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	ベイズ正準相関分析 (Bayesian CCA)	Canonical Correlation Analysis
分野	統計学	統計学
系統	Latent structure	Latent structure
提唱年	2005-2013	1936
提唱者	Francis Bach & Michael Jordan (probabilistic formulation, 2005); Klami, Virtanen & Kaski (fully Bayesian treatment, 2013)	Harold Hotelling
種類	Latent variable model / dimensionality reduction	Multivariate linear dimension reduction and association
原典	Bach, F. R. & Jordan, M. I. (2005). A probabilistic interpretation of canonical correlation analysis. Technical Report 688, Department of Statistics, University of California, Berkeley.	Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3–4), 321–377.
別名	Bayesian CCA, probabilistic CCA, BCCA	CCA, canonical variate analysis, canonical analysis, multiple canonical correlation
関連	5	4
概要	Bayesian canonical correlation analysis is a probabilistic generative model that identifies shared latent structure between two or more sets of observed variables. It extends classical CCA by placing priors on model parameters, enabling principled uncertainty quantification, automatic determination of the number of shared dimensions, and robustness when sample sizes are small relative to dimensionality.	Canonical Correlation Analysis (CCA) is a multivariate statistical method that identifies pairs of linear combinations — one from each of two variable sets — such that the correlation between each pair is maximised. Introduced by Harold Hotelling in his landmark 1936 Biometrika paper, CCA provides the most general linear framework for studying the association between two multivariate batteries of measurements, and many classical procedures (multiple regression, MANOVA, discriminant analysis) are special cases of it.