Re: singular value decompostion

["H T Onishi" <htonishi(at)home.com>]

> Thanks, that clarifies some points.  You were correct, I copied down a .46
> rather than a -.46.
>
> I will run through your exercise to make sure I understand correctly.
>
> Do you have any experience with Principal component analysis and how that
can
> be done with SVD?
>
> Thanks again,
>
> Dave
>

I am not an expert in the SVD algorithm.  The note by Fogel should be heeded
and you may want to search the appropriate newsgroup for more info.  I
believe that the SVD algorithm implemented in IDL was taken from Numerical
Recipes and there seems to be a lot of controversy over those routines.  You
may want to read http://math.jpl.nasa.gov/nr/nr-alt.html for more info.  I
know that I had to "tweak" an early version of the SVD routine from
Numerical Recipes to get it to work properly -- problems with underflow.

Regarding Principal Component Analysis, I believe that SVD is the key
algorithm used to extract the PC's.  I know that it has been used with some
success to remove background clutter from imagery that contains moving
targets.  Again I am not an expert here (in fact not even a novice) but from
what I understand a set of images of the same scene -- possibly
multi-spectral -- is combined into a large matrix.  Each image is turned
into a vector and the set of vectors is combined into a large matrix.  These
vectors span a vector space and the PCs corresponding to the largest
singular values represent clutter vectors that can then be subtracted from
the original image.  I think the PCs are in the V matrix, but there is a 50%
chance that I'm wrong about that.  That's about all I know.  I'm sure there
are many more applications.  I suggest you do a search with AltaVista to see
what you can find!  Or you can be more conventional and do a literature
search, which might be more fruitful.

Howard