Case 1 is fine, in case 2, I don't think that a dot product (without normalization) will yield a meaningful distance measure. Cosine distance or a Pearson correlation would be better. The situation is similar to Latent Semantic Indexing in which documents are represented by their low rank approximations and similarities between them (that is, approximations) are computed using cosine similarity. There is no need to make any normalization in case 1 since the values in the feature vectors are formed to approximate the rating values.
On Sat, Jan 25, 2014 at 5:08 AM, Koobas <koo...@gmail.com> wrote: > A generic latent variable recommender question. > I passed the user-item matrix through a low rank approximation, > with either something like ALS or SVD, and now I have the feature > vectors for all users and all items. > > Case 1: > I want to recommend items to a user. > I compute a dot product of the user’s feature vector with all feature > vectors of all the items. > I eliminate the ones that the user already has, and find the largest value > among the others, right? > > Case 2: > I want to find similar items for an item. > Should I compute dot product of the item’s feature vector against feature > vectors of all the other items? > OR > Should I compute the ANGLE between each par of feature vectors? > I.e., compute the cosine similarity? > I.e., normalize the vectors before computing the dot products? > > If “yes” for case 2, is that something I should also do for case 1?
