User specific recommendations

During the remainder of this chapter, we will focus on user-specific ratings. Let's start by considering a model of the recommendation system.

Let's assume:

C = Set of customers.

I = Set of items (could be movies, books, news items, and so on).

R = Set of ratings. This is an ordered set, where higher numbers indicate the high likeness of a particular item, whereas the lower value indicates a low likeness of a particular item. Generally this is represented by a real value between 0 and 1.

Let's define a utility function u, which looks at every pair of customers and items and maps it to a specific rating:

u: C * I → R

Let's give an example of a utility matrix, for a set of movies and users:

	Godfather I	Godfather II	Good Will Hunting	A Beautiful Mind
Roger			1	0.5
Aznan	1	0.7	0.2
Fawad	0.9	0.8	0.1
Adrian			1	0.8

A utility matrix is generally a sparse matrix, as users rate fewer movies than they watch. The areas where ratings are missing can be either...