Yeah, I think the idea of confidence is a bit different than what I am
looking for using implicit factorization to do document clustering.
I basically need (r_ij - w_ih_j)^2 for all observed ratings and (0 -
w_ih_j)^2 for all the unobserved ratings...Think about the document x word
matrix where r_ij is the count that's observed, 0 are the word counts that
are not in particular document.
The broadcasted value of gram matrix w_i'wi or h_j'h_j will also count the
r_ij those are observed...So I might be fine using the broadcasted gram
matrix and use the linear term as \sum (-r_ijw_i) or \sum (-rijh_j)...
I will think further but in the current implicit formulation with
confidence, looks like I am really factorizing a 0/1 matrix with weights 1
+ alpha*rating for . It's a bit different from LSA model.
On Sun, Jul 26, 2015 at 12:34 AM, Sean Owen wrote:
> confidence = 1 + alpha * |rating| here (so, c1 means confidence - 1),
> so alpha = 1 doesn't specially mean high confidence. The loss function
> is computed over the whole input matrix, including all missing "0"
> entries. These have a minimal confidence of 1 according to this
> formula. alpha controls how much more confident you are in what the
> entries that do exist in the input mean. So alpha = 1 is low-ish and
> means you don't think the existence of ratings means a lot more than
> their absence.
>
> I think the explicit case is similar, but not identical -- here. The
> cost function for the explicit case is not the same, which is the more
> substantial difference between the two. There, ratings aren't inputs
> to a confidence value that becomes a weight in the loss function,
> during this factorization of a 0/1 matrix. Instead the rating matrix
> is the thing being factorized directly.
>
> On Sun, Jul 26, 2015 at 6:45 AM, Debasish Das
> wrote:
> > Hi,
> >
> > Implicit factorization is important for us since it drives recommendation
> > when modeling user click/no-click and also topic modeling to handle 0
> counts
> > in document x word matrices through NMF and Sparse Coding.
> >
> > I am a bit confused on this code:
> >
> > val c1 = alpha * math.abs(rating)
> > if (rating > 0) ls.add(srcFactor, (c1 + 1.0)/c1, c1)
> >
> > When the alpha = 1.0 (high confidence) and rating is > 0 (true for word
> > counts), why this formula does not become same as explicit formula:
> >
> > ls.add(srcFactor, rating, 1.0)
> >
> > For modeling document, I believe implicit Y'Y needs to stay but we need
> > explicit ls.add(srcFactor, rating, 1.0)
> >
> > I am understanding confidence code further. Please let me know if the
> idea
> > of mapping implicit to handle 0 counts in document word matrix makes
> sense.
> >
> > Thanks.
> > Deb
> >
>