Re: SVD Algorithm

From: Luigi Napolitano (uniluigiXXX_at_virgilio.it)
Date: 12/14/04 

Date: Tue, 14 Dec 2004 14:44:10 GMT

"Paige Miller" <paige.miller@kodak.com> ha scritto nel messaggio
news:cpmqig$lfn$1@news.kodak.com...
> I'm terribly curious, Luigi -- why is it necessary that the algorithm
> produce singular values in descending order?
I will use SVD for Latent Semantic Indexing (Information Retrieval).
So I need singular value in descending order (to take the first "k"
elements).

> What is the impediment that prevents you from sorting the singular values
> (and equivalently re-ordering eigenvectors) upon completion of the
> algorithm?
I could sort the singular values but, then, the columns of U and the rows of
V must be interchanged.

> Regarding the rows < number of columns, if you transpose the matrix and
> then do an SVD (which is now possible because after transposition, number
> of rows > number of columns), you will have a solution that is essentially
> the same -- the left eigenvectors of the transposed matrix are the right
> eigenvectors of the untransposed matrix, and vice versa.
Rows = words; Columns = documents. I can't transpose the matrix.

How can I do?
Thank you for reply.

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