did it... if you use the orthogonal distance (regular euclidean distance), it turns out that the solution is the same as that given by PCA... that's where an eigendecomposition solves this problem... ;)
just to fix notation, the solution (k-flat) corresponds to the vector space spanned by the eigenvectors associated to the k largest eigenvalues of the matrix \sum_i{x_i x_i^T}, x_i being the points on that sphere...
if you really want the proof, I guess I could take some time later to write it down for you or just meet me at UBC some day...
nice exercise, tough... I guess the geodesic distance would be way more complicated...
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
krja
(no subject)
Date: 2009-10-16 01:47 am (UTC)just to fix notation, the solution (k-flat) corresponds to the vector space spanned by the eigenvectors associated to the k largest eigenvalues of the matrix \sum_i{x_i x_i^T}, x_i being the points on that sphere...
if you really want the proof, I guess I could take some time later to write it down for you or just meet me at UBC some day...
nice exercise, tough... I guess the geodesic distance would be way more complicated...
cheers,
Ives