Hello Sean,
Thank you very much for your explanation. I agree with you as to which items
should be considered when compute P_{u,i}. They need to be both rated by
user u and similar (non-zero similarity) to item i.
I think you brought up a good point as to dealing with negative
similarities, which I have not realized before. Here is my other thought.
Based on your example and the proposed method, we will get a predicted
rating of 5 in such case after normalization. This seems counter-intuitive
to me, since we know that these two items are very dissimilar (actually
opposite correlated), a predicted rating close to 1 will be more intuitive
to me. Maybe we need to think more about the expression in section 3.2.1 of
that paper.
Any thoughts or comments?
Thank you,
Guohua
On Wed, Feb 10, 2010 at 5:16 PM, Sean Owen <[email protected]> wrote:
> You would only consider those items j that user u has rated. That is
> how I understand the expression in 3.2.1, and happens to be what
> GenericItemBasedRecommender does too.
>
>
> For the expression in 3.2.1, you are right that similarities of 0
> could be ignored, since they would not affect the calculation.
>
> However I am not sure I agree with this expression (or else I
> misunderstand it). It suggests using similarities as weights, and
> normalizing by the absolute values of weights. Similarities can be
> negative though. Say that only one item enters into this expression,
> and its rating is 5 on a scale of 1 to 5, and the item similarity is
> -1. This says the prediction is (-1*5)/1 = -5. Oops.
>
> For this reason I did something different in
> GenericItemBasedRecommender. I weight with 1+similarity. These weights
> are nonnegative then. The sense of the expression is preserved.
>
>
> Sean
>
>
> On Wed, Feb 10, 2010 at 10:59 PM, Guohua Hao <[email protected]> wrote:
> > Hello All,
> >
> > In item-based CF algorithms, when we predict the rating P_{u, i} of some
> > user 'u' for some item 'i', shall we consider all available items j,
> whose
> > similarities with item 'i' are not zero, or shall we only consider those
> > items whose have been both rated by user u and their similarities with
> item
> > i are not zero. This will affect the normalization part as we need to sum
> up
> > all those considered similarity scores.
> >
> > I am reading the following paper,
> >
> > Item-Based Collaborative Filtering Recommendation Algorithms (
> > www.grouplens.org/papers/pdf/www10_sarwar.pdf)
> >
> > The normalization part is in the middle left of page 5.
> >
> > Thank you very much,
> > Guohua
> >
>
