Canonical Correlation Analysis

Wolfgang Karl Härdle and Zdeněk Hlávka
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics
Zdeněk Hlávka: Charles University in Prague, Faculty of Mathematics and Physics Department of Statistics

Chapter Chapter 16 in Multivariate Statistics, 2015, pp 281-287 from Springer

Abstract: Abstract The association between two sets of variables may be quantified by canonical correlation analysis (CCA). Given a set of variables $$X \in \mathbb{R}^{q}$$ and another set $$Y \in \mathbb{R}^{p}$$ , one asks for the linear combination $$a^{\top }X$$ that “best matches” a linear combination $$b^{\top }Y$$ . The best match in CCA is defined through maximal correlation. The task of CCA is therefore to find $$a \in \mathbb{R}^{q}$$ and $$b \in \mathbb{R}^{p}$$ so that the correlation $$\rho (a,b) =\rho _{a^{\top }X,b^{\top }Y }$$ is maximized. These best-matching linear combinations a ⊤ X and b ⊤ Y are then called canonical correlation variables; their correlation is the canonical correlation coefficient. The coefficients a and b of the canonical correlation variables are the canonical vectors.

Keywords: Random Vector; Singular Value Decomposition; Canonical Correlation; Canonical Correlation Analysis; Canonical Variable (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-642-36005-3_16

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