Having covered distances, we are ready to delve into the topic of collaborative filtering, which will help us define a strategy for making recommendations. Collaborative filtering describes an algorithm, or more precisely a family of algorithms, that aims to create recommendations for a test user given only information about the ratings of other users via the rating matrix, as well as any ratings that the test user has already made.

There are two very common variants of collaborative filtering, memory-based collaborative filtering and model-based collaborative filtering. With memory-based collaborative filtering, the entire history of all the ratings made by all the users is remembered and must be processed in order to make a recommendation. The prototypical memory-based collaborative filtering method is user-based collaborative filtering. Although this approach uses all the ratings available, the downside is that it can be computationally expensive as the entire database...