=Paper=
{{Paper
|id=Vol-1099/paper1
|storemode=property
|title=How to Improve Group Homogeneity in Online Social Networks
|pdfUrl=https://ceur-ws.org/Vol-1099/paper1.pdf
|volume=Vol-1099
|dblpUrl=https://dblp.org/rec/conf/aiia/MeoFRS13
}}
==How to Improve Group Homogeneity in Online Social Networks==
https://ceur-ws.org/Vol-1099/paper1.pdf
1
How to Improve Group Homogeneity in Online
Social Networks
Pasquale De Meo, Emilio Ferrara, Domenico Rosaci, and Giuseppe M. L. Sarné
Abstract— The formation and evolution of interest groups in people sharing similar interests [12] (i.e., the group formation
Online Social Networks is driven by both the users’ preferences accounts for some definition of users similarity).
and the choices of the groups’ administrators. In this context, Satisfaction, on the other hand, is often related to the notion
the notion of homogeneity of a social group is crucial: it accounts
for determining the mutual similarity among the members of of group homogeneity: when the similarity/inter-connectivity
a group and it’s often regarded as fundamental to determine among group participants is high, according to both structural
the satisfaction of group members. In this paper we propose a and semantic dimensions, a OSN group is regards as homoge-
group homogeneity measure that takes into account behavioral neous and this yields better satisfaction among its users [27].
information of users, and an algorithm to optimize such a However, if we assume that homogeneity should reflect users
measure in a social network scenario by matching users and
groups profiles. We provide an advantageous formulation of such
satisfaction, we argue that other behavioral characteristics
framework by means of a fully-distributed multi-agent system. of members and groups should be considered as important
Experiments on simulated social network data clearly highlight components [8]. For example, in virtual communities, users
the performance improvement brought by our approach. are often characterized by multiple interests, and groups enact
Index Terms—Multi-agent systems, Online Social Networks, common rules, define accepted behaviors, exhibit a manifold
Group Recommendation, Group Homogeneity. of communication styles and implement different facilities for
sharing media content.
In this paper, we define a novel measure of group ho-
I. I NTRODUCTION mogeneity that exploits users similarity and the other users’
Online Social Networks (OSNs) such as Facebook, Google+ features cited above. By means of our new definition we are
and Twitter have become very complex realities [6], [7], able to provide an algorithm to match the individual users’
significantly grown in scale and content [5], [18], [26], with profiles with group profiles. The goal of this method is to find
significant social effects [10], [11], [19], [30]. In this context, a the matching between users and groups capable of improving
relevant role is played by social groups, that are sub-networks the homogeneity of the social groups. More in detail:
of users sharing common interests [4], [21], [28], [29], [37]. • We introduce the notion of group profile in the context of
Recent studies investigated the relationships between users OSNs considering a set of categories of interests, com-
and groups in OSNs [2], [23], [24]. For example, Hui et al. mon rules, behaviors, communication styles and facilities
[23] considered four popular OSNs and empirically computed for sharing media content. This definition of group profile
the probability that a user joins a group; the problem of is coherent with the definition of a user profile containing
choosing which group to join has been studied in [2] for a information comparable with those of a group profile.
single user and in [24] for a group of users. So far, to the best • Each OSN group is associated with a group agent [15]–
of our knowledge, no study considers the evolution of a group [17], capable of creating, managing and updating the
as a problem of matching between users and groups profiles. group profile defined above. Similarly, a user agent is
Although the concept of social profile is known in the associated with each OSN user.
context of virtual communities [25], that of group profile is • We present a distributed agent platform to handle group
rather novel. The definition of such concept is useful to face formation [31], [32], [34]–[36]. The agents automatically
the problem of suggesting a user the groups she could affiliate and dynamically compute a matching between user and
to, so that to improve her satisfaction. group profiles in a distributed fashion. We provide the
Commonly, a group might be considered (i) as a set of nodes user agent with a matching algorithm, named Group
(i.e., users) more densely connected among each other than Homogeneity Maximization (GHM), and introduce a ho-
to the others (i.e., the group formation is viewed as a graph mogeneity measure between user and group profiles able
clustering problem [13], [14], [20]); or, (ii) as a community of to determine the group profiles best matching user ones.
• The GHM algorithm will be executed to improve the
P. De Meo is with the Dept. of Ancient and Modern Civilizations, University intra-group homogeneity as follows: (i) the user agent
of Messina, 98166 Messina, Italy, e-mail: pdemeo@unime.it submits some requests for joining with the best groups;
E. Ferrara is with the Center for Complex Networks and Systems Research,
School of Informatics and Computing, Indiana University, Bloomington (IN), (ii) each group agent accepts only those requests whose
USA, e-mail: ferrarae@indiana.edu originators have profiles matching with the group profile.
D. Rosaci is with the Dept. DIEES, University of Reggio Calabria, Loc. • The experimental evaluation of our matching algorithm,
Feo di Vito, 89122 Reggio Calabria, Italy, e-mail: domenico.rosaci@unirc.it
G.M.L. Sarné is with the Dept. DICEAM, University of Reggio Calabria, carried out on a set of simulated users and groups, clearly
Loc. Feo di Vito, 89122 Reggio Calabria, Italy, e-mail: sarne@unirc.it shows the advantages of our proposal.
2
II. T HE R EFERENCE S CENARIO information stored in its profile. In particular, every time u
In our scenario, we consider an OSN, the set of its users, deals with a category c, the associated value Iu (c) is updated
and the set of its groups, denoted by S, U and G, respectively. as the weighted mean between its previous value and the new
In S, each group of users g ∈ G represents a subset of U (i.e, contribution to Iu (c) = α · Iu (c) + (1 − α) · δ. In detail, α
g ⊆ U ∀g ∈ G). A multi-agent system is associated with S, and δ are real values arbitrarily set by u in [0..1], where δ is
such that: (i) each user u is supported by her personal agent the increment to give to the u’s interest in c due to her action,
au in the activities of participation to groups; and, (ii) each while α weights the two components of Iu (c). Similarly, every
group g is supported by an administrator agent ag managing time the Iu (c) value of any user u ∈ g changes, the Ig (c) value
all the received requests to join with the group. of a group g is updated by the agent ag as the mean of all the
Iu (c) values ∀c ∈ g. For each action performed by the user u
(e.g. publishing a post, etc.) its agent au sets the appropriate
A. The agents knowledge boolean values of the variables in Bu . Analogously, the agent
To represent the knowledge that each agent au (resp., ag ) ag updates the variables contained in Bg every time the
has about the orientations of its user u (resp., group g), a administrator of g changes the associated rules. Besides, when
profile pu (resp., pg ) is associated with it. This profile stores u (resp., the administrator of g) modifies her preferences about
preference and behavioral information referred to the user the access mode, the associated agent updates Au (resp., Ag ).
u (resp., the users of g) in four section (called interests, Also, when u (resp., a user of g) modifies her friends list, the
access preference, behaviors and friends) storing data on associated agent updates Fu (resp., Fg ). Note that ag computes
topics of interest, mode to access groups, ways of performing Fg as the union of the sets Fu of all the users of g.
activities and friends, respectively. The profile of a user u Periodically, the agent au (resp., ag ) executes the user (resp.,
(resp., a group g) is represented by a 4-tuple ⟨Iu , Au , Bu , Fu ⟩ group) agent task described above, to contribute to the group
(resp., ⟨Ig , Ag , Bg , Fg ⟩), where each component describes the matching activity of the OSN.
properties of u (resp., g). To perform the above tasks, the agents can reciprocally
Let C be the set of all categories considered in the OSN, interact, send and receive messages thanks to a Directory
where each element c ∈ C is an identifier representing a Facilitator agent (DF), associated with the OSN, that provides
given category (e.g. music, sport, etc.). Each OSN user u a indexing service. The DF stores the names of each user and
(resp., group g) deals with some categories belonging to C group belonging to the OSN and those of their agents. Note
where Iu (resp., Ig ) denotes a mapping that, for each category that the DF is the only centralized component in the proposed
c ∈ C, returns a real value Iu (c) (resp., Ig (c)), ranging in scenario, while the the GHM matching algorithm is completely
[0..1]. This represents the level of interest of the user u (resp., distributed on the whole agent network.
the users of the group g) with respect to discussions and
multimedia content dealing with c. The values of this mapping
are computed based on the actual behavior of u (resp., of the C. Definition of homogeneity
users of g) — see Section II-B for the details.
In order to represent the potential attitude of the user u to
The access mode property represents the policy regulating
stay in the same group with the user v (resp., to stay in the
the access to a group (described by an identifier, e.g. open,
group g), we define the homogeneity between two users u and
closed, secret, etc.) preferred by u (set by the administrator of
v (resp., a user u and a group g) as a measure representing
the group g) and denoted by Au (resp., Ag ).
how much u and v (resp., u and g) are similar (or, different)
The property Bu represents the types of behavior adopted with respect to the properties I, A, B and F .
(resp., required) by u in her OSN activities, for instance
The homogeneity hu,v between the users’ profiles of u and
“publishing posts shorter than 500 characters”. Let b ∈ B
v is defined as a weighted mean of the contributions cI , cA ,
a behavior adoptable by user u (admitted in the group g)
cB and cF , associated with the properties I, A, B and F ,
and described by a boolean variable set to true if b is
measuring how much the values of each property in pu and
adopted (resp., tolerated) or f alse otherwise and let B be
pv are similar. To this purpose:
the set of possible behaviors associated with the OSN (e.g.,
B = {b1 , b2 , · · · , bn }). Therefore, let Bu (resp., Bg ) be a • cI is the average of the differences (in the absolute
mapping that, for each b ∈ B, returns a boolean value Bu (b) value) of the interests values of u and v for all the
(resp., Bg (b)), where Bu (bi ) = true means that such behavior categories
∑ present in the social network, that is cI =
is adopted by u (resp., tolerated in g). |I
c∈C u (c) − Iv (c)|/|C|.
The property Fu (resp., Fg ) represents the set of all users • cA is set to 0 or 1 if Au is equal or not equal to Av .
that are friends of u (resp., that at least have a friend among • cB is the average of all the differences between the
the members belonging to the group g). boolean variables stored in Bu and Bv , where this differ-
ence is set to 0 or 1 if the two corresponding variables
are equal or different.
B. The agents tasks • cF is computed as the percentage of common friends of u
The agent au (resp., ag ) automatically updates the profile and v, with respect
∩ to the ∪ total number of friends of u or
pu (resp., pg ) of its user u (resp., group g) after that u v as cF = |Fu Fv |/|Fu Fv |. Note that, to make them
(resp., a user affiliated to g) performs an action involving an comparable, the contributions are normalized in [0..1].
3
ag2 group i
u,g2 g,u2
1 1 3 u2
3 ag1
group 2 au2
u,g1 2 g,u1
au monitors u 2 agi u1
u au group 1 u
user profile pu ag3 u,g3 au au1 g,u3
4 4 u3
group 3 g,u au3
Fig. 1. User agent task schema. Fig. 2. The group agent task schema.
The homogeneity hu,v is then computed as • For each user u ∈ K such that dateu > η (i.e., a fixed
wI · cI + wA · cA + wB · cB + wF · cF threshold), it sends a message to the agent au to require
hu,v = (1) the profile pu associated with u (cf Action 1, of Fig. 2).
wI + wA + wB + wF
• When ag receives the required users’ profiles (cf. Action
Similarly, homogeneity hu,g between a user u and a group g
is simply computed as hu,v substituting user v with group g. 2, Fig. 2), it computes the homogeneity ∪ measure hg,u
between the profile of each user u ∈ K {r} and the
III. T HE GHM A LGORITHM profile of the group g (cf. Action 3, Fig. 2).
• The user u having the highest homogeneity values such
The GHM algorithm is a global activity distributed and that hg,u > π, where π is a real value ranging in [0..1],
periodically executed by each user agent au (resp., group agent is inserted by ag in the set of good candidates, named
ag ), where we call epoch every time the task is executed and GOOD, to join with (up to a maximum of kM AX users).
T the (constant) period between two consecutive epochs. If u ∈ GOOD, ag accepts its request to join with g (cf.
Action 4, Fig. 2). Moreover, if u ∈ K but u ̸∈ GOOD,
A. The user agent task ag deletes u from g.
Let X be the set of the n groups u is affiliated to, where
n ≤ nM AX and nM AX is the maximum number of groups
a user can join with. We suppose that au stores into a cache IV. E VALUATION
the profile pg of each group g ∈ X, contacted in the past, We evaluate the effectiveness of the GHM algorithm in
with the date dateg of its acquisition. Let m be the number increasing the homogeneity of the groups of an OSN by using
of group agents that at each epoch is contacted by au . In such a simulator, called GHM-Sim, capable of modeling all the
a context, au behaves as follows (see Figure 1): required users and groups activities. The experiments involve
• From the DF repository, au randomly selects a set Y of a simulated OSN having 30.000 users and 100 groups, ad hoc
∩ ∪
m groups so that X Y = {0} and let Z = X Y the generated by GHM-Sim, each one provided with a profile,
groups present in X or in Y .
set consisting of all the ∩ having the structure described in Section II. More in detail,
• For each group g ∈ Y X such that dateg > ψ (i.e., the profile pu of a user u is generated as follows:
a fixed threshold), u sends a message to the agent ag to • The values of Iu (c) are randomly chosen from a uniform
ask the profile pg associated with g (cf. Action 1, Fig. 2). distribution in the interval [0..1];
• For each received pg (cf. Action 2, Fig. 1), u computes
• Au is assigned the value open (resp., closed and secret )
the homogeneity measure hu,g between her profile and with a probability of 0.7 (resp., 0.2, 0.1) to implement
that of the group g (cf. Action 3, Fig. 1). the variability of OSNs group access restrictions;
• The groups belonging to Z and having the highest
• Bu contains the values, randomly generated, of six
homogeneity values such that hu,g > τ , where τ is a boolean variables representing in average the user’s at-
real value ranging in [0..1], are inserted by au in the set titude to: (i) publish more than 1 post per day; (ii)
of good candidates, named GOOD, to join with (up to a publish posts longer than 200 characters; (iii) comment
maximum of nM AX groups). For each group g ∈ GOOD at least two posts of other users per day; (iv) respond to
if g ̸∈ X, au sends a join request and the profile pu of comments associated with her posts; (v) leave at least 2
u to ag (cf. Action 4, Fig. 1). Otherwise, if g ∈ X but “Like” rates per day; (vi) respond to the messages.
g ̸∈ GOOD, then au deletes u from g. • The set of friends Fu are randomly generated choosing
in the set of the users.
B. The group agent task Users are initially randomly assigned to at least 2 and at
Let K be the set of the k users affiliated to the group g, most 15 of the available groups. The properties Ig , Ag , Bg and
where k ≤ kM AX , being kM AX the maximum number of Fg of the profile pg of each group g are randomly generated.
members allowed by the administrator of g. Suppose that ag The values of the parameters introduced in Section III are
stores into its cache the profiles of the users u ∈ K obtained in shown in Table I. We also limit to: (i) 250 the users who can
the past along with the date dateu of their acquisition. When join a given group; (ii) 15 the groups that a user can be joined
ag receives a join request by a user agent u (along with u’s with; (iii) 5 the maximum number of requests that a user can
profile pu ), it behaves as follows (see Fig. 2): send in each epoch to new groups.
4
TABLE I ui ∈ U and an item ik ∈ I as input and returns an element
T HE VALUES OF THE PARAMETERS USED IN THE GHM-S IM SIMULATOR . rik ∈ R as output. Building the profile of G is equivalent to
compute a function fG : I → R receiving an item ik as input
τ π KM AX N M AX N REQ
and returns how much the members of G are satisfied by ik .
0.4 0.4 250 15 5 To compute fG ( ) two popular strategies are: (i) Average [1],
where fG (ik ) is equal to the average of the ratings the member
0,400 of G have given to ik . If none of the users in G has rated in
0,350
ik , then fG (ik ) is set equal to ⊥ (this symbol specifying a not
0,300
rated item)); (ii) Least Misery [3], where the rating that group
MAH / DAH x 10
0,250
MAH
0,200
DAH
G would assign to ik is defined as fG (ik ) = min r(ui , ik )
0,150 if ∃ui ∈ U : r(ui , ik ) ̸= ⊥ and ⊥ otherwise.
0,100
In the Average strategy the score of an item ik depends on
0,050
0,000
how many users in G liked it and, if fG (ik ) is large, ik could
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
be recommended also to whom in G dislikes it. Otherwise,
epoch
with Least Misery the opinion of who liked the less ik has the
biggest weight in computing fG (ik ) to minimize the chance
Fig. 3. Variation of MAH and DAH (x10) vs epochs obtained with the GHM-
comp and GHM-diff algorithms, for a SN with 30.000 users and 100 groups.
that ik is recommended to someone in G who dislikes it.
For example, if all of the group members but one like ik
and the Least Misery strategy is applied, ik will automatically
To measure the internal homogeneity of a group g we use get a low score although almost all users in G are interested
average homogeneity AHg , derived by [33], computed
the ∑ in it. Differently, in the Average strategy few low ratings on
as x,y∈g,x̸=y hx,y /|g|, while to measure the global homo- ik are largely compensated by the ratings of other users.
geneity of the OSN groups we compute the mean average Besides, most approaches assume that user’s preferences are
homogeneity M AH and the standard deviation average ho- independent of users joining (or not) with a group: if a user
mogeneity DAH of all the AHg , defined as alone likes (or dislikes) an item, she will continue liking (or
∑ disliking) it if she decides to join a group.
g∈G AHg
M AH = (2) In the literature there are few papers dealing with the
|G|
√∑ matching of a user and a group profile. Most of this work
g∈G (AHg − M AH)
2 has been designed to recommend to an OSN user groups to
DAH = (3) join with (such a problem is also called affiliation recommen-
|G|
dation in [39]). This differs from the group recommendation
In the simulations, the initial values for the above measures problem where the objects to recommend are items whereas
were M AH = 0.266 and DAH = 0.0011, denoting a very the affiliation recommendation problem deals with groups.
low homogeneity, due to the random generation. Applying the Spertus et al. [38] presented a proposal that describes an
GHM algorithm we have simulated 15 epochs of execution empirical comparison of six distinct measures for computing
per user. We can observe that the GHM algorithm quickly the similarity of a user and a community to exploit for
converges after few iterations (see Figure 3). The experimental communities recommendation. Chen et al. [9] provide an
results show that the GHM algorithm increases the homogene- algorithm called CCF (Combinational Collaborative Filtering)
ity in OSN groups of about 14 percent on average, with respect which is able to suggest users new friendship relationships as
to a random assignment of users to groups, achieving a stable well as the communities they could join with. CCF considers
configuration (e.g., M AH = 0.320 and DAH = 0.0052) a community from two different but related perspectives (e.g.,
after about 10 epochs. It is reasonable to suppose that the users and interests) to alleviate the data sparsity arising when
GHM algorithm, when applied to real OSNs, should lead to only information about users (resp., on words) is used.
concrete benefits in terms of homogeneity. Vasuki et al. [39] studied the co-evolution of the user’s
social network of relationships with the affiliation network
V. R ELATED W ORK modelling the affiliation of users to groups. The authors show
In this section we describe some recent research results how such information can be a good predictor to recommend
achieved in the fields covered by this paper, illustrating the to a user the groups she should join in the future.
main novelties brought in by our approach. Summarizing the benefits provided by our approach are:
In the latest years, an increasing number of authors focused (i) to models user interests, behaviors, friendship relationships
on the problem of recommending items to the member of a and the policies for accessing groups; (ii) to manage both
group [1], [22]. This implies the need to construct a group group and user profiles by means of a multi-agent architecture
profile, often by simply aggregating the individual orientations where agents provide all the required affiliation activities; (iii)
of its members. This task is usually called group modelling. to provide a distributed greedy algorithm to match users and
More formally, let U, I and G ⊆ U be the user population, a groups that computes, at each stage, how good a group is for
collection of items and a group of users, respectively. Suppose a given user and selects, uniformly at random, some of these
that a rating function r : U × I → R is available, where R groups; (iv) to manage large networks with a large number of
(rating space) is a discrete set. The function r receives a user groups in a flexible and computationally feasible manner.
5
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