Geodesic
Optimal subspaces and constrained principal component analysis
The electronic journal of linear algebra, Tome 10 (2003), pp. 201-211.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The main result of this article allows formulas of analytic geometry to be elegantly unified, by readily providing parametric as well as cartesian systems of equations. These systems characterize affine subspaces in Rp passing through specified affine subspaces of lower dimension. The problem solved is closely related to constrained principal component analysis. A few interesting applications are pointed out, notably a measure of the relative loss of optimality due to the constraints. The results pave the way for further research.
Classification : 15A03
Keywords: optimal subspace problem, constrained principal component analysis, affine subspace 
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     author = {Rolle, Jean-Daniel},
     title = {Optimal subspaces and constrained principal component analysis},
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Rolle, Jean-Daniel. Optimal subspaces and constrained principal component analysis. The electronic journal of linear algebra, Tome 10 (2003), pp. 201-211. http://geodesic.mathdoc.fr/item/ELA_2003__10__a9/