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ground truth or predicted value) is observable, the estimation of
R
UI
will be skipped
in this iteration. Otherwise, Pr
R
UI
¼
A
0
¼
a
0
I
;
ð
k
j
A
¼
a
U
;
f
R
VI
¼
r
VI
:
8
V
2
U
ð
I
Þ
\
, will be estimated by immediate friend inference, and
R
UI
is then
obtained from (4.11). Because user rating is an integer value, in order to continue
the iterative process, we round
R
UI
to a close integer value, and insert into or update
U
(
I
) with
R
UI
if different. This entire process iterates
M
times or until no update
occurs in the current iteration. In our experiment, the process usually converges
within ten iterations.
It is worth pointing out that after we compute, Pr
R
UI
¼
N
ð
U
ÞgÞ
A
0
¼
a
0
I
;
ð
k
j
A
¼
a
U
;
f
, there are two other options for updating
R
UI
besides rounding the expectation in distant friend inference. The first option is to
select
R
UI
with the value
k
such that it maximizes Pr
R
UI
¼
R
VI
¼
r
VI
:
8
V
2
U
ð
I
Þ\
N
ð
U
Þ
gÞ
A
0
¼
a
0
I I
;
ð
k
j
A
¼
a
U
;
f
. However, by doing so, we are actually discard-
ing clues of small probabilities at the same time. After several iterations, the
errors caused by the greedy selection will be exacerbated. The target users are likely
to be classified with the majority class. The other option is to directly use Pr
R
UI
¼
R
VI
¼
r
VI
:
8
V
2
U
ð
I
Þ\
N
ð
U
Þ
gÞ
ð
A
0
¼
k
j
a
0
I
;
¼
f
R
VI
¼
r
VI
:
8
V
2
U
ð
I
Þ\
N
ð
U
Þ
gÞ
, as soft evidence to classify
other users. However, in our experiments, this approach does not return results as
good as those obtained by rounding the expectation.
A
a
U
;
4.5 Experiments
We evaluate the performance of SNRS on the Yelp dataset, mainly focusing on the
issues of the prediction accuracy, data sparsity, and cold-start. We used a restau-
rant's price range as the item attribute. Since there is no useful user attribute, we
substituted Pr(
R
I
¼
k
) when estimating item likability. As
a comparison, we implemented CF and trust-based collaborative filtering (TCF)
[
26
]. The basic idea of TCF is to combine trust-based weighting with filtering. It
first estimates two types of implicit trust: profile-level and item-level trust among
users based on their ratings. Then it filters out users with low trust values. To make
predictions, it uses the CF. Instead of using user similarity as in (4.1), TCF uses a
harmonic mean of user trust and user similarity. Compared with their use of implicit
user trust, SNRS in fact utilizes interpersonal trust underlying friend relationships.
For this reason, we are interested in comparing the performance of SNRS with that
of TCF.
k
j
A
¼
a
u
) with Pr(
R
I
¼
4.5.1 Cross-Validation
We carried out this experiment in a tenfold cross-validation. The prediction accu-
racy was measured by the mean absolute error (MAE), which is defined as the
average absolute deviation of predictions about the ground truth data over all the
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