Design Considerations for a Social Network-Based Recommendation System (SNRS) - Community-Built Databases: Research and Development - page 82

immediate friends and computes the probability distribution of user U' s rating of
item I based on U' s immediate friends' ratings on item I ; and finally (4) an
aggregator takes the results from the aforementioned three inference engines,
combines them, and predicts user U' s rating distribution for item I . We shall discuss
these components of SNRS in the following sections.

4.4.2 Immediate Friend Inference

Since the immediate friend inference engine considers homophily from immediate
friends only, the probability distribution it estimates is actually Pr R UI ¼ A 0 ¼ ð k j

a 0 I ; . The set of user V is limited from all

reviewers of item I to U 's immediate friends who also rate item I . Note that
information from other reviewers of item I will be used in the distant friend
inference engine. Since direct computing Pr R UI ¼

A ¼ a U ; R VI ¼ f r VI : 8 V 2 U ð I Þ\ N ð U Þ gÞ

A 0 ¼ a 0 I ;

ð k j A ¼ a U ; R VI ¼ f

r VI is difficult, we assume that the influence of three factors,

i.e., item attributes, user attributes, and ratings of immediate friends, are indepen-
dent of each other. Therefore, we factorize this probability as follows.

: 8

V 2 U ð I Þ\ N ð U ÞgÞ

A 0 ¼ a 0 I ;

Pr R UI ¼

ð k j ¼ f R VI ¼ r VI

: 8

V 2 U ð I Þ\ N ð U Þ g Þ

A a U ;

1
Z Pr R UI ¼

A 0 ¼ a 0

¼ ð k j Þ Pr R UI ¼ ð k j A ¼ a U Þ (4.3)

Pr R UI ¼ ð k j f R VI ¼ r VI

: 8

V 2 U ð I Þ\ N ð U Þ g Þ :

A 0 ¼ a 0 I is the conditional probability that the target user U

will give a rating k to an item with the same attribute values as item I .This
probability represents U 's preference for items similar to I . Because this value
depends on the attribute values of items rather than an individual item, we drop the
subscript I in R UI for simplification. Second, Pr( R I ¼

First, Pr R U ¼ ð k j Þ

a u ) is the probability
that the target item I will receive a rating value k from a reviewer whose attribute
values are the same as U . This probability reflects the general likability of the target
item I by users like U . For the same reason, because this value depends on the
attribute values of users rather than a specific user, we drop the subscript U in R UI .
Finally, Pr( R UI ¼

k j A ¼

N( U )}) is the probability that the
target user U gives a rating value k to the target item I given the ratings of U 's
immediate friends for item I . This is where we actually take homophily effects into
consideration in SNRS. We shall present the components for estimating each of the
above probabilities in the following sections.

k j { R VI ¼ r VI : 8 V 2 U( I ) \

4.4.2.1 User Preference

A 0 ¼ a 0 I Þ

Pr measures the target user U 's preference for the items similar to

item I . For example, if we want to predict Angela's rating to “Revolutionary Road”,
Pr

ð R U ¼ k j

A 0 ¼ a 0 I Þ ð R U ¼ k j gives us a hint of how likely it is that Angela will give a rating

k to a drama movie which also has Kate Winslet in the cast. To estimate this