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Event-based Social Networks: Linking the Online and
Offline Social Worlds
Xingjie Liu
?
, Qi He
†
, Yuanyuan Tian
†
, Wang-Chien Lee
?
, John McPherson
†
, Jiawei Han
?
The Pennsylvania State University,
†
IBM Almaden Research Center,
University of Illinois at Urbana-Champaign
?
{xzl106, wlee}@cse.psu.edu,
†
{heq, ytian, jmcphers}@us.ibm.com,
hanj@cs.uiuc.edu
ABSTRACT
Newly emerged event-based online social services, such as
Meetup and Plancast, have experienced increased popularity
and rapid growth. From these services, we observed a new
type of social network – event-based social network (EBSN).
An EBSN does not only contain online social interactions
as in other conventional online social networks, but also in-
cludes valuable offline social interactions captured in offline
activities. By analyzing real data collected from Meetup, we
investigated EBSN properties and discovered many unique
and interesting characteristics, such as heavy-tailed degree
distributions and strong locality of social interactions.
We subsequently studied the heterogeneous nature (co-
existence of both online and offline social interactions) of
EBSNs on two challenging problems: community detection
and information flow. We found that communities detected
in EBSNs are more cohesive than those in other types of
social networks (e.g. location-based social networks). In the
context of information flow, we studied the event recom-
mendation problem. By experimenting various information
diffusion patterns, we found that a community-based diffu-
sion model that takes into account of both online and offline
interactions provides the best prediction power.
This paper is the first research to study EBSNs at scale
and paves the way for future studies on this new type of
social network. A sample dataset of this study can be down-
loaded from http://www.largenetwork.org/ebsn.
Categories and Subject Descriptors
H.3.4 [Information Storage and Retrieval]: Systems
and Software - Information networks
General Terms
Algorithms, Experimentation.
Keywords
Event based Social Networks, Social Network Analysis, So-
cial Event Recommendation, Online and Offline Social Be-
haviors, Heterogeneous Network
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission and/or a fee.
KDD’12, August 12–16, 2012, Beijing, China.
Copyright 2012 ACM 978-1-4503-1462-6 /12/08 ...$10.00.
1. INTRODUCTION
Newly emerged event-based online social services, such as
Meetup (www.meetup.com), Plancast (www.plancast.com),
Yahoo! Upcoming (upcoming.yahoo.com) and Eventbrite
(www.eventbrite.com) have provided convenient online plat-
forms for people to create, distribute and organize social
events. On these web services, people may propose so-
cial events, ranging from informal get-togethers (e.g. movie
night and dining out) to formal activities (e.g. technical
conferences and business meetings). In addition to support-
ing typical online social networking facilities (e.g. sharing
comments and photos), these event-based services also pro-
mote face-to-face offline social interactions. To date, many
of these services have attracted a huge number of users and
have been experiencing rapid business growth. For example,
Meetup has 9.5 million active users, creating 280, 000 social
events every month; Plancast has over 100, 000 registered
users and over 230, 000 visits per month.
Meetup Service
Users:
Events:
Social
Groups:
Users:
Events:
Following
links:
Plancast Service
Plancast
Event-based Social Network
Meetup
Event-based Social Network
Online Network:
Offline Network:
Offline Network:
Online Network:
Figure 1: Event-based Social Network Examples
As these event-based services continue to expand, we iden-
tify a new type of social network – event-based social net-
work (EBSN) – emerging from them. Like conventional on-
line social networks, EBSNs provide an online virtual world
where users exchange thoughts and share experiences. But
what distinguishes EBSNs from conventional social networks
is that EBSNs also capture the face-to-face social interac-
tions in participating events in the offline physical world.
Fig. 1 depicts two example EBSNs from Meetup and Plan-
cast. In Meetup, users may share comments, photos and
event plans with members in the same online social groups
(e.g. “bay area photographers”, “Nevada county walkers”).
In Plancast, users may directly “follow” others’ event calen-
dars. Bi-directional co-memberships of online social groups
in Meetup or uni-directional subscriptions in Plancast ulti-
mately constitute an online social network represented as
the dashed lines on the right side of Fig. 1. Meanwhile, in
both cases, users’ co-participations of the same events derive
their offline social connections. These connections collec-
tively form an offline social network denoted as dotted lines
in Fig. 1. The online and offline social interactions jointly
define an EBSN.
Recent location-based online social networking services,
such as Foursquare (foursquare.com) and Gowalla (gowalla.
com), represent another type of popular social network, called
a location-based social network (LBSN). They are somewhat
similar to EBSNs, as they capture online social interactions
as well as offline location checkins. However, unlike the of-
fline social events that incur a group of people with social
interactions, location checkins from LBSNs mostly represent
individual behaviors, i.e. a particular user was at a specific
location at a specific time. Although in [5], adjacent check-
ins were treated as one kind of reason for social network tie
creation. It is estimated that adjacent checkins have only a
24% chance to lead to a new social friendship in Gowalla.
Therefore, in this paper, we only compare EBSNs against
the online social networks in LBSNs.
To the best of our knowledge, this paper is the first work
to identify an event-based social network as a co-existence
of both online and offline social interactions, and compre-
hensively study its properties. Our study revealed the many
aspects of EBSNs that are significantly different from con-
ventional social networks. As to be shown in our analysis,
social events present very regular temporal and spatial pat-
terns. In addition, both online and offline social interactions
in EBSNs are extremely local. For example, we found that
70.65% of Meetup online friends and 84.61% of Meetup of-
fline friends live within 10 miles of each other. To our sur-
prise, the degree distributions of the Meetup EBSN do not
follow the usual power law distribution, but are more heavy-
tailed than power law. Furthermore, we found that the on-
line and offline social interactions in an EBSN are positively
correlated, implying a synergistic relationship between the
two parts.
Community structure detection is a very useful approach
for analyzing social networks. However, to correctly detect
communities in an EBSN, one has to consider both online
and offline social interactions. In this paper, we employ an
extended Fiedler method to incorporate this heterogeneity
during the community detection process. Through exper-
iments, we demonstrate the advantage of this method to
other approaches. We also observed that the detected com-
munities in the Meetup EBSN are more cohesive than those
of the Gowalla LBSN.
To further investigate information flow over EBSNs, we
also study the problem of event participation recommenda-
tion. Due to the short life time of an event, the event partic-
ipation recommendation problem significantly differs from
the usual recommendation problem for movies or places.
Recommendation of an event is only valid after the event
is created and before the event starts. This leads to a cold-
start problem. In this paper, we design a number of diffusion
patterns that capture the information flow over the heteroge-
neous EBSNs. Through experiments we demonstrate that
the diffusion pattern that takes the community structures
into account yields the best prediction power.
The rest of this paper is organized as follows. We describe
the related work in Section 2 and formally define EBSNs in
Section 3 . We examine the properties of EBSNs in Sec-
tion 4 and further investigate the community structures in
Section 5. In Section 6, we tackle the event participation
prediction problem to study the information flow over EB-
SNs. Finally, we conclude the paper in Section 7.
2. RELATED WORK
Offline social interactions in the physical world have al-
ways been important in sociology [9]. One line of work is
to study the origin of social relationships. In [12], Feld pro-
posed a focus theory in which individuals organize their so-
cial interactions around foci, such as workplaces, families,
etc; whereas [20, 16, 3] utilized affiliation to explain the con-
struction of social connections. Chapter 4 of [11] provides
a nice summary on these topics. Under the above theories,
social events can be viewed as one type of focus or affiliation
that creates the social interactions between participants.
Thanks to the popularity of event-based social network
services, such as Meetup and Plancast, we are now able to
get our hands on large scale social data with rich information
on both online activities and offline social events. In [24],
Sander and Seminar attended 40 social events in Meetup and
concluded that participants in Meetup social events have
social structures instead of just strangers meeting strangers.
Similar to event-based social networks, location-based so-
cial networks also contains “online” social interactions and
“offline” checkin information. Although adjacent location
checkins may indicate implicit social interactions and social
ties [5], checkins are usually sporadic [21] and largely rep-
resent individual behaviors. The geographical features of
users were also examined to infer social ties in [7, 26]. In
comparison to these work, the “offline” information (social
events) studied in this paper does not only contain location,
but also time and people involved.
3. EVENT-BASED SOCIAL NETWORKS
In this section, motivated by popular event-based social
services, we define event-based social networks and describe
how to construct the networks from collected datasets.
3.1 Event-based social services
As various online social networking services become preva-
lent, a new type of event-based social service has emerged.
These web services help users to create social event propos-
als, disseminate the proposals to related people, and keep
track of all participants. To foster efficient communication
and sharing, these event-based services also provide online
social networking platforms to connect users with others
with similar interests. Below, we describe two examples of
such event-based social services: Meetup and Plancast.
Meetup is an online social event service that helps people
publish and participate in social events. On Meetup, a social
event is created by a user by specifying when, where and
what the event is. Then, the created social event is made
available to selected users or public, controlled by the event
creators. Other users may express their intent to join the
event by RSVP (“yes”, “no” or “maybe”) online. To facilitate
online interactions, meetup.com also allows users to form
social groups (e.g. “bay area single moms”, “Nevada county
walkers”) to share comments, photos and event plans.
Similar to meetup.com, Plancast is another web service
that helps users create and organize events online. Users
also RSVP to express their intent to join social events. In
Meetup Gowalla
# Users 5, 153, 886 # Users 565, 642
# Events 5, 183, 840 # Locations 2, 838, 143
# RSVPs 42, 733, 136 # Checkins 36, 804, 656
# Groups 97, 587 # Social links 2, 431, 625
# Memberships 10, 704, 068
Table 1: Dataset Statistics
contract to Meetup which adopts social groups to connect
users online, Plancast allows users to “follow” others’ social
event calendars to establish online connections.
3.2 Event-based Social Networks Definition
Based on the event-based social services described above,
we formulate a new type of social network, called an event-
based social network (EBSN).
Like any social network, EBSNs capture social interac-
tions among users. However, different from others, ESBNs
incorporate two forms of social interactions: online social
interactions and offline social interactions.
Online social interactions. In EBSNs, users can in-
teract with each other online without the need of physical
contact. For example, people can share thoughts and ex-
periences with those in the same social group in Meetup.
In Plancast, user comments and event plans are pushed to
those who “follow” the user.
Offline social interactions. Social events play a ma-
jor role in ESBNs. In a social event, people physically get
together at a specific time and location, and do something
together. Therefore, the social events in EBSNs represent
the offline social interactions among event participants.
Definition: Formally, we define an EBSN as a heteroge-
neous network G = hU, A
on
, A
off
i, where U represents the set
of users (vertices) with |U | = n, A
on
stands for the set of on-
line social interactions (arcs), and A
off
denotes the set of of-
fline social interactions (arcs). The online social interactions
of an EBSN form an online social network G
on
= hU, A
on
i,
and the offline interactions of an EBSN compose an offline
social network G
off
= hU, A
off
i.
Note that the online social network or the offline social
network of a EBSN can be either directed or undirected.
For simplicity, we only focus on undirected online and offline
networks in this paper.
The online social network [1, 18] or the offline social net-
work [2, 22] alone is not new and has been studied exten-
sively before. But the co-existence of both is what makes
EBSNs special. As shown later in this paper, these two
forms of social networks in EBSNs are intertwined but also
have their own distinct characteristics at the same time.
3.3 Representative Datasets Description
To effectively study EBSNs and explore the unique prop-
erties against related LBSNs, we collected data from the
popular event-based web services Meetup and the popular
location-based social service Gowalla. In this section, we
introduce the basic dataset statistics, as well as how EBSN
and LBSN are established from these datasets.
Meetup EBSN. We crawled meetup.com from Oct 2011
to Jan 2012. The collected data statistics are shown in Ta-
ble 1. With the Meetup dataset, the online EBSN is con-
structed by capturing the co-membership of online social
groups: users u
i
and u
j
are connected in the online social
network G
on
if they are members of the same social group.
Let g
r
denote a group with |g
r
| members, then (u
i
, u
j
) ∈ A
on
if and only if ∃g
r
such that u
i
∈ g
r
and u
j
∈ g
r
. We consider
users of a smaller group more closely connected than those
of a larger group. Therefore, we adopt a similar approach
as in [19] to define the edge weights:
w
on
i,j
=
X
∀g
k
,u
i
∈g
k
∧u
j
∈g
k
1
|g
k
|
. (1)
The offline social network of the EBSN, G
off
, is constructed
in a similar way based on the co-participation of social events:
user u
i
and u
j
are connected if they co-participated in the
same social event. If we use e
k
to represent a social event
with |e
k
| participants, and u
i
∈ e
k
to denote the fact that
u
i
participated e
k
, then the weight of the offline social in-
teraction between u
i
and u
j
is defined as
w
off
i,j
=
X
∀e
k
,u
i
∈e
k
∧u
j
∈e
k
1
|e
k
|
. (2)
Gowalla LBSN. Gowalla is a popular online location-
based social networking service that allows individual user to
“checkin”their current locations (as well as comments/photos)
and share with their friends. Gowalla requires users to ex-
plicitly specify their friends. Users need to mutually accept
each other as friends to establish an online social link.
We crawled Gowalla from Sep 2011 to Nov 2011 and col-
lected a subset of the users’ online social networks and place
checkins. The total numbers of users and locations are
also summarized in Table 1. As discussed before, although
this LBSN provides offline location checkins, these check-
ins cannot directly form an offline social network. Thus,
the Gowalla LBSN only has an online social network in this
study.
4. PROPERTIES OF EBSNS
In this section, we analyze the Meetup dataset to highlight
the unique properties of EBSNs. As social events play a cen-
tral role in EBSNs, we first study those properties specifi-
cally associated with social events. Then, we examine the
network properties of EBSNs.
4.1 Social Events
Social events provide a platform for users to get-together
physically. A social event is characterized by two major
features: event time and event location. First, we observe
Mon Tue Wed Thu Fri Sat Sun’
0
5
10
15
x 10
4
Event Start Time over Every Hour
Count
← 2PM
← 8PM
← 11AM
← 2PM
← 8PM
Figure 2: Social event time histogram over every
hour of one week.
that social events exhibit regular temporal patterns. Fig. 2
depicts the social event time pattern on weekly scale. It is
clear that in every weekday there is a small spike around
2pm in the afternoon, followed by a higher spike at 8pm in
the evening. On weekends, events distribute relatively even
throughout the day.
count: 8100
count: 29139
count: 13166
count: 14736
count: 20126
Figure 3: Social event geographical histogram. Each
bar represents the number of social events in 100
square miles.
We also observe that social events are mainly located in
urban areas. Fig. 3 depicts a US event geographical his-
togram with 100 square miles as a geographical unit.
4.2 Event and Group Participation
To understand the basic network properties of the Meetup
EBSN, we need to first study the event participation and
group membership in Meetup. As shown in Fig. 4(a), most
of the events are small with just a few participants, but
big events with a large number of participants (the heavy
tail) do exist in a non-trivial quantity. Similarly, Fig. 4(b)
shows that large groups do have significant presence. We
examine how these two distributions fit the power law curve
by Kolmogorov-Smirnov test [6]. This approach estimates
the following 3 parameters:
• xmin: the best fitted cutoff value so that only values
larger than xmin fit a power-law distribution;
• ˆα: the slope of the best fitted power-law distribution so
that values larger than xmin follow distribution x
− ˆα
;
• p-value: the statistical significance of the goodness of
the power-law fitting, (p-value larger than 0.1 suggests
a significant good fit).
10
0
10
1
10
2
10
3
10
4
10
−7
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
# Participants per Event
Noramlized Frequency
Data Distribution
Fitted xmin = 250
Fitted Slope = 3.46
(a) # participants per event
10
0
10
1
10
2
10
3
10
4
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
# Members per Social Group
Normalized Frequency
Data Distribution
Fitted xmin = 1045
Fitted Slope = 3.28
(b) # members per group
Figure 4: Histogram of the number of participants
per event and number of members per group.
By estimating the above parameters, we find that only
after xmin= 250 does the event size follow a power-law dis-
tribution with a high statistical significance (with p-value
0.357). Similarly, the number of members per group follows
a power-law distribution non-significantly with ˆα = 3.28
only after the number of events is greater than 1045 (with p-
value 0.088). These two results suggest that although most
events and social groups are in small scale, large events and
large groups do show significant presence in the Meetup
dataset.
4.3 Network Properties
Now we study the network properties of the Meetup ESBN
by comparing it against the Gowalla LBSN. Table 2 lists
some network properties of the Meetup EBSN online social
network G
on
, offline social network G
off
, combined network
G as well as the Gowalla LBSN social network. First, it
can be clearly seen that the EBSN online social network is
much denser than the EBSN offline social network, (larger
strongly connected component SCC, higher clustering co-
efficient and lower average degree of separation). This is
due to the fact that a user connects to more people online
than in actual social events. Secondly, all three EBSN so-
cial networks (G
on
, G
off
and G) are much denser than the
Gowalla LBSN, because Meetup users interact with each
other by co-joining social groups or co-participating social
events whereas Gowalla users have to mutually establish
friendships to get connected.
Meetup EBSN Gowalla LBSN
G
on
G
off
G
Mean Degree 1, 786.1 140.7 1, 560.6 10.64
Median Degree 623 40 463 3
SCC. Ratio 0.999 0.993 0.997 0.987
Clustering Coef. 0.438 0.267 0.429 0.137
Degree Separation 3.00 4.25 3.07 4.47
Degree Fitted xmin 3, 765 536 7, 490 47
Degree Fitted ˆα 2.49 2.53 2.50 2.53
Degree Fitting p-value 0.000 0.000 0.000 0.124
Table 2: Network statistics comparison between
EBSN and LBSN.
To dig deeper into the network properties of EBSN, we
first study the degree distributions in Fig. 5. Again, we ap-
ply the Kolmogorov-Smirnov statistic to examine whether
these distributions fit the power law distribution. The es-
timated parameters are listed in the bottom of Table 2.
While the Gowalla LBSN conforms to the power law distri-
bution, all three of the EBSN forms are more heavy-tailed
than power law. This heavy tail phenomenon in the Meetup
EBSN is correlated with the significant presence of big events
and big social groups found in Section 4.2.
Figure 5: Degree distribution comparison between
EBSN and LBSN.
Next, we analyze the correlation between each user’s on-
line interactions and offline interactions. By applying Pear-
son correlation, we observe positive correlation between on-
line and offline degrees (0.368) as well as between online
and offline cluster coefficients (0.393). This implies that the
online social network and the offline social network work to-
gether synergistically in the Meetup EBSN – each have a
positive effect on the other.
4.4 Locality of Social Interactions
10
0
10
1
10
2
10
3
10
4
0
0.2
0.4
0.6
0.8
1
User Home to Event/Checkin Location Distance (miles)
CDF
User Home To Event Location (meetup)
User Home To Checkin Location (gowalla)
(a) locality of events
10
0
10
1
10
2
10
3
10
4
0
0.2
0.4
0.6
0.8
1
Geographical Distance between Friend Homes (miles)
CDF
meetup EBSN online (G
on
)
meetup EBSN offline (G
off
)
meetup EBSN full (G)
gowalla LBSN
(b) locality of friends
Figure 6: Localities of Meetup EBSN and Gowalla
LBSN.
In the following, we further analyze on the geographic as-
pects of social interactions. In Fig. 6(a), we examine the
distance of a Meetup event location and a Gowalla checkin
location to the user’s home location [4, 5]. As illustrated
by this figure, although both events and checkins tend to
be local to users’ home locations, the possibility of an event
participation in Meetup decreases more dramatically as the
distance increases. As observed, 81.93% of events partici-
pated in by a user are within 10 miles of his/her home loca-
tion. This indicates that people’s social activities are much
more location constrained than place checkins. This is be-
cause people’s checkins are usually sporadic [21] and largely
represent individual behaviors. Social events, which need all
participants to meet at the same spot, must be located close
to all the participants in most cases.
Next we compare the distances between friends’ home lo-
cations in the Meetup EBSN against the Gowalla LBSN.
As depicted in Fig. 6(b), friends in Meetup, no matter in
online, offline, or the combined social networks, are much
geographically closer to each other than in Gowalla LBSN.
This is because both online and offline social networks in
Meetup EBSN revolve around social events, which require
participants to physically get together at the same location.
In comparison, it is perfectly fine and usual for a Gowalla
user to share a location checkin when he/she visits some new
places. Not surprisingly, offline friends in Meetup EBSN
tend to live closer to each other than the online friends.
84.61% of offline friends live within 10 miles to each other.
5. EBSNS COMMUNITY STRUCTURE
In this section, we investigate the community structures
of EBSNs. Due to the heterogeneity of EBSNs, communities
are defined by both online and offline interactions
1
. As a
result, previous community detection algorithms on homo-
geneous networks do not directly apply to EBSNs. Thus, we
employ an extended Fiedler method to detect communities
in EBSNs and compare it against the previous approaches.
We also use the Gowalla LBSN as a comparison to further
study the unique features of the Meetup EBSN.
5.1 Clustering on Homogeneous Networks
For homogeneous social networks like the online or offline
network of an EBSN, we use the popular Fiedler method
offered by the Graclus tool [10] to partition networks. The
partitioned clusters are treated as user communities. Let
1
Although a group or an event in Meetup somewhat cap-
tures the behaviors of a set of users either online or offline,
it is the combination of online and offline interactions that
defines a community in EBSNs.
A define the adjacency matrix of a network. The popular
Normalized Cut (NCut) [27] shown in Eq. 3 is applied as the
graph partition objective function for each binary cut.
min
y
T
Ly
y
T
Dy
, subject to y
T
D1 = 0, y 6= 0. (3)
In Eq. 3, D is the diagonal matrix in which each diagonal
value is the sum of the corresponding row (D
ii
=
P
j
A
ij
),
L = D − A is the Laplacian matrix, y is the column vector
with y
i
∈ {1, −b} and b is some data-dependent constant.
The column vector y represents the graph cutting results
of the current binary cut, since all nodes with y
i
= 1 are
clustered into one cluster and the other nodes with y
i
= −b
are clustered into another cluster. If y is relaxed to take
on real values, Eq. 3 is equivalent to solving the generalized
eigenvalue system Ly = λDy, where y is the Fiedler vector
corresponding to the second smallest eigenvalue.
5.2 Clustering on Heterogeneous EBSNs
5.2.1 Baseline 1: Linear Combination
Given an EBSN G, we have two separate but correlated
networks G
on
= hU, A
on
i and G
off
= hU, A
off
i. Both G
on
and G
off
share the same user set U. As a result, the cluster-
ing process should consider the correlation between G
on
and
G
off
. The simplest way to leverage both online and offline
social interactions is to combine them linearly
A = γ ∗ A
on
+ (1 − γ) ∗ A
off
. (4)
Here A defines a linearly combined adjacency matrix with
a weighting parameter γ to differentiate two types of inter-
actions. We name this naive method as LinearComb and
use it as a baseline for comparison. The major problem of
LinearComb is that after the linear combination, the social
interaction type information is missing in the new matrix A.
5.2.2 Baseline 2: Generalized SVD
As another baseline, we utilize Generalized Singular Vec-
tor Decomposition (GSVD) to incorporate online and offline
social interactions in the clustering process by following The-
orem 5.1.
Theorem 5.1. Given two EBSN social interaction ma-
trices A
on
∈ R
n×n
and A
off
∈ R
n×n
, there exists unitary
matrics µ, ν ∈ R
n×n
, reversible matrix Y ∈ R
n×n
and rect-
angular diagonal matrices Σ
1
and Σ
2
such that:
A
on
= µΣ
1
Y
T
, A
off
= Y Σ
2
ν
T
.
The proof of Theorem 5.1 can be found in [14]. In Theo-
rem 5.1, the singular vectors of matrix Y (from the second
columns and onwards) collectively offer a consistent clus-
tering on users by leveraging both online and offline social
interactions. In this method, the singular vectors of the 2
nd
to m
th
smallest singular values are used as m − 1 dimen-
sional indicator vectors for users. Then, a classic K-means
algorithm is conducted on this space to generate user com-
munities. We name this method GSVD.
One shortcoming of GSVD is that as Y is not a unitary
matrix, its values on different column vectors vary a lot in
ranges. Therefore, the partitioning information embedded
in Y cannot be simply differentiated by the symbol sign as
the classic SVD does. In experiments, we also found that
the performance of GSVD is rather sensitive to the choice
Algorithm 1: HeteroClu
Input: EBSN G = hU, A
on
, A
off
i, # clusters K
Output: User cluster set C
1 Initialize C = {C
1
, C
2
, . . . , C
n
}, where each C
i
= {u
i
};
2 Initialize normalized weights
¯w
ij
← (
P
u
a
∈C
i
,u
b
∈C
j
w
ab
)/(|C
i
| · |C
j
|) for connected
C
i
, C
j
;
3 while |C|>M do /* bottom-up cluster */
4 Find the largest ¯w
ij
;
5 Merge C
i
and C
j
, update related normalized weights;
6 while |C| < K do /* top-down partition */
7 Binary cut all M clusters following the objective Eq. 5;
8 if C
i
is the cluster with the minimum cut cost then
9 delete C
i
from C;
10 Add spitted parts of C
i
into C;
11 return C
of similarity measures on the singular vectors of Y . After
many comparions, we chose the city block similarity measure
for GSVD.
5.2.3 Extended Fiedler Method
We now propose an algorithm that clusters online and
offline interactions at the same time. This algorithm em-
ploys the following objective function based on normalized
cut (Eq. 3):
min α
y
T
(D
on
− A
on
)y
y
T
D
on
y
+ (1 − α)
y
T
(D
off
− A
off
)y
y
T
D
off
y
, (5)
subject to y
T
D
on
1 = 0, y
T
D
off
1 = 0, y 6= 0.
The above objective function contains two parts, each part
alone is a normalized cut objective function on individual
online or offline social networks. But the linear combination
of both defines a global optimization over the heterogeneous
EBSN. Coupling factor α is used to weigh the importance
of each network. Note that each part is a normalized value
between 0 and 1. Therefore, the size of the individual online
or offline network is not captured in Eq. 5. A naive way
to assign the importance of the two parts is to set α =
0.5. However, since online and offline networks have different
network density, we set α as
sum(A
on
)
sum(A
on
)+sum(A
off
)
.
Similar objective functions to Eq. 5 have been used in the
high-order co-clustering problem on multiple types of het-
erogeneous objects [13]. Solving the new objective function
(Eq. 5) is non-trivial, as it represents a typical quadratic
fractional programming problem. In [13], the similar func-
tion was first approximated to be a quadratically constrained
quadratic programming problem by fixing two denomina-
tors of the function as constants. Then, the standard semi-
definite programming is applied to compute y efficiently.
In this paper, we use a heuristic algorithm shown in Al-
gorithm 1 to solve the clustering problem with the objective
function defined in Eq. 5. This algorithm first employs a
bottom-up clustering algorithm on the linear combination
of online and offline social networks as defined in Eq. 4, to
generate M (M << K) giant loose clusters in a bottom-up
fashion. This step defines a local greedy merge procedure.
Then it uses the top-down recursive binary cut procedure
to cut large clusters to smaller ones until K clusters are
achieved. This step defines a global recursive cut procedure.
0.5 1 1.5
x 10
5
1.5
2
2.5
3
3.5
4
4.5
# Clusters (K)
Davies−Bouldin Index
Online EBSN Partition
Offline EBSN Partition
EBSN LinearComb
EBSN GSVD
EBSN HeteroClu
1 2 3 4
x 10
4
1.5
2
2.5
3
3.5
4
4.5
# Clusters (K)
Online LBSN (Gowalla)
2.93
2.53
2.02
1.80
2.20
1.98
Figure 7: Community dectection performance. The
score inside the grey rectangle is the DB index under
the optimal K based on the “knee” method.
5.3 Community Structure Evaluation
5.3.1 Evaluation Settings
To measure the quality of user communities, we use the
collected user tags as the external ground truth of latent
community semantics. 78, 158 unique user tags were col-
lected from Meetup and treated as the Meetup tag space T
with |T | = m. For each user u
i
, we built a binary user-tag
vector u
i
= {t
i1
, t
i2
, . . . , t
im
} where t
ik
= 1 if u
i
selects the
tag t
k
; otherwise t
ik
= 0. After normalization, the similarity
between two users u
i
and u
j
is measured by the cosine sim-
ilarity u
i
· u
j
. There are no user tags available in Gowalla.
Instead, we aggregated all location tags of a user’s checkins
to build the user-tag vector, in which t
ik
is the number of
checkins associated to tag t
k
of user u
i
. In total, 680 unique
tags were collected in Gowalla.
The standard Davies-Bouldin (DB) index [8] was used to
measure the cohesiveness of communities, which is given by
DB =
1
K
K
X
k=1
max
k6=j
(
2 − σ
k
− σ
j
1 − c
k
· c
j
), (6)
where K is the number of communities, c
k
= 1/|C
k
|
P
u
i
∈C
k
u
i
is the centroid vector of cluster C
k
after renormalization, and
σ
k
= 1/|C
k
|
P
u
i
∈C
k
u
i
· c
k
is the average similarity of users
in cluster C
k
to their centroid. A smaller DB index value
indicates a more cohesive community.
5.3.2 Results
Determining the optimal K for a clustering has been an
open problem for decades. For a fair comparison on vari-
ous approaches and datasets, we used a simple yet popular
method that identifies the “knee” [15] in the plot of DB in-
dex vs. K to determine the optimal K for each clustering
first; and then compare the corresponding DB index under
the optimal K. The DB index value corresponding to the
“knee” can be seen as the best clustering performance that
one method can achieve.
Fig. 7 compares the best DB index of each method based
on the “knee” method. Note that since the DB index av-
erages over all the worst separated clustering pairs, it is
possible that the DB index has a value greater than 2.
As shown in Figure 7, the communities for the Meetup
EBSN are more cohesive than those for Gowalla LBSN.
One interesting finding is that users in online Meetup EBSN
communities are more cohesive than users in offline Meetup
EBSN communities (by 0.33), indicating that users tend to
have more similar interests if they belong to same groups,
compared to those who participated similar events. How-
ever, the combination of online and offline interactions does
play an important role in the clustering process, as three
methods LinearCom, GSVD and HeteroClu outperformed
individual networks. The LinearCom is only slightly better
than individual networks (by 0.18) but worse than HeteroClu
(by 0.22), indicating that a simple linear combination can-
not differentiate heterogeneous types of social interactions
effectively. The GSVD has almost the same performance as
LinearCom, suggesting that after relaxing the constraint on
the unitary matrix of SVD decomposition, the generalized
SVD lost some disambiguation power on clustering. Lastly,
HeteroClu leads the pack in comparisons. It is the only
method that achieved the best DB index (around 1.8) suf-
ficiently under 2, indicating that its worst pairs of clusters
were reasonably separated.
6. EBSNS INFORMATION FLOW
In this section, we study how information flows over this
unique network structure. A good scenario that can be used
to examine the information flow on EBSNs is the problem
of recommending users to participate in social events only
based on the topological structure of EBSNs. With this
application, we can study how information flows from one
user to the online/offline friends and how the information
flow pathways latently drive the social event participation
process.
Unlike classic movie/book recommendations, event par-
ticipation recommendation is more challenging due to the
short life time of social events. An event is non-existent un-
til its creation time t
c
. And after the start time t
s
of an
event, participation recommendation becomes meaningless.
Due to the very limited history of an event from time t
c
to t
s
, event participation recommendation suffers from the
cold-start problem heavily.
Now, let’s formally define the event participation problem
as follows: given an event e, at time t (t
c
< t < t
s
), the task
is to predict users who will RSVP “yes” to event e between
t and t
s
. The EBSN built upon the collective data before t
will serve as the network structure and all the users who re-
sponded “yes” to e between t
c
and t are the positive training
examples for the prediction, notated as set S
2
.
6.1 Event-Centric Diffusion
Not to deviate from our goal of studying the information
flow over the EBSNs’ unique network structures, we only
rely on the topological structure of EBSNs and the already
responded users for event participation prediction.
6.1.1 Basic Event-Centric Diffusion
We design a simple yet efficient event-centric diffusion
model for the problem. We define f
i
≥ 0 as the initial
score of node u
i
, where only users in set S (the set of users
already RSVPed “yes”) have f > 0 and the rest of the users
have f = 0. For simplicity, we initialize f = 1/|S| for users
in S. We use the column vector v
k
= {v
k
1
, v
k
2
, . . . , v
k
n
} to
represent the probabilities that users have been visited after
the k-th diffusion step, and v
0
i
= f
i
.
The basic event-centric diffusion, named DIF, can be ex-
pressed as v
k+1
= D·v
k
, where D defines the non-symmetric
information transition matrix of a network for time t. Each
2
For simplicity, the event creator is treated as the first user with
RSVP “yes”.
G
on
U
U
G
on
U
U
G
off
G
off
G
on
U
U
G
off
G
on
U
(1) single channel (2) cascaded channels (3) paralleled channels
G
off
U
U
G
on
G
off
U
U
Figure 8: Typical EBSN information flow patterns.
element in D is defined as d
ij
=
w
ij
P
l
w
il
. If we run the model
on the heterogeneous EBSN, we can use the linearly com-
bined adjacency matrix (Eq. 4). d
ij
is the empirical prob-
ability of information flow from user u
i
to user u
j
. Clearly,
d
ij
6= d
ji
. If u
i
has a larger degree than u
j
, the influence of
u
i
on u
j
is less than that of u
j
on u
i
.
This basic diffusion model is event-centric because v
k
rep-
resents personalized probabilities only corresponding to the
current event e. A similar diffusion method has also been
studied by [17] for link prediction. Because this diffusion
process does not converge to the stationary distribution of
information flow, a self-loop on every node is necessary; oth-
erwise the information will be diverged far away quickly.
The self-loop weight follows the same definitions of Eq. 1
and Eq. 2.
6.1.2 Diffusion over EBSNs
An EBSN contains both online and offline social interac-
tions, but the basic diffusion model DIF does not take this
heterogeneity into account. Accommodating different forms
of social interactions, there exist at least three information
flow patterns, as shown in Figure 8. The online and offline
social networks G
on
and G
off
of an EBSN basically defines
two kinds of channels for the flow of information. Figure 8(1)
depicts the basic diffusion model DIF over a single channel
exclusively, whereas Figure 8(2) define a cascade model, ab-
breviated as DIF-cascade, in which information interchange-
ably flows from one channel to the other. The simplest
cascade diffusion model can be defined as v
k+1
= D
c
· v
k
,
where D
c
is a cascaded transition matrix for time t, and
D
c
= D
on
· D
off
or D
off
· D
on
. Finally, in Figure 8(3), infor-
mation flows over two channels concurrently. We call this
model DIF-parallel. The simplest parallel diffusion model is
v
k+1
= D
p
· v
k
, where D
p
defines a linearly combined tran-
sition matrix for time t, and D
p
= γD
on
+ (1 − γ)D
off
. The
parameter γ is used to measure the importance of each type
of social interactions. It plays the same role of γ in Eq. 4.
Thus, DIF-parallel is equivalent to DIF on the linearly com-
bined adjacency matrix (Eq. 4). Undoubtedly, there are
more complex information diffusion processes (i.e., a mix-
ture of DIF-cascade and DIF-parallel). But we will leave
them for future work.
6.1.3 Community-Based Diffusion
Information is often circulated more rapidly inside its own
community, especially for those small-scale local communi-
ties. As a result, we design a community-based diffusion
model in which information tends to, but is not restricted
to, flow within the scope of its own community.
Specifically, in this model, v
k+1
= D
m
· v
k
, where D
m
defines the community-based information transition matrix.
Each element of D
m
is defined as
d
0
ij
=
(
(1−β)w
ij
N
if u
j
/∈ C(u
i
),
βw
ij
N
if u
j
∈ C(u
i
),
where C(u
i
) is the community of u
i
, β is a parameter used
to control weight of information flows inside its community
versus outside, and N is the normalization factor so that
P
j
d
0
ij = 1. We name this model DIF-com.
Since DIF-com only adjusts the weights of edges on top
of the basic DIF model (can be seen as a combination with
DIF), it can be further combined with other complex diffu-
sion models, including DIF-cascade and DIF-parallel. The
names of the two combinations are DIF-com-cascade and
DIF-com-parallel, respectively. Note that DIF-com on G
based on the linearly combined adjacency matrix (Eq. 4) is
equivalent to DIF-com-parallel.
6.2 Information Flow Evaluation
6.2.1 Experimental Settings
As discussed before, event participation recommendation
suffer from a typical cold-start problem. When an event is
created, except for the creator, it is unknown to all the other
users. To simplify the problem, we treat the event creator as
the first user who responded “yes” to the event. In evalua-
tion, we can start the recommendation process immediately
after the event creation, or wait for a while until there are a
few responded users. We first focus on the latter case: given
a testing event, we set the first k responded participants as
the seed users, where k is randomly determined. The former
case is a much harder problem and is examined at the end
of the evaluation.
We split the Meetup data into two sequential parts (cut
around Mar 2011). The first part of data (on or before Mar
2011, take up 80%) are used for training and the second part
of data (after Mar 2012, take up 20%) are used for testing.
Given a testing event, we recommend top 5, 10, 20, 50, 100,
200, 400, 800 users to it respectively. We choose to recom-
mend a large number of users, because 1) in practice event
organizers often broadly advertise their events to the public;
and 2) we want to see the long-term trend of such a recom-
mendation system. For the recommended top N users, we
compute recall to evaluate the performance. recall is defined
as the percentage of users who would respond “yes” to the
testing event that are covered by the top N recommenda-
tions. Finally, we average the recall for all testing events
under the same top N.
6.2.2 Compare Event-Centric Diffusion Models with
Classic Baselines
There are two popular baselines found in the prior art
that can be efficiently applied to such an event participation
recommendation problem. One is Collaborative Filtering
(CF) [25], and the other is the random walk model [23].
Note that due to the extremely short life time of events, most
supervised recommendation (link prediction) methods suffer
from severe sparsity of labeled data. As a result, they do not
apply to the event participation recommendation problem.
For the baseline CF, the users who ever participated in
similar groups or events in the Meetup training data are
recommendation candidates. They are then ranked by their
Jaccard similarities to the responded users. The Jaccard
similarity between two users is simply based on their past
group or event participation count vectors.
For the baseline random walk model, we applied the ran-
dom walk with restart (RWR) model. In the RWR baseline,
there is a certain chance (probability β) with which the in-
5 10 20 50 100 200 400 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Top N
Recall
DIF
DIF−com
CF
RWR (0)
RWR (0.15)
RWR (0.3)
RWR (0.6)
(a) Online EBSN
5 10 20 50 100 200 400 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Top N
Recall
DIF
DIF−com
CF
RWR (0)
RWR (0.15)
RWR (0.3)
RWR (0.6)
(b) Offline EBSN
Figure 9: Prediction on individual EBSNs.
formation will flow back to the starting users at each step
of information flow. By setting various β, we have various
RWR baselines with names like RWR (0.3). When β = 0,
RWR downgrades to the basic random walk model.
As both CF and RWR were initially designed for homo-
geneous networks, we compared them with the basic event-
centric diffusion models on individual G
on
and G
off
in Fig. 9.
From all diffusion models on G
on
in Fig. 9(a) and G
off
in
Fig. 9(b), DIF-com outperforms DIF and CF, and RWR
models perform the worst. By soft-restricting information
flow in the same user communities, DIF-com can guarantee
most closely related friends are recommended. The weight-
ing strategies of DIF and CF differ only slightly, thus they
yield similar prediction results. The poor performance of
RWR indicates that identified network hubs are not rele-
vant to the testing event. By raising return probabilities of
RWR, the prediction performance does not improve much
even with β as high as 0.6. In addition, by comparing
Fig. 9(a) and Fig. 9(b), we find the offline EBSN has better
prediction power when N is small but online EBSN gradu-
ally catches up and even surpasses the offline EBSN as N
grows large. This is because offline social interactions are
able to capture closely related friends who are very likely to
participate in the same events, but the recommended users
tend to be regulars to similar events. In comparison, online
social interaction can introduce non-regulars to the events
and increase the coverage of the recommendation.
6.2.3 Compare Various Diffusion Patterns on EBSNs
In the previous section, we showed that DIF-com has the
best recommendation performance for individual online and
offline social networks of an EBSN. As discussed in Sec-
tion 6.1.3, DIF-com actually represents one kind of diffusion
pattern on a whole EBSN (equivalent to DIF-com-parallel
based on the linearly combined adjacency matrix (Eq. 4)).
It is thus interesting to further compare various diffusion
models we discussed in Section 6.1.2 on the whole EBSNs
(with both online and offline social interactions). All diffu-
sion models can be enhanced by communities since DIF-com
has been shown to outperform the rest of the methods in the
previous section. For a fair comparison, we use communi-
ties detected by Algorithm 1 for all methods. The detailed
comparisons are given by Fig. 10. Fig. 10(a) compares three
diffusion models over the heterogeneous EBSNs against indi-
vidual online/offline networks. Only the paralleled diffusion
model outperforms the online or offline only model. This
means that the joint presence of online and offline social
interactions can improve the prediction performance. The
reason that cascade diffusions are worse is because values
are diffused twice to those far away users. Similarly, In
5 10 20 50 100 200 400 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Top N
Recall
DIF−com Online
DIF−com Offline
DIF−com−parallel
DIF−com−cascade (On−>Off)
DIF−com−cascade (Off−>On)
(a) EBSN diffusion patterns
5 10 20 50 100 200 400 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Top N
Recall
DIF−com−parallel
DIF−com−parallel Twice
DIF−com−parallel 3 Times
(b) EBSN recursive diffusion
Figure 10: Prediction on the heterogeneous EBSNs.
5 10 20 50 100 200 400 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Top N
Recall
DIF−com Online
DIF−com Offline
DIF−com−parallel
DIF−com Online Cold Start
DIF−com Offline Cold Start
DIF−com−parallel Cold Start
Figure 11: Comparison to cold-start scenarios.
Fig. 10(b), we see that repeating the parallel diffusion model
also deteriorates the performance.
6.2.4 Examine the Effect of Cold-Start
In this section, we would like to examine how the cold-
start phenomena hurts the recommendation performance. It
is well-accepted that as the size of responded users decreases,
the recommendation performance will get worse. We simply
verify this well-known conjecture using Fig. 11. In Fig.11,
the prediction performances for those cold start cases (the
event creator is the only seed for an event) are slightly worse
than random-start cases. However, the recalls achieved by
diffusion from a single user are still fairly good, indicating
that using diffusion to predict event participation on EBSNs
is satisfactory even on the extreme cold start cases.
7. CONCLUSION
In this paper, we have identified and formally defined a
new type of social network, EBSN. By using the Meetup
dataset, we studied the unique features of EBSNs includ-
ing basic network properties, community structures and in-
formation flow over EBSNs. Our research revealed many
aspects of EBSNs that are significantly different from con-
ventional social networks and LBSNs. We hope this paper
paves the way for future studies on this interesting type of
social networks.
Acknowledgements
We would like to thank Jon Kleinberg for helping us nail
down the background of the problem, Bin Gao for his ex-
planation on the related work [13] and Jiang Bian and Mao
Ye for their valuable discussions.
8. REFERENCES
[1] Y. Ahn, S. Han, H. Kwak, S. Moon, and H. Jeong. Analysis
of topological characteristics of huge online social
networking services. In WWW, 2007.
[2] P. S. Bearman, J. Moody, and K. Stovel. Chains of
Affection: The Structure of Adolescent Romantic and
Sexual Networks. American Journal of Sociology, 2004.
[3] C. Borgs, J. Chayes, J. Ding, and B. Lucier. The
hitchhiker’s guide to affiliation networks: A game-theoretic
approach. arXiv:1008.1516v1, 2010.
[4] Z. Cheng, J. Caverlee, K. Lee, and D. Sui. Exploring
millions of footprints in location sharing services. In
ICWSM, 2011.
[5] E. Cho, S. A. Myers, and J. Leskovec. Friendship and
mobility: user movement in location-based social networks.
In KDD, 2011.
[6] A. Clauset, C. Shalizi, and M. Newman. Power-law
distributions in empirical data. Arxiv preprint
arxiv:0706.1062, 2007.
[7] D. Crandall, L. Backstrom, D. Cosley, S. Suri,
D. Huttenlocher, and J. Kleinberg. Inferring social ties
from geographic coincidences. PNAS, 2010.
[8] D. Davies and D. Bouldin. A cluster separation measure.
Pattern Analysis and Machine Intelligence, IEEE
Transactions on, 1979.
[9] I. de Sola Pool Manfred. Contacts and influence. Social
networks, 1979.
[10] I. Dhillon, Y. Guan, and B. Kulis. Kernel k-means: spectral
clustering and normalized cuts. In KDD, 2004.
[11] D. Easley and J. Kleinberg. Networks, Crowds, and
Markets: Reasoning About a Highly Connected World.
Cambridge University Press, 2010.
[12] S. L. Feld. The focused organization of social ties.
American Journal of Sociology, 1981.
[13] B. Gao, T.-Y. Liu, X. Zheng, Q.-S. Cheng, and W.-Y. Ma.
Consistent bipartite graph co-partitioning for
starstructured high-order heterogeneous data co-clustering.
In KDD, 2005.
[14] G. Golub and C. Loan. Matrix Computations. Johns
Hopkins Univ. Press, 1996.
[15] A. K. Jain and R. C. Dubes. Algorithms for Clustering
Data. Prentice-Hall Prentice-Hall advanced reference series,
1988.
[16] S. Lattanzi and D. Sivakumar. Affiliation networks. In
STOC, 2009.
[17] R. N. Lichtenwalter, J. T. Lussier, and N. V. Chawla. New
perspectives and methods in link prediction. In KDD, 2010.
[18] A. Mislove, M. Marcon, K. Gummadi, P. Druschel, and
B. Bhattacharjee. Measurement and analysis of online
social networks. In SIGCOMM, 2007.
[19] M. Newman. Scientific collaboration networks. ii. shortest
paths, weighted networks, and centrality”. Physical Review
E, 2001.
[20] M. E. J. Newman, D. J. Watts, and S. H. Strogatz.
Random graph models of social networks. In National
Academy of Sciences, 2002.
[21] A. Noulas, S. Scellato, C. Mascolo, and M. Pontil. An
empirical study of geographic user activity patterns in
foursquare. In ICWSM, 2011.
[22] J. F. Padgett and C. K. Ansell. Robust Action and the Rise
of the Medici, 1400-1434. The American Journal of
Sociology, 1993.
[23] L. Page, S. Brin, R. Motwani, and T. Winograd. The
pagerank citation ranking: Bringing order to the web. 1999.
[24] T. Sander and S. Seminar. E-associations? using
technology to connect citizens: The case of meetup.com. In
Annual Meeting of the American Political Science
Association, 2005.
[25] B. Sarwar, G. Karypis, J. Konstan, and J. Reidl.
Item-based collaborative filtering recommendation
algorithms. In WWW, 2001.
[26] S. Scellato, A. Noulas, and C. Mascolo. Exploiting place
features in link prediction on location-based social
networks. In KDD, 2011.
[27] J. Shi and J. Malik. Normalized cuts and image
segmentation. TPAMI, 2000.
