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characteristics of the target item. A user's preference, such as Angela's interest in
drama movies, is usually reflected in the user's past ratings of other similar items,
for example, the number of drama movies that Angela previously viewed and the
average rating that Angela gave to those movies. Knowledge about the target item
can be obtained from public media such as magazines, television, and the Internet.
Meanwhile, the feedback from friends is another source of knowledge regarding the
item, and they are often more trustworthy than advertisements. When a user starts
considering the feedback from his/her friends, this user is then influenced by his/her
friends. Note that such an influence is not limited to that from our immediate
friends. Distant friends can also indirectly exert their influence on us; in the previous
scenario, for example, Angela was influenced by Linda's office mate. Each one of
these three factors has an impact on a user's final buying decision. If the impact
from all of them is positive, it is very likely that the target user will select the item.
On the contrary, if any has a negative influence, for example, very low ratings in
other user reviews, the chance that the target user will select the item will decrease.
Bearing this in mind, we propose SNRS in the following sections.
4.4.1 SNRS Architecture
Let us now introduce the variables used in this chapter and formalize the problem that
we are dealing with. Specifically, we use capital letters to represent variables, and use
capital and bold letters to represent their corresponding variable sets. The value for
each variable or variable set is represented by the corresponding lowercase letter.
Formally, we consider a social network as a graph G
(U, E) in which U
represents nodes (users) and E represents links (social relationships). Each user U
in U has a set of attributes A U as well as immediate neighbors (friends) N( U ) such
that if V
¼
E. The values of attributes A U are represented as a U .
Moreover, a recommender system contains the records of users' previous ratings,
which can be represented by a triple relation of T
2
N( U ), then ( U , V )
2
¼
(U, I, R) in which U is the users
in the social network G ; I is the set of items (products or services), and each item I in
I has a set of attributes A 0 I . R is a set of item ratings for item I ; that is, R
¼
{ R UI }
user U 0 s rating on item I and takes a numeric value k (e.g., k
where R UI ¼
{1,
2, ... , 5}). Moreover, we define I( U ) as the set of items that user U has reviewed, and
refer to the set of reviewers of item I as U( I ). The goal of this recommender system is
to predict Pr R UI ¼
¼
; i.e., the proba-
bility distribution of the target user U 's rating of the target item I given the attribute
values of item I , the attribute values of user U , and V 's rating on item I for all
reviewers V on item I . Once we obtain this distribution, R UI is equal to the expected
value of the distribution. Items with high estimated ratings will be recommended to
the target user, and users with high estimated ratings on the target item are the
potential buyers.
To achieve the goal, we propose SNRS as shown in Fig. 4.3 . SNRS consists of
two major components: an immediate friend inference engine and a distant friend
inference engine . As we pointed out in Angela's story, a user's buying decision is
A 0 ¼
a 0 I ;
k
j
A
¼
a U ; R VI ¼
f
r VI
: 8
V
2
U
ð
I
Þ
g
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