Oct 28, 2010
Mean/Centroid of rank-deficient symmetric positive definite matrices (SPDs)
Post @ 18:20:43 | Riemannian mean
Geometry of matrix manifolds is fascinating.
(I will give a talk on this topic next December)
A very recent and neat work generalizes the Riemannian mean of (SPD) positive semi-definite matrices to
rank deficient sets
using quotient geometry:
Rank-preserving geometric means of positive semi-definite matrices
by Silvere Bonnabel, Rodolphe Sepulchre.
http://arxiv.org/abs/1007.5494
Frank.
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2 Comments
Re: Mean/Centroid of rank-deficient symmetric positive definite matrices (SPDs)
Interesting...I'm wondering if their approach gives the same answer as the "usual" mean (ie, geometric mean of eigenvalues) for symmetric strictly positive definite matrices
From : Yaroslav Bulatov @ 2010-10-29 05:36:56 Edit
Re: Mean/Centroid of rank-deficient symmetric positive definite matrices (SPDs)
Well, I would say it is different since it deals internally with Stiefel submanifolds and Grassman submanifolds.
Worth a careful reading as tools appear in other papers as well.
From : Frank @ 2010-11-05 00:09:27 Edit