The use and interpretation of principal component analysis in applied research

By Calyampudi R. Rao. 1964

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Citations in the corpus

Procrustean co-inertia analysis for the linking of multivariate datasets (2003, methodology): “Hence, coupling multivariate analyses such as coin rtia analysis (CIA: Dolédec & Chessel, 1994), redundancy analysis (RDA: Rao, 1964), or canonical correspondence analysis (CCA: ter Braak, 1986), which provide graphical r presentation of the results, are preferred.”
Port privatization, efficiency and competitiveness: Some empirical evidence from container ports (terminals) (2005, methodology): “Martines, Diaz, Navarro, and Ravelo (1999) and Tongzon (2001) build on the work of Roll and Hayuth (1993) through applying the DEA approach to actual performance data from selected ports.”
Functional responses in polar bear habitat selection (2003, methodology): “To explore the relationships among the different ice variables (relative availability very open, open ice and closed ice and distance to ice edge) we used principal component analysis on the instrumental variables population, season, and reproductive status ( Rao 1964, Lebreton et al. 1991).”
Diabetes Prediction Using Ensembling of Different Machine Learning Classifiers (2020, methodology): “In this literature, three most commonly used methods for the feature selection namely Principle Component Analysis (PCA) [25], Independent Component Analysis (ICA) [26], and Correlation-based [27] technique were used to compare their performance for the PID dataset.”
Beta diversity of stream fish assemblages: partitioning variation between spatial and environmental factors (2017, methodology): “Relationships between principal coordinates and Hellinger-transformed fish assemblage data (Legendre & Gallagher, 2001) were assessed using redundancy analysis, and significant levels were determined via permutation with 9,999 randomisations (RDA; Rao, 1964; Legendre & Legendre, 1998; Oksanen, 2015)”
Outlier Detection (2008, unknown): “E-mail: hpeng@math.iupui.edu.”
Constrained Principal Component Analysis: Various Applications (2002, methodology): “Component loadings from the higher order structure analysis of the Roche et al. (1999) data, showing the attachment loadings associated with incorporating Bartholomew's model of attachment into CPCA.”
CO‐INERTIA ANALYSIS AND THE LINKING OF ECOLOGICAL DATA TABLES (2003, methodology): “…methods for this task are: canonical correlation analysis (CANCOR, Hotelling 1936); principal component analysis with instrumental variables (Rao 1964), also named ‘‘redundancy analysis’’ (RDA); co-inertia analysis (COIA, Dolédec and Chessel 1994); and canonical correspondence analysis…”
MULTIVARIATE REGRESSION TREES: A NEW TECHNIQUE FOR MODELING SPECIES–ENVIRONMENT RELATIONSHIPS (2002, methodology): “MRT is then compared to redundancy analysis (RDA; Rao 1964) and canonical correspondence analysis (CCA; ter Braak 1986) using simulated data and a previously published set of field data.”
All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices (2002, methodology): “This is necessary because we need our spatial information to be represented in a form compatible with applications of multiple regression or canonical ordination (RDA or CCA) i.e. as an object-byvariable matrix.”
The singular values and vectors of low rank perturbations of large rectangular random matrices (2011, background): “extracting the r largest singular values and the associated singular vectors of X̃ - these are referred to as the r principal components [48] and the Eckart-Young-Mirsky theorem states that they provide the best rank-r approximation of the matrix X̃ for any unitarily invariant norm [26, 41].”
Should the Mantel test be used in spatial analysis? (2015, methodology): “The analysis involvesmultiple linear regression when the response data are univariate (as in our simulation study) or redundancy analysis (RDA, Rao 1964) when it is multivariate.”
Review: Multivariate analysis in weed science research (2002, background): “This approach is lucidly described by Rao (1964): When a large number of measurements [variables] are available, it is natural to enquire whether they could be replaced by a fewer number of the measurements or of 282 • Weed Science 50, May–June 2002 their functions, without loss of much…”