Canonical correlation

References

William Press, Canonical Correlation Clarified by Singular Value Decomposition

Most statistical tests are canonical correlation analysis, apparently. (Knapp 1978).

tl;dr classic statistical tests are linear models where your goal decide if a coefficient should be regarded as non-zero or not. Jonas Kristoffer Lindeløv explains this perspective: Common statistical tests are linear models. FWIW I found that perspective to be a real 💡 moment.

References

Allen-Zhu, Zeyuan, and Yuanzhi Li. 2017. “Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition.” In PMLR, 98–106.

Bach, Francis R, and Michael I Jordan. 2002. “Kernel Independent Component Analysis.” Journal of Machine Learning Research 3 (July): 48.

Borello, Melinda. 2013. “Standardization and Singular Value Decomposition in Canonical Correlation Analysis.”

Cherry, Steve. 1996. “Singular Value Decomposition Analysis and Canonical Correlation Analysis.” Journal of Climate 9 (9): 2003–9.

Cichocki, A., N. Lee, I. V. Oseledets, A.-H. Phan, Q. Zhao, and D. Mandic. 2016. “Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1.” arXiv:1609.00893 [Cs], September.

Ewerbring, L. Magnus, and Franklin T. Luk. 1989. “Canonical Correlations and Generalized SVD: Applications and New Algorithms.” Journal of Computational and Applied Mathematics, Special Issue on Parallel Algorithms for Numerical Linear Algebra, 27 (1): 37–52.

Horváth, Lajos, and Piotr Kokoszka. 2012. Inference for functional data with applications. Vol. 200. Springer series in statistics. New York: Springer.

Knapp, Thomas R. 1978. “Canonical Correlation Analysis: A General Parametric Significance-Testing System.” Psychological Bulletin 85 (2): 410.

Lopez-Paz, David, Suvrit Sra, Alex Smola, Zoubin Ghahramani, and Bernhard Schölkopf. 2014. “Randomized Nonlinear Component Analysis.” arXiv:1402.0119 [Cs, Stat], February.

McWilliams, Brian, David Balduzzi, and Joachim M Buhmann. 2013. “Correlated Random Features for Fast Semi-Supervised Learning.” In Advances in Neural Information Processing Systems 26, edited by C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, 1050:440–48. Curran Associates, Inc.

Ramsay, Jim O., and B.W Silverman. 2005. Functional Data Analysis. Springer Series in Statistics. New York: Springer-Verlag.

Witten, Daniela M., Robert Tibshirani, and Trevor Hastie. 2009. “A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis.” Biostatistics, January, kxp008.

Witten, Daniela M, and Robert J. Tibshirani. 2009. “Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data.” Statistical Applications in Genetics and Molecular Biology 8 (1): 1–27.

Yang, Yanrong, and Guangming Pan. 2015. “Independence Test for High Dimensional Data Based on Regularized Canonical Correlation Coefficients.” The Annals of Statistics 43 (2).

References

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