Principal Components Analysis

By Stu Daultrey. Applied Univariate, Bivariate, and Multivariate Statistics Using Python, 2018

2,158 citations recorded by the source corpus.

Examples: – Clustering: partition data into groups of similar/nearby points. – Dimensionality reduction: data often lies near a low-dimensional subspace (or manifold) in feature space; matrices have low-rank approximations. [Whereas clustering is about grouping similar sample points, dimensionality reduction is more about identifying a continuous variation from sample point to sample point.] – Density estimation: fit a continuous distribution to discrete data. [When we use maximum likelihood estimation to fit Gaussians to sample points, that’s density estimation, but we can also fit functions more complicated than Gaussians.]

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Citations in the corpus

The Fallacy of Formative Measurement (2011, methodology): “Formative measurement is consistent with principal components analysis (Dunteman, 1989; Jolliffe, 2002), 1 University of North Carolina, Chapel Hill, USA Corresponding Author: Jeffrey R. Edwards, University of North Carolina, Chapel Hill, Box No 3490, NC 27599, USA Email: jredwards@unc.edu in which…”
Tools for Composite Indicators Building (2005, background): “Social scientists may also find the shorter monograph by Dunteman (1989) to be helpful.”
Workforce agility: the new employee strategy for the knowledge economy (2002, methodology): “PCA is widely used when the researcher is faced with numerous correlated measures and aims to reduce a large number of independent variables systematically to a more conceptually coherent set (Dunteman, 1989).”
Author ' s personal copy Partial Least Squares ( PLS ) methods for neuroimaging : A tutorial and review (2011, unknown): “For convenience, Appendix A also lists our main notations and acronyms (see also Abdi and Williams, 2010c, for more details on matrices).”
Measuring Human-Computer Trust (2000, methodology): “It should be noted that loadings of 0.6 and above are considered to be strong and reliable (Dunteman 1989).”
Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction (2006, methodology): “PCA is commonly used in the analysis of near-equilibrium fluctuations sampled by molecular dynamics simulations (29–36), because one can usually assume that the manifold of interest can be reasonably approximated by its tangent hyperplane around an equilibrium point.”
Corporate Governance and Firm-Specific Stock Price Crashes (2016, unknown): “We also employ the scree test [Jolliffe (2002)] to affirm that this approach delivers the same number of factors as with the eigenvalue approach.”
Online Learning Self-Efficacy in Students With and Without Online Learning Experience (2016, methodology): “PCA is an exploratory multivariate statistical technique that was used to reduce the twenty-two-item scale to a smaller number of subscales for easier interpretation (see Dunteman 1989; Sainani 2014).”
Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models (2014, background): “These models have been a mainstay in Statistics for nearly a century—principal component analysis (Pearson , 1901; Hotelling, 1933), factor analysis (Thurstone, 1931, 1938; Thomson, 1939), and canonical correlation analysis (Hotelling, 1936) can all be interpreted this way, although the…”
Ecological Identity: The Development and Assessment of a Measurement Scale (2018, methodology): “Recall that PCA takes a more inductive and less restrictive approach by modeling the items in a scale as independent variables from which components are extracted (Jolliffe, 2002).”
Statistical arbitrage in the US equities market (2008, unknown): “The commonly used solution to extract meaningful information from the data is Principal Components Analysis.4 We consider the eigenvectors and eigenvalues of the empirical correlation matrix and rank the eigenvalues in decreasing order:”
miRTarBase update 2022: an informative resource for experimentally validated miRNA–target interactions (2021, methodology): “After obtaining the representation vectors, we applied principal component analysis (42) to adjust each vector dimension to reduce dimensionality and also optimize the model performance.”
VARIATION IN FEEDING VOCALIZATIONS OF HUMPBACK WHALES MEGAPTERA NOVAEANGLIAE FROM SOUTHEAST ALASKA (2001, methodology): “A varimax rotation was used in the PCA to maximize loadings of specific variables into specific components and thereby facilitate interpretation of resultant factors (Dunteman 1989).”