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. > >
