China Communications • December 2015
23
have also utilized the information of time and
content to provide better recommendation re-
sults. For example, Gao[18] et al. studied the
temporal cyclic patterns of check-ins in terms
of temporal non-uniformness and temporal
consecutiveness, and they proposed a time-
aware POI recommendation model; Yin[19]
et al. proposed a location-content-aware topic
model in consideration of both personal inter-
est and local preference.
PROBLEM D
We explore the information of user preference,
social inuence and personalized geographical
inuence, and then integrate them into a uni-
ed probabilistic model to recommend proper
POIs for target users. Next, we formalize the
problem of this study.
Given a set of venues (POIs) V = {v
1
, v
2
,…,
v
M
}, L = {l
1
, l
2
,…, l
M
} is the set of locations
of POIs, where M is the number of POIs and
each location has longitude and latitude coor-
dinates. Let U = {u
1
, u
2
,…, u
N
} be the set of
users and G be the matrix of the relationships
between users, where N is the number of us-
ers. C = (c
ij
)
N×M
is a check-in frequency matrix
with each element (also defined as check-in
variable) representing the frequency of check-
ing in POI v
j
(with l
j
) by user u
i
. Assuming that
C
L
is an observed check-in action matrix, the
set of observations can be denoted as O = (U;
V; G; C
L
). According to all the observations,
our task is to predict the probability that a giv-
en user visits a new POI, and to recommend
the top-k POIs to the user.
MP
According to the Tobler’s first law of geog-
raphy[20], the locations near the place where
a user usually visits, are more likely to be
recommended to the user. Users differ in the
geographic spatial distribution of already-vis-
ited locations. The frequency distribution of
a user’s historical check-ins reflects his/her
preference for different locations, and the pref-
sure accurate POI recommendation results,
which suggests that more additional informa-
tion should be considered together.
The geographical feature of POIs is actual-
ly a unique identier distinguishing them from
other non-spatial items[7]. On the one hand,
some prior studies[3] calculated the similarity
between users in terms of their geographical
influence, and then recommended possible
POIs using collaborative ltering techniques.
On the other hand, other prior studies investi-
gated the geographical inuence of locations.
For example, Cheng[15] et al. viewed loca-
tions as ordinary non-spatial items and quan-
tified the geographical influence of locations
by predefining a range; Kurashima[16] et al.
proposed a geo-topic model based on the as-
sumption that if a location is closer to a user’s
current location or the locations he/she visit-
ed, it is more likely to be visited by the user;
Lian[17] et al. proposed a weighted matrix
factorization model which augmented user’s
and POI’s latent factors in the model with ac-
tivity area vectors of users and inuence area
vectors of POIs, respectively.
In many prior studies[1, 2, 4, 5], the dis-
tances between locations visited by the same
user were modeled based on a common distri-
bution for all users, e.g., a power-law distri-
bution or a multi-center Gaussian distribution.
Although this benefits the quality of POI
recommendation to some extent, a common
distribution for all users often ignores the per-
sonalized geographical influence. Therefore,
Zhang[6] et al. utilized kernel density estima-
tion to estimate the distribution of distances
between pairs of locations for each individual
user. Furthermore, a latest study[7] attempted
to characterize user check-in behavior using
two-dimensional kernel density estimation.
Inspired by the ndings in traditional social
networks, several POI recommendation ap-
proaches[3, 5, 14] took into consideration the
social inuence, but the results indicated that
the effect of such a factor was not signicant,
because there was, on average, a small over-
lap of a user’s check-ins to his/her friends’
check-ins. Besides this one, some researchers