Well, I think what you are suggesting is to define popularity as being similar to other items. So in this way most popular items will be those which are most similar to all other items, like the centroids in K-means.
I would first check the correlation between this definition and the standard one (that is, the definition of popularity as having the highest number of ratings). But my intuition is that they are different things. For example. an item might lie at the center in the similarity space but it might not be a popular item. However, there might still be some correlation, it would be interesting to check it. hope it helps On Wed, Feb 5, 2014 at 3:27 AM, Pat Ferrel <p...@occamsmachete.com> wrote: > Trying to come up with a relative measure of popularity for items in a > recommender. Something that could be used to rank items. > > The user - item preference matrix would be the obvious thought. Just add the > number of preferences per item. Maybe transpose the preference matrix (the > temp DRM created by the recommender), then for each row vector (now that a > row = item) grab the number of non zero preferences. This corresponds to the > number of preferences, and would give one measure of popularity. In the case > where the items are not boolean you'd sum the weights. > > However it might be a better idea to look at the item-item similarity matrix. > It doesn't need to be transposed and contains the "important" > similarities--as calculated by LLR for example. Here similarity means > similarity in which users preferred an item. So summing the non-zero weights > would give perhaps an even better relative "popularity" measure. For the same > reason clustering the similarity matrix would yield "important" clusters. > > Anyone have intuition about this? > > I started to think about this because transposing the user-item matrix seems > to yield a fromat that cannot be sent directly into clustering.
