Slope One recommenders are a part of a family of algorithms introduced in a 2005 paper by Daniel Lemire and Anna Maclachlan. In this chapter, we'll introduce the weighted Slope One recommender.
Note
You can read the paper introducing the Slope One recommender at http://lemire.me/fr/abstracts/SDM2005.html.
To illustrate how weighted Slope One recommendation works, let's consider the simple example of four users, labeled W, X, Y, and Z, who have rated three movies—Amadeus, Braveheart, and Casablanca. The ratings each user has provided are illustrated in the following diagram:
As with any recommendation problem, we're looking to replace the question marks with some estimate on how the user would rate the movie: the highest predicted ratings can be used to recommend new movies to users.
Weighted Slope One is an algorithm in two steps. Firstly, we must calculate the difference between the ratings for every pair of items. Secondly, we'll use this set of differences to make predictions...