We have already pointed out that companies such as Amazon track purchases and page views to make recommendations, Goodreads and Yelp use five-star ratings and text reviews, and sites such as Reddit or Stack Overflow use simple up/down voting. You can see that preference can be expressed in the data in different ways, from Boolean flags, to voting, to ratings. However, these preferences are expressed by attempting to find groups of similarities in preference expressions in which you are leveraging the core assumption of collaborative filtering.

More formally, we understand that two people, Bob and Alice, share a preference for a specific item or widget. If Alice too has a preference for a different item, say, a sprocket, then Bob has a better than random chance of also sharing a preference for a sprocket. We believe that Bob and Alice's taste similarities can be expressed in an aggregate via a large number of preferences, and by leveraging the collaborative...