Weighted least squares best fit plane

[daviddoria]

I know that the plane through the center of mass whose normal is the eigenvector corresponding to the smallest eigenvalue of the scatter matrix of a set of points is the best fit plane. I now want to do a "weighted least squares" - would I simply multiply the
$\sum(x_j-\overline{x})(x_j-\overline{x})^T$
(from here http://en.wikipedia.org/wiki/Scatter_matrix)

by the weighting kernel

$\sum(x_j-\overline{x})(x_j-\overline{x})^T w(x_j-\overline{x})$

and then proceed to find the eigenvalues as normal?

Thanks,

David

 

[Valkarie]

Yes, that is correct. You would multiply the scatter matrix with the weighting kernel and then proceed to find the eigenvalues as normal.