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Fig. 4.4 Comparison of the (a) MAEs and the (b) coverage of CF, TCF, and SNRS for different
testing set sizes
TCF is 0.713 and 0.401, respectively. The decrease in the coverage of SNRS is also
the slowest as the training set becomes sparser. In particular, the ratio of the
decrease in the coverage of SNRS is 9% when the size of the testing set changes
from 10 to 70% of the entire dataset, while the same ratio of CF is 85.4%.
4.5.3 Cold-Start
Cold-start is an extreme case of data sparsity where a new user has no reviews, in
which CF cannot make recommendations to the new user. Neither can SNRS do so if
this new user has no friends. However, in some cases of cold-start, when a new user
is invited by some existing users in the system, the preference of this new user can be
estimated by those of the user's friends. In this study, we simulated the latter case of
cold-start by creating the following experimental settings: (1) Since there is no prior
ratings of the target user, we simply set the output from Pr
A
0
¼
a
0
I
Þ
as a
uniform distribution. (2) Because we cannot learn the rating correlation between this
new user and the user's friends, we directly used the friends' rating distributions on
the target item, Pr(
R
UI
ð
R
U
¼
k
j
U(
I
)}), as the result from friend
inference. (3) Except for the target user, the ratings of all other users were known.
We simulated cold-start for every user in the dataset. The resulting MAE is 0.753
and the coverage is 1. This result demonstrates that even in cold-start, SNRS can
still perform decently. The coverage of SNRS is high compared with that in the
tenfold cross-validation (0.807) because the ratings of every target user's friends
are all observable in the setting of this experiment.
j
{
R
VI
:
8
V
2
N(
U
)
\
4.5.4 Role of Distant Friends
In Sect.
4.5.1
, we noticed SNRS achieved the highest coverage because it is able to
make use of estimated ratings of immediate friends which are inferred from distant
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