Canonical analysis relative to a closed subspace

An extension of Fisher's discriminant analysis for stochastic processes

“…(see, also, related work by Dauxois and Nkiet [8], Dauxois et al [9] and He et al [23]) Although beyond the scope of this paper, we note in passing that it is possible to extend the well-known connection between the finite dimensional Fisher's LDA and canonical correlation analysis (see, e.g., [28,Chapter 7]) to the infinite dimensional setting that was considered here. Further, through the use of Parzen's formulation for the density functional of a Gaussian process (e.g., [33]) it is possible to develop a parallel of the classical finite dimensional Bayes' classifier that can be used in an infinite dimensional context.…”

An RKHS framework for functional data analysis

“…Other approaches to functional (and more general) forms of canonical correlation include the works of Dauxois and Pousse (1976), Dauxois et al (2004) and He et al (2003). In the context of functional data all these references can be viewed as working with the Hilbert space indexed processes /X,f S L 2 ðTÞ ,/Y,gS L 2 ðTÞ ,f ,g 2 L 2 ðTÞ which leads to a singular value decomposition of the operator K À1=2 X…”

“…With the Dauxois and Pousse (1976), Dauxois et al (2004) and He et al (2003) formulations providing cases in point, we can say that the RKHS approach outlined in this section provides a viable setting for rigorous development of functional CCA methodology for two reasons. First, it produces optimal solutions in L 2 X , L 2 Y that provide true extension of the finite dimensional multivariate approach via inclusion of elements from L 2 (T) as well as finite dimensional linear combinations of the processes.…”

On invariance in canonical analysis with applications to covariate discriminant analysis

“…Assertion (ii) of the preceding lemma shows that E 2.3 has the form of subspaces that are involved in relative canonical analysis (see Dauxois et al 2004aDauxois et al , 2004b; that is why we will term the DA of Y and X 2·3 , the relative discriminant analysis (RDA) of Y and X 2 relative to X 3 , and we put…”