Canonical analysis of two euclidean subspaces and its applications

A new decomposition for square matrices

“…In [9,20,22] we can find how these angles were discovered and rediscovered again several times. Computation of canonical angles between subspaces is important in many applications including statistics [8,15], information retrieval [16], and analysis of algorithms [23]. There are many equivalent definitions of the canonical angles (see [11]).…”

Linear relative canonical analysis of Euclidean random variables, asymptotic study and some applications

“…Our approach consists in defining LRCA by using the CA of Euclidean spaces (see Dauxois and Nkiet (1997a)); one of the interests of this approach is that it permits to see several classical methods as particular cases of this CA. Two examples are given below.…”

“…This is an important goal since in multivariate analysis it often occurs that, in order to reduce dimensions, one have to work with linear transformations, and not necessarily projections, of original variables; so it may be convenient that these transformations do not affect the results of the given analysis. For the case of linear canonical analysis (LCA), this generalizing approach have been tackled by Dauxois and Nkiet (1997a) who determined conditions for having the aforementioned invariance. We will now extend this problem to the case of LRCA.…”

“…3 for the pair (A~, A2). Then, by applying Proposition 4.2 of Dauxois and Nkiet (1997a) Remark 2.3. The previous notion of invariance for LRCA is related to the problem of additional information in canonical analysis which interested some authors.…”

On invariance in canonical analysis with applications to covariate discriminant analysis

“…We first consider the more general framework of Canonical Analysis (CA) of Euclidean subspaces; the known invariance property of this CA given in Dauxois and Nkiet (1997) is improved so that it can be used when the considered subspaces are not included in the original ones. Then, using this result, we obtain a necessary and sufficient condition for having the invariance of DA with a covariate having the same means in the given groups, when both variable and covariable are transformed by linear maps.…”