Utility matrices
Most recommender systems use input that quantify users' preferences for items. These preferences are typically arranged in a matrix that has one row for each user and one column for each item. Such a matrix is called a utility matrix. For example, Netflix asks its users to rate movies from one to five stars. So, each entry in that utility matrix would be an integer uij in the range 0 to 5, representing the number of stars that user i gave to movie j, with 0 representing no rating.
For example, Table 9.1 shows a utility matrix that represents users' ratings of beers on a scale of 1-5, with 5 representing the greatest approval. Blanks represent no rating by that user for that item. The beers are: BL = Bud Light, G = Guinness, H = Heineken, PU = Pilsner Urquell, SA = Stella Artois, SNPA = Sierra Nevada Pale Ale, and W = Warsteiner.
Note
Most of the entries are blank.
|
BL |
G |
H |
PU |
SA |
SNPA |
W | |
|---|---|---|---|---|---|---|---|
|
x1 |
5 |
4 |
2 | ||||
|
x2 |
2 |
3 |
5 |
3 | |||
|
x3 |
1 |
4 |
3 | ||||
|
x4 |
3 |
4 |
5 |
4 | |||
|
x5 | ... |
