Design Considerations for a Social Network-Based Recommendation System (SNRS) - Community-Built Databases: Research and Development - page 83

probability, we adopt the na¨ve Bayes assumption. We assume that the item attri-
butes in A ' , for example, category and cast, are independent of each other. There-
fore, we adopt this approach and have

Pr ð R U ¼ k Þ Pr ð A 1 ; A 2 ; :::; A n j R U ¼ k Þ

Pr R U ¼ ð k j A ¼ a I Þ ¼

Pr ð A 1 ; A 2 ; :::; A n Þ

Þ Q j¼n
j

Pr ð R U ¼ k

1 Pr

ð A j j R U ¼ k Þ

¼

¼ A ¼f A 1 ; A 2 ; :::; A n g ;

;

Pr ð A 1 ; A 2 ; :::; A n Þ

(4.4)

where Pr A 0 1 ; A 0 2 ; ...; A 0 n

ð Þ

can be treated as a normalizing constant, Pr( R U ¼

k )is

A 0 J j

the prior probability that U gives a rating k , and Pr is the conditional

probability that each item attribute A 0 J in A 0 has a value a 0 J given U rated k ; for
example, Pr(movie type ¼ drama

ð R U ¼ k Þ

4). The last two probabilities can be
estimated from counting the review ratings of the target user U . Specifically,

j R U ¼

j I ð R U ¼ k Þ j þ 1

Pr ð R U ¼ k Þ¼ (4.5)

;

j I ð U Þ j þ n

and

þ

A 0 j ¼ a 0 j ; I ð R U ¼ k Þ 1

A j ¼ a j j

Pr ð R U ¼ k Þ¼ (4.6)

;

j I ð R U ¼ k Þ j þ m

where j I( U ) j is the number of reviews of user U in the training set, j I( R U ¼ k ) j is

A j ¼ a j ;

the number of reviews that user U gives a rating value k , and is

the number of reviews to which U gives a rating value k while attribute A j of the
corresponding target item has a value a j . Notice that we insert an extra value 1 to
the numerators in both equations, and add n , the range of review ratings, to the
denominator in (4.5), and m , the range of A j s values, to the denominator in (4.6).
This method is also known as the Laplace estimate, a well-known technique in
estimating probabilities [ 21 ], especially on a small size of training samples.
Because of the Laplace estimate, “strong” probabilities, like 0 or 1, from direct
probability computation can be avoided.
Moreover, in some cases when item attributes are not available, we can approxi-
mate Pr

j I ð R U ¼ k Þj

A 0 ¼ a 0 I Þ ð R U ¼ k j by the prior probability Pr( R U ¼ k ). Even though Pr

( R U ¼ k ) does not contain information specific to certain item attributes, it does

take into account U 's general rating preference; for example, if U is a generous
person, U gives high ratings regardless of the items.

4.4.2.2 Item Likability Inference Engine

Pr( R I ¼ a u ) captures the general likability of item I from users like user U .

For example, from a reviewer who is similar to Angela (e.g., the same gender and
age), how likely is it that “Revolutionary Road” will receive a rating of 5? Similar

k j A ¼