In this section, let's formalize the recommender system problem. We have a set of users, 
, a set of items, 
(movies, tracks, products, and so on), and a set of estimates, 
. Each estimate is given by user 
, object 
, its result 
, and, possibly, some other characteristics.
We are required to predict preference as follows:
We are required to predict personal recommendations as follows:
We are required to predict similar objects as follows:
Remember—the main idea behind collaborative filtering is that similar users usually like similar objects. Let's start with the simplest method, as follows:
- Select some conditional measures of similarity of users according to their history of
ratings. - Unite users into groups (clusters) so that similar users will end up in the same cluster:
. - Predict the item's user rating...