Commonly the square root of S is applied to both U and V. S is a set of importance weightings for the otherwise normalized columns of U and V.
On Mon, Nov 22, 2010 at 10:10 AM, Sean Owen <[email protected]> wrote: > 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 > themselves). > > Anyone smarter have a nice pithy analogy? > > On Mon, Nov 22, 2010 at 11:06 AM, Sean Owen <[email protected]> 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. > > > > >
