Adaptive Canonical Correlation Analysis Based On Matrix Manifolds

Given two views (or representations) of the same set of objects, it aims at finding projections for each representation such that their correlation is maximized in the projection space. As every popular method in machine learning, since its first formulation (Hotelling, 1936) CCA has been extended to a kernel version (Lai & Fyfe, 2000; Akaho, 2001), to online and recursive versions (V ıa et al., 2007) and quite recently to a sparse version (Hardoon & Shawe-Taylor, 2011). CCA is usually formulated as the Generalized Singular Value Decomposition (Generalized SVD) of the cross-covariance matrix (Sun et al., 2009). Besides, it aims at finding projections that are orthogonal with respect to the auto-covariance matrices of each view. As CCA belongs to the class of Latent Variables methods, it shares close connections with those methods. Indeed, according to Rosipal & Kr amer (2006); Sun et al. (2009), CCA is a generalization of Orthonormal-ized Partial Least Squares.