Database Reference
In-Depth Information
to the estimation in user preference, we use the na¨ve Bayes assumption and assume
that user attributes are independent. Thus, we have
Pr
ð
R
I
¼
k
Þ
Pr
ð
A
1
;
A
2
; :::;
A
m
j
R
I
¼
k
Þ
ð
R
I
¼
Pr
k
j
A
¼
a
U
Þ¼
Pr
ð
A
1
;
A
2
; :::;
A
m
Þ
Þ
Q
j¼m
Pr
ð
R
I
¼
k
j¼
1
Pr
ð
A
j
j
R
I
¼
k
Þ
¼
A
¼f
A
1
;
A
2
; :::;
A
m
g
;
;
Pr
ð
A
1
;
A
2
; :::;
A
m
Þ
(4.7)
where Pr(
R
I
¼
k
) is the prior probability that the target item
I
receives a rating value
k
,
and Pr(
A
j
j
k
) is the conditional probability that user attribute
A
j
of a reviewer has
a value of
a
j
given item
I
receives a rating
k
from this reviewer. These two probabilities
can be learned by counting the review ratings on the target item
I
in a manner similar to
what we did in learning user preferences. When user attributes are not available, we
use Pr(
R
I
¼
R
I
¼
k
), i.e., item
I
's general likability, regardless of users, to approximate Pr
(
R
I
¼
k
j
A
¼
a
u
). In addition, Pr(
A
1
,
A
2
,
,
A
m
) is a normalizing constant.
...
4.4.2.3 Homophily Inference Engine
Finally, Pr(
R
UI
¼
N(
U
)}) is where SNRS utilizes homo-
phily effects from immediate friends. To estimate this probability, SNRS needs to
learn the correlations between the target user
U
and each of
U
's immediate friends
V
from the items that they both have rated previously, and then assume each pair of
friends will behave consistently on reviewing the target item
I
also. Thus,
U
's rating
can be predicted from
r
VI
according to the correlations. A common practice for
learning such correlations is to estimate user similarities or coefficients, based on
either user profiles or user ratings. However, user correlations are often so sensitive
that they cannot be fully captured by a single similarity or coefficient value.
Different measures return different results and have different conclusions on
whether or not a pair of users is really correlated [
16
]. At another extreme, user
correlations can be also represented in a joint distribution table of
U
's and
V
's ratings
on the same items that they have rated; i.e., Pr(
R
UJ
,
R
VI
)
k
j
{
R
VI
¼
r
VI
:
8
V
2
U(
I
)
\
I(
V
). This table
fully preserves the correlations between
U
's and
V
's ratings. However, in order to
build such a distribution with accurate statistics, it requires a large number of
training samples. This is especially a problem for recommender systems, because
in most of these systems, users review only a few items compared with the large
amount of items available in the system, and the co-rated items between users are
even fewer. Therefore, in this study, we use another approach to remedy the pro-
blems in both cases.
In Sect.
4.3
, we showed that it is true that immediate friends tend to give similar
ratings more than do non-friends. Therefore, for each pair of immediate friends
U
and
V
,
we consider their ratings on the same item to be close with some error
8
J
2
I(
U
)
\
e
.Thatis,
R
UI
¼
R
VI
þ e
;
I
2
I
ð
U
Þ\
I
ð
V
Þ
;
V
2
N
ð
U
Þ\
U
ð
I
Þ
:
(4.8)
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