This reminds me: I never moved over the "folding-in" code from decomposer. Not that it's particularly complex, but it would probably be useful in "utils" at least. -jake On Thu, Jun 3, 2010 at 10:48 PM, Ted Dunning wrote: > You are correct. The paper has an appalling treatment of the folding in > approach. > > In fact, the procedure is dead simple. > > The basic idea is to leave the coordinate system derived in the original > SVD > intact and simply project the new users into that space. > > The easiest way to see what is happening is to start again with the > original > rating matrix A as decomposed: > > A = U S V' > > where A is users x items. If we multiply on the right by V, we get > > A V = U S V' V = U S > > (because V' V = I, by definition). This result is (users x items) x (items > x k) = users x k, that is, it gives a k dimensional vector for each user. > Similarly, multiplication on the left by U' gives a k x items matrix > which, > when transposed gives a k dimensional vector for each item. > > This implies that if we augment U with new user row vectors U_new, we > should > be able to simply compute new k-dimensional vectors for the new users and > adjoin these new vectors to the previous vectors. Concisely put, > > ( A ) ( A V ) > ( ) V = ( ) > ( A_new ) ( A_new V ) > > This isn't really magical. It just says that we can compute new user > vectors at any time by multiplying the new users' ratings by V. > > The diagram in figure one is hideously confusing because it looks like a > picture of some kind of multiplication whereas it is really depicting some > odd kind of flow diagram. > > Does this solve the problem? > > On Thu, Jun 3, 2010 at 9:26 AM, Sean Owen wrote: > > > Section 3 is hard to understand. > > > > - Ak and P are defined, but not used later > > - Definition of P has UTk x Nu as a computation. UTk is a k x m > > matrix, and Nu is "t" x 1. t is not defined. > > - This only makes sense if t = m. But m is the number of users, and Nu > > is a user vector, so should have a number of elements equal to n, the > > number of items > > - Sk * VTk is described as a k x "d" matrix but d is undefined > > - The diagram suggests that VTk are multiplied by all the Nu, which > > makes more sense -- but only if Nu are multiplied by VTk, not the > > other way. And the diagram depicts neither of those. > > - Conceptually I would understand Nu x VTk, but then P is defined by > > an additional product with Uk > > > > In short... what? > > > > > > On Thu, Jun 3, 2010 at 4:15 PM, Ted Dunning > wrote: > > > Fire away. > > > > > > On Thu, Jun 3, 2010 at 3:52 AM, Sean Owen wrote: > > > > > >> Is anyone out there familiar enough with this to a) discuss this paper > > >> with me or b) point me to another writeup on the approach? > > >> > > > > > >