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From Sean Owen <>
Subject Re: Interpreting the output of SVD
Date Mon, 22 Nov 2010 18:10:14 GMT
Hmm. I think I need to fix the second half of my analogy.

It's really U x S that could be said to be users' preferences for
pseudo-items. and S x VT could be said to be pseudo-users preferences for
real items. S itself is a diagonal matrix of course and those values are
kind of like "scaling factors" ... but I actually struggle to come up with a
good intuitive explanation of what S itself is (or really, U and V by

Anyone smarter have a nice pithy analogy?

On Mon, Nov 22, 2010 at 11:06 AM, Sean Owen <> wrote:
> In more CF-oriented terms, S is an expression of pseudo-users' preferences
> for pseudo-items. And then U expresses how much each real user corresponds
> to each pseudo-user, and likewise for V and items.
> To put out a speculative analogy -- let's say we're looking at users'
> preferences for songs. The "pseudo-items" that the SVD comes up with might
> correspond to something like genres, or logical groupings of songs.
> "Pseudo-users" are something like types of listeners, perhaps corresponding
> to demographics.
> Whereas an entry in the original matrix makes a statement like "Tommy likes
> the band Filter", an entry in S makes a statement like "Teenage boys in
> moderately affluent households like industrial metal". And U says how much
> Tommy is part of this demographic, and V tells how much Filter is industrial
> metal.

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