Collaborative filtering
Most of us will have used eBay, Amazon, or any other popular web retailer. And most of us will have seen recommendations based on our past choices. For example, if you buy an electric toothbrush, Amazon would recommend you some extra brush heads as these items normally go together. All of these suggestions are based on recommended systems, which are typically based on collaborative filtering techniques.
Collaborative filtering algorithms recommend items (this is the filtering part) based on preference information from many users (this is the collaborative part). The collaborative filtering approach is based on similarity; the basic idea is people who liked similar items in the past will like similar items in the future.
In the following example, Adrian likes the movies Mission Impossible, Skyfall, Casino Royale, and Spectre. Bob likes the movies Skyfall, Casino Royale, and Spectre. Andrew likes the movies Skyfall and Spectre.
To recommend a movie to Andrew, we calculate...