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K Twi
v Twi
u Twi
v Twi
t
u Twi
k
matching
(
u
,
v
) = <
,
> =
·
(5.6)
,
k
k =
1
where K Twi is number of Twitter followee topics. A rank function defined on the
followees can be obtained accordingly to identify the optimal Twitter referrer.
To evaluate the proposed overlapped user-based approach for cross-network
YouTube video promotion, 2,061 videos on which more than 15 overlapped users
have social activity are selected to construct the YouTube test video set. Meanwhile,
79,169 Twitter followees who are followed by more than 50 users construct the can-
didate Twitter followee set. Normalized Discounted Cumulative Gain (NDCG) is
employed as the evaluation metric, which is defined as:
k
2 rel ( j )
1
Z
1
NDCG@ k
=
(5.7)
log
(
1
+
j
)
j
=
1
where rel
is a ground-truth relevance function between the test YouTube video
and the Twitter followee candidate. We combine two information retrieval metrics of
precision and recall to define rel
( · )
, i.e., the more the Twitter followees' followers
involve with the YouTube video, the higher the relevance score.
In addition to the proposed Transition Probability , Regression_l1 and Regres-
sion_l2 , we also consider two baselines for comparison: (1) Random : randomly
select k followees from the followee candidate set; and (2) Popularity : select k pop-
ular Twitter followees with the most #followers. NDCG@5 for the five methods
is shown in Fig. 5.6 . We can see that the overlapped user-based association mining
solutions generally outperforms the simple baselines. Among the three proposed
solutions, formulating the association mining as an optimization problem, Regres-
sion is more robust to noisy users than Transition Probability .The l 1 regularization
assumes sparse correlation between heterogeneous topics and achieves slightly better
performance than the l 2 regularization.
( · )
Fig. 5.6 NDCG@5 for different methods
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