Abstract
Canonical correlation analysis (CCA) , which is a multivariate analysis method, tries to quantify the amount of linear relationships between two sets of random variables, leading to different modes of maximum correlation (Hotelling in Biometrika 28:321–377, 1936, [1]).
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Notes
- 1.
The same approach discussed in this section can be applied when \(\varvec{\Phi }_{\mathbf {b}}\) is singular or when both \(\varvec{\Phi }_{\mathbf {a}}\) and \(\varvec{\Phi }_{\mathbf {b}}\) are singular.
References
H. Hotelling, Relations between two sets of variables. Biometrika 28, 321–377 (1936)
D.V. Ouellette, Schur complements and statistics. Linear Algebr. Appl. 36, 187–295 (1981)
G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd edn. (The Johns Hopkins University Press, Baltimore, Maryland, 1996)
J. Benesty, J. Chen, Y. Huang, On the importance of the Pearson correlation coefficient in noise reduction. IEEE Trans. Audio Speech Lang. Process. 16, 757–765 (2008)
J.R. Kettenring, Canonical analysis of several sets of variables. Biometrika 58, 433–451 (1971)
T.W. Anderson, Asymptotic theory for canonical correlation analysis. J. Multivar. Anal. 79, 1–29 (1999)
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Benesty, J., Cohen, I. (2018). Canonical Correlation Analysis. In: Canonical Correlation Analysis in Speech Enhancement. SpringerBriefs in Electrical and Computer Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-67020-1_2
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DOI: https://doi.org/10.1007/978-3-319-67020-1_2
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