I'm new to recommender systems, and I've been reading about how user-based collaborative filtering can group similar users together and (for example) use their ratings to suggest movies to other similar users. However, I'm having trouble understanding exactly how a recommender system incorporates user characteristics into its modeling.
In the typical modeling framework (eg. linear models, decision trees, etc.) the analyst would explicitly define the variables to be used in the modeling process, thus allowing them to explicitly define the user features that go into the model. However, in a recommender system, the model is simply created from a matrix that contains only three data points (germane to the movie rating example I've been using): user ID, movie ID, and movie rating.
The matrix doesn't have any room for user characteristics like demographics or movie preferences, so how exactly can a recommender system claim to incorporate these characteristics in its modeling? Are they somehow incorporated implicitly through some kind of ordering of the matrix?
Any thoughts or resources in understanding this would be greatly appreciated.