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 >
