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
Kmeans.
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 <pat@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 itemitem similarity matrix. It doesn't
need to be transposed and contains the "important" similaritiesas calculated by LLR for
example. Here similarity means similarity in which users preferred an item. So summing the
nonzero 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 useritem matrix seems to yield
a fromat that cannot be sent directly into clustering.
