GSVD-package: GSVD

In derekbeaton/GSVD: The generalized singular value decomposition

Description

The generalized singular value decomposition (GSVD) generalizes the standard SVD (see svd) procedure through addition of (optional) constraints applied to the rows and/or columns of a matrix.

Details

A package specifically designed for the generalized eigen decomposition, generalized singular value decomposition, and generalized partial least squares-singular value decomposition. Each decomposition allows for the use of weights (or constraints) applied to the columns and/or rows of each data matrix. This package provides these decompositions as the core for a very large list of standard statistical—and typically multivariate—approaches, including but not limited to principal components analysis, metric multidimensional scaling, standard and multiple correspondence analysis, partial least squares, canonical correlation analysis, and multivariate linear regression/reduced rank regression/redundancy analysis.

Author(s)

Maintainer: Derek Beaton [e-mail]

References

Abdi, H. (2007). Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics.Thousand Oaks (CA): Sage. pp. 907-912.
Beaton, D., Fatt, C. R. C., & Abdi, H. (2014). An ExPosition of multivariate analysis with the singular value decomposition in R. Computational Statistics & Data Analysis, 72, 176-189.
Cherry, S. (1996). Singular Value Decomposition Analysis and Canonical Correlation Analysis. Journal of Climate, 9(9), 2003–2009. Retrieved from JSTOR.
Gower, J. C., Gardner-Lubbe, S., & Le Roux, N. J. DATA ANALYSIS: GOOD BUT…. Statistica Applicata - Italian Journal of Applied Statistics, 29.
Greenacre, M. (1984). Theory and applications of correspondence analysis. Academic Press.
Holmes, S. (2008). Multivariate data analysis: the French way. In Probability and statistics: Essays in honor of David A. Freedman (pp. 219-233). Institute of Mathematical Statistics.
Holmes, S., & Josse, J. (2017). Discussion of “50 Years of Data Science”. Journal of Computational and Graphical Statistics, 26(4), 768-769.
Husson, F., Josse, J., & Saporta, G. (2016). Jan de Leeuw and the French school of data analysis. Journal of Statistical Software, 73(6), 1-17.
Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 374(2065).
Lebart L., Morineau A., & Warwick K. (1984). Multivariate Descriptive Statistical Analysis. J. Wiley, New York.
Nguyen, L. H., & Holmes, S. (2019). Ten quick tips for effective dimensionality reduction. PLOS Computational Biology, 15(6), e1006907. https://doi.org/10.1371/journal.pcbi.1006907
Yanai, H., Takeuchi, K., & Takane, Y. (2011). Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer-Verlag, New-York.

See Also

gsvd, geigen, gplssvd

derekbeaton/GSVD documentation built on Jan. 2, 2021, 9:21 p.m.