechnometricsCross-Validatory Choice of the Number of Components from a Principal Component Analysis
84 Citations1982H. T. Eastment, W. J. Krzanowski
Journal of Multivariate AnalysisThe distribution of the sphericity test criterion
75 Citations1973B. N. Nagarsenker, K. C. S. Pillai
StatisticsStability of principal component analysis studied by the bootstrap method
69 Citations1988J.J. Daudin, C. Duby +1 more
Statistics & Probability LettersPCA stability and choice of dimensionality
63 Citations1992Philippe Besse
Journal of the American Statistical AssociationAn Analysis of a Two-Way Model with Interaction and No Replication
57 Citations1972Dallas E. Johnson, Franklin A. Graybill
TechnometricsOn Analyzing Two-Way AoV Data with interaction
49 Citations1976Victor Hegemann, Dallas E. Johnson
Principal Component Analysis
43 Citations2023Hang Li
Journal of Multivariate AnalysisOn the ratios of the individual latent roots to the trace of a Wishart matrix
34 Citations1972A. W. Davis
Journal of Statistical Computation and SimulationCross-validatory choice in principal component analysis; some sampling results
30 Citations1983W. J. Krzanowski
StatisticsPrincipal components analysis and optimization of graphical displays
20 Citations1988Ph. Besse, Henri Caussinus +2 more
Journal of Multivariate AnalysisPrincipal components in the nonnormal case: The test of equality of Q roots
16 Citations1984Christine Waternaux
Communication in Statistics- Theory and MethodsOn a statistic useful in dimensionality reduction in multivariable linear stochastic system
16 Citations1976Takatoshi Sugiyama, Howell Tong
StatisticsAsympotic study of the multivariate functional model. application to the metric choice in principal component analysis
13 Citations1992Jeanne Fine, Alain Pousse
TechnometricsOn Analyzing Two-Way AoV Data with Interaction
12 Citations1976Victor Hegemann, Dallas E. Johnson
Computational Statistics & Data AnalysisComparing the parameters of a model for several units by means of principal component analysis
12 Citations1992Henri Caussinus, Louis Ferré
StatisticsPca stability studied by the bootstrap and the infinitesimal jackknife method
9 Citations1989J.J. Daudin, C. Duby +1 more
Statistique et analyse des donnéesRecherche de la dimension de l'espace latent en ACP
1 Citations1986Pablo Gonzalez Vicente