P1: Trim: 6.125in×9.25in Top: 0.5in Gutter: 0.75in
CUUS2079-09 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:28
9.2 Classical Recommendation Algorithms 251Now, assuming that the neighborhood size is 2, then Jorge and Joe are
the two most similar neighbors. Then, Jane’s rating for Aladdin computed
from user-based collaborative filtering isrJane,Aladdin=r ̄Jane+sim(Jane,Joe)(rJoe,Aladdin−r ̄Joe)
sim(Jane,Joe)+sim(Jane,Jorge)+
sim(Jane,Jorge)(rJorge,Aladdin−r ̄Jorge)
sim(Jane,Joe)+sim(Jane,Jorge)= 1. 33 +
0 .88(4− 2 .75)+ 0 .84(2− 1 .25)
0. 88 + 0. 84
= 2 .33 (9.15)
Item-based Collaborative Filtering. In user-based collaborative filtering,
we compute the average rating for different users and find the most similar
users to the users for whom we are seeking recommendations. Unfortu-
nately, in most online systems, users do not have many ratings; therefore,
the averages and similarities may be unreliable. This often results in a dif-
ferent set of similar users when new ratings are added to the system. On
the other hand, products usually have many ratings and their average and
the similarity between them are more stable. In item-based CF, we perform
collaborative filtering by finding the most similar items. The rating of user
ufor itemiis calculated asru,i=r ̄i+∑
j∈N∑(i)sim(i,j)(ru,j−r ̄j)
j∈N(i)sim(i,j), (9.16)
wherer ̄iandr ̄jare the average ratings for itemsiandj, respectively.Example 9.2.In Table9.1,rJane,Aladdinis missing. The average ratings for
items arer ̄Lion King=3 + 5 + 1 + 3 + 2
5
= 2. 8. (9.17)
r ̄Aladdin=0 + 4 + 2 + 2
4
= 2. (9.18)
r ̄Mulan=3 + 0 + 4 + 1 + 0
5
= 1. 6. (9.19)
r ̄Anastasia=