=Paper= {{Paper |id=Vol-1867/w7 |storemode=property |title=Improving Agent Group Homogeneity Over Time |pdfUrl=https://ceur-ws.org/Vol-1867/w7.pdf |volume=Vol-1867 |authors=Fabrizio Messina,Domenico Rosaci,Pasquale De Meo,Giuseppe M.L. Sarné |dblpUrl=https://dblp.org/rec/conf/woa/MessinaRMS17 }} ==Improving Agent Group Homogeneity Over Time== https://ceur-ws.org/Vol-1867/w7.pdf

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1

Improving Agent Group Homogeneity Over Time
Pasquale De Meo∗ , Fabrizio Messina† , Domenico Rosaci‡ , Giuseppe M. L. Sarné ‡
∗
University of Messina, Italy, pdemeo@unime.it
†
University of Catania, Italy, messina@dmi.unict.it
‡
University of Reggio Calabria, Italy, {domenico.rosaci,sarne}@unirc.it

Abstract—In social communities the composition of thematic of the group homogeneity in terms of similarity. In this
groups varies over time due to changes occurring in users’ respect, recent studies on group formation processes consider
behaviors. To study the time evolution of such a process, we trust [13]–[15] to increase the level of the group member’s
design a conceptual framework exploiting a distributed algorithm
driving group formation. The results of tests carried out on real engagement over time and avoiding the group failure [16].
data extracted by the social network CIAO, show as groups However, all the approaches reviewed in [16] do not face the
formed by combining similarity and trust measures are i) more problem of combining similarity with trust.
time-stable, independently by the weight of the trust component, In [17]–[20] we proposed to integrate similarity and trust
and ii) more time-homogeneous, independently by the presence in a unique measure to form groups and finding those most
of uncorrelated random agents’ behaviors affecting the similarity
component. suitable for joining with. In this paper, we extended this
work to study how changes occurring in the similarity and
Index Terms—Homogeneity, Similarity, Social Communities,
trust measures impact on the groups formation over time. To
Trust.
test this approach, we used a new conceptual framework by
means of which we verified, always by using the data of the
I. I NTRODUCTION social network CIAO, that groups formed by considering both
Many online communities include thematic groups [1] and similarity and trust have higher time-stable homogeneity, in
many studies investigated on the users motivations to join terms of similarity, than groups formed by adopting the only
with groups [2], as well as the impact of their growth [3], similarity criterion. This result is valid also when both the
[4] and failure [1]. Important issues in forming groups re- weight assigned to the trust component is low or random (i.e.,
quire to an agent of selecting those groups able to satisfy “uncorrelated”) behavior components considered in computing
its expectation [5]–[8] and, in a complementary way, the the similarity have a relevant weight. We assume that this
members of a group search to accept only new agents able behavior is mainly due to the effect of trust in balancing
to improve their utility. Many studies present algorithms potential incongruence of the similarity measures. Besides, we
effective in driving such group formation processes (e.g., by found as the function used to aggregate similarity and trust
using diffusion processes [3], [4]) by analyzing i) the group measures is not fundamental. Therefore, for a good trade-off
evolution in terms of surviving or failure and ii) the reasons between the need of producing accurate results and that of
for which an agent will join with/left a group. Many of such having an easy interpretation model, we aggregated similarity
studies assume that groups should be formed by like-minded and trust by simply computing their weighted sum, as in [17].
members. To this aim, many measures exist to evaluate the The remaining of the paper is structured as follows: in
similarity degree among the groups members (e.g., based Section II we present the related literature, in Section III the
on the number of affiliations to groups [7], member/group adopted reference scenario is introduced, while in Section IV
interests [5], individual preferences [6] and so on). deal with the similarity and trust measures computation. Sec-
In such a context, the aptitude of a group to retain its tions V and VI illustrate the A2G algorithm and our conceptual
members (i.e., time stability) [9], [10] is a major factor for framework. Section VII describes the experimental campaign,
its survival or extinction. The evolution of these groups is, discuss its results and, finally, conclusions ends the paper.
in the most part of the cases, driven only by the mutual
similarity criterion [11], although it has evident limitations.
II. R ELATED W ORK
Indeed, the problem of recommending groups to a potential
member usually relies only on the mutual similarity between In the group formation the common identity and bond
the profile features of a candidate at the time t and the interests theory [21] identifies as main mechanisms to join with a group
of a group. When such interests vary in a relatively short time (i) the strong personal ties and (ii)) the shared interests with
frame then groups selected at the time t could not be the best other group members. Differently, in [2] the authors applied
choice at the time t + ∆t. the community detection algorithms to identify clusters into
Based on data of the social network CIAO [12], we verified OSNs and comparing their structural features with user-defined
as the mutual similarity alone does not ensure the group communities. A study on the group affiliation mechanisms is
homogeneity over time. In particular, when uncorrelated (e.g., presented in [3], where in two different kind of networks the
random) users’ behavior aspects assume a relevant weight. authors noted as the act to join with a group can be modeled
Consequently, we investigated on improving the time-stability in terms of new ideas spreading for both the networks.
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2

Kairam et al. [4] compared the growth processes in which user u, whereas an administrator agent ag assists a group g.
groups attract new members in presence/absence of social ties The agents knowledge representation, the agent tasks and our
with existing/any group members. Their main finding is that definitions of similarity and trust will be introduced below.
more a group is highly clustered and more likely it grows for
a diffusion process. It is in accord with [1], where 500,000 A. The agents’ knowledge representation
Facebook groups created in an 8-day period were monitored Interests and preferences of each owner (i.e., u, g) are taken
for 3 months after which the most part of groups were inactive. into account by the associated agent a ∈ A and stored into its
The analysis of [1] highlighted that group survival depends profile pa consisting of (i) interests, (ii) behaviors, (iii) access
on the social capital brought by group founders and of their modes and (iv) trust levels, as follows:
behavior. Differently from us, any of the papers above explored Interests: The interest of the agent a in a category x is a
the homogeneity of such groups to verify if they result time- function Ia (x) : A × X → [0, 1] ∈ R computed as the overall
stable homogeneous in terms of similarity. ratio of reviews for items belonging to x. More formally, Ia (x)
Homogeneous processes are defined as those whose pa- is expressed by Ia (x) = |{ra,i : i ∈ x}|/|ra |, where ra is
rameters are time-stable with respect to some measure. Usual the review history of a, and we denote by ra,i each review
group formation processes do not assure that properties like contained in ra and referred to an item i.
to similarity, social identity and so on, will be time-stable. Behaviors: The behavior field informs us about the activ-
Conversely, some affiliation recommendation [7] processes ities admitted or not within a group. It is assumed to be a
suggest to an OSN user only time-stable groups. From a statement of the form “The average rating of items is greater
wide experimentation involving Social Identity and Cohesion than 3.0” and so on. Targets (e.g., average rating, frequency
theories on more Twitter datasets, the authors of [22] verified of posts, etc.) and goals (e.g., discriminating thresholds) of
that groups based on the users’ social identity and formed by the statements depend on the specific considered community.
users interested in a great variety of topics are less cohesive Therefore, let b be a behavior (e.g., performed by a user,
over time in presence of transient events. admitted into a group) and let B = {b1 , b2 , . . . , bp } be a
A flexible framework in which group affiliation is treated given a set of behaviors. We assume to dispose of a function
as an event impacting on user’s preferences is proposed and ζa (b) : A × B → {True, False} which takes an agent a ∈ A
validated in [6], where a probabilistic framework provides and a behavior b ∈ B and checks whether the behavior b
to model the individual preferences when he/she joins with matches with the a’s past behaviors. The set of behaviors
a group. In other words, it affiliates to a group those users associated with an agent a will be defined as Ba , i.e., we
maintaining a high similarity level into the group over time set Ba = {ζa (b)| b ∈ B}.
and keeping homogeneous the group under this point of view. Access modes: An access mode identifies a modality for
In this scenario, we note as friendships and time-homogeneity accessing/allowing the access to a group, arbitrarily set by
of their relationships strictly depend by the mutual trust among the agent owner, like to open, closed or secret, and let L be
individuals. Differently, in the literature the most part of the a list specifying such accessing modes. More in general, we
proposals to form time-stable groups consider it as a problem supposed that a function M : A → L is available to associate
essentially involving some form of similarity among users. an agent a ∈ A with a mode l ∈ L for accessing to a group.
Among the cited contributions, only [9] indirectly refers to This components of the user profiles can be considered as fully
trust, in the mean derived by the social theories [23], while the random, and not correlated with the other components.
other consider some form of similarity as the unique criteria Trust levels: We suppose that an asymmetric trust function
to form possible time-stable homogeneous groups. returning how much an agent j perceives another agent k as
trustworthy is available (i.e., in general if j trusts k it does
III. T HE R EFERENCE F RAMEWORK S CENARIO not mean that k trusts h too, tj→k 6= tk→j ). Trust levels
are assigned during the agent interactions and mostly depend
Our framework involves a community C = hA, Gi, where
on the specific community. For instance, in CIAO everyone
A and G are the sets of agents and groups active in C. Let
can explicitly declare the own trust about each other member.
I a set of available items, each one belonging to a specific
Similarly, the trust perceived by an agent au withX respect to a
category x, belonging to the set of categories X 1 , that in C
can be reviewed by each agent a ∈ A with an integer in group g of agents can be defined as tau →g = tau →av /|g|.
v∈g
the range [0, 5]. Moreover, let ra,i be the generic review of Note that for a group g: (i) its administrator sets the admitted
an item i ∈ I released by a, which consists of: (i) a rating behaviors access modalities (denoted as Mg ); (ii) the interest
assigned to i by a; (ii) a category x ∈ X associated with for a category x ∈ X is computed as the average of the
i; (iii) a numerical score specifying the helpfulness2 of ra,i ; interests of its agent members for x that are stored in their
(iv) a timestamp. Finally, we denote by ra the set of reviews profiles; (iii) how the members of g perceive as trustworthy
associated with a, called review history, and by R the set of X
an agent au is computed as tg→au = tav →au /|g|.
all the review history in C. In such a scenario, we assume to av ∈g
adopt a multi-agent platform where, each agent au assists a
1
B. The agents’ tasks
The set of categories associated with C only depends by the goals of C
2
The helpfulness is a measures of the utility of the rating of a review is An agent updates its profile when an action involving
useful in making a decision and it is computed as the average of the scores. information stored therein is performed. More precisely:
39
3

• After each performed action, an agent au updates in av ). Usually, reliability can assume values ranging in [0..1] ∈
its profile the interests and the boolean values of the R and the higher relau →av , the higher the perception of the
involved behavioral variables. Similarly, an agent ag in reliability of av by au . Note that reliability is an asymmetric
its profile updates the behavioral variables every time the measure. The second trust component, named reputation and
administrator of g changes the associated rules. Besides, denoted it by repa in the interval [0..1] ∈ R, is a global
each time that the preferred access modes change then measure of the trust perceived by the whole community about
the associated agent updates its profile. each other agent. The reputation is computed by averaging all
• When u expresses his/her evaluation about another user the reliability values relau →av for each av ∈ A.
v then au updates the trust measure. The two trust components are joined in a unique value to
We also assume that a Distributed Directory Facilitator compute the trust au about av as tau →av = αau · relau →av +
agent (DDF) supports the other agents in C with an Agent (1−αau )·repav , where αau ∈ [0..1] ∈ R is set by au to weight
Indexing Service and a Communication Layer enabling the the relevance it assigns to the first trust term with respect to the
agent message exchange. second one. Note that trust is an asymmetric measure because
in the formulation it takes into account the reliability. Besides,
IV. S IMILARITY AND T RUST each time a reliability value is updated by au , it sends the new
value to the DF that, in turn, returns a reputation value to au
To investigate the time-stability of groups in terms of
when it needs to compute a trust measure.
similarity, by means of the model previously presented, we
As defined in [17], compactness is a measure combining
consider agents’ similarities and trust relationships, as follows.
trust and similarity, say γau →av , able to exploit importance
given to the mutual similarity with respect to the mutual trust.
A. Similarity measure We model this level of importance by the coefficient W s,
Let su,v be the measure of similarity between the profiles ranging in [0..1] ∈ R and, consequently, we define γau →av as
of agents au and av computed as a weighted mean of the γau →av = W s · sau ,av + (1 − W s) · tau →av . Remember that
contributions of interests (cI ), behaviors (cB ) and access trust is an asymmetric measure γu→v 6= γv→u .
modes (cM ) normalized in [0, 1]. More formally, In Table I the meaning of the symbols is reported.
sau ,av = (wI · cI + wB · cB + wM · cM )/(wI + wB + wM )
TABLE I
where wI , wB , wM ∈ [0, 1] ∈ R are system weights for the M AIN SYMBOLS USED IN THE PAPER AND THEIR MEANING .
contributes cI , cB and cM , in turn, are computed as follows: Symbol Meaning
• cI is based on the average difference between the interest tu→v level of trust perceived by the user u w.r.t. the user v
values of au and av for each category x ∈ X : tu→g level of trust perceived by user u w.r.t. the group g
X tg→u level of trust perceived by the group g w.r.t. the user u
cI = 1 − |Iau (x) − Iav (x)|/|X | su,v similarity between users u and v
c∈C su,g similarity between the user u and the group g
• cB is computed on the average difference between the relu→v reliability perceived by the user u w.r.t. av
repu reputation of the user u
boolean variables contained in Bau and Bav . This dif- αu weight that au assigns to the reliability w.r.t. the reputation
ference is 0/1 if the two corresponding variables are γu→v compactness perceived by au w.r.t. av
equal/different. W su weight that au assigns to the similarity w.r.t. the trust
WI weights the interest in computing su,v
• cA is set to 1/0 if Mau is equal/different to Mau .
WB weights the behavior in computing su,v
The similarity su,g between an agent and a group is WM weights the access mode in computing su,v
computed in the same manner described above, simply by
substituting av with ag .
V. A2G: M ATCHING AGENTS WITH G ROUPS
B. Trust and compactness measures In this section the algorithm (A2G), enabling user agents to
We view trust as two terms specifying how much an select the groups to join with, is presented.
agent trusts another agent, and how much the community Let G = {g1 , g2 , . . . , gn } be the groups of C, with |G| =
perceives an agent as trustworthy. A feedback mechanism n. Moreover, let kMAXau
be the upper bound ranging in [0, n]
usually allows each agent to record its satisfaction for its which specifies the number of groups au desires to join with
interactions with other agents in order to compute/update and reasonably it will be kMAXau << n. In the following, for
its trust measures [24]–[26] based on the concept of social convenience, the notation kMAX will be used instead of kMAX au
.
capital [27]. In fact, a high rate of positive interactions means Algorithm A2G selects kMAX groups having the largest value
that an agent can receive an advantage to interact with another of compactness of au vs the joined groups. We assume
agent and, therefore, trust should increase/decrease in presence that au continues to receive the whole benefit from all the
of positive/negative interactions. The first component, known K ⊆ G groups which it is joined with, so that the overall
in the trust theory as reliability, represents the satisfaction of received benefit in joining with X all the K groups, in term
au about av , i.e. relau →av , and can specify several types of of compactness, is given by γu→gi . Finding the subset
trust relationships (e.g., the honesty, the dependability or, as in gi ∈K
this work, how much au is satisfied by the services provided by K? ⊆ G producing the best benefit for au under the constraint
40
4

|K? | = kMAX is equivalent to solve an optimization problem. Data: r: an agent which has asked to join with the group, K, the set of
In this work, we assume that each user agent au is unable agents in g
to know, in advance, the compactness of all groups in G. for (au ∈ K)[ do {ag sends a message to au };
for (au ∈ K {r}) do {Compute γg→u };
Furthermore, we assume that: (i) au is able to sample m P P
uj ∈g γui →uj
random groups from G; (ii) au will record into an internal Let π =
ui ∈g
∀hui , uj i ∈ g and let S = ∅;
cache, denoted as H the profiles of the groups au joined with [ |g|2 [
for (u ∈ K {r}) do {if (γg→u ≥ π) {S = S {u}}};
in the past; (iii) m is the number of the group agents that at
Let TopS be the set of top-nMAX users in S;
each epoch must be contacted by au . Algorithm 1 describes if (r ∈ S) {ag accepts the join request of r};
the steps au performs to find the kMAX groups it can join with, for (u ∈ K ∧ u 6∈ S) do {ag deletes u from g};
while the Algorithm 2 runs on the group agent. In particular,
it is assumed that (i) the size of each group g ∈ G is ≤ than Algorithm 2: The Group Agent Task
a threshold nMAX ; (ii) nMAX is fixed by the group administrator;
(iii) each agent ag stores into an internal cache the profiles of
the agents who joined with g;
P P
g∈G ACg x,y∈g,x6=y γx→y
M AC(wI , W s) = ACg = .
VI. T HE PROPOSED COMPUTATIONAL FRAMEWORK |G| |g|
(1)
P P
In our framework, a community is associated with a tem- g∈G ASg s
x,y∈g,x6=y x→y
poral dataset of events consisting of a matrix EM , where M AS(wI , W s) = ASg = .
|G| |g|
each row represents an event containing a timestamp, an agent (2)
identifiers and the event attributes. An events can be an action More in detail, ACg (resp., ASg ) is defined as the Aver-
performed by an agent or an external event changing the state age Compactness (resp., Average Similarity), similarly to the
of the community. Furthermore, we assume that a (non time- average dissimilarity commonly exploited in Clustering Anal-
varying) matrix T M of trust relationships is available, where ysis [28], since a group g can be viewed as a cluster of agents.
each row is a pair of agent IDs (au , av ) representing a trust Note that M AC is computed in the training phase of the A2G-
relationship among agent au and agent av . Moreover, A2G- Comp algorithm (i.e. it only drives group formation), while
Comp and A2G-Sim are two versions of the algorithm A2G. In M AS is computed in the test phase. Therefore measuring the
the former the compactness γ is computed by setting W s < 1 variation of M AS can be useful to verify the homogeneity, in
(i.e., it is driven by similarity and trust) and for the latter terms of similarity, of the groups formed in the training phase.
W s = 1 (i.e., it is driven only by similarity).
The framework provides the weights wI and W s in the
range [0, 1] ∈ R influencing the A2G algorithm results. wI A. Experimental approach and main parameters
represents the weight assigned to the agent interest, while
1 − wI is divided between wB , representing the weight We considered the time-variation of the average similarity
assigned to the agents behavior (see Section IV), and wM . of the groups in two different cases: (i) (Comp) Groups
cM is set as random not being into the original dataset. formed by the A2G-Comp algorithm are driven by compact-
The lower the value of wI , the higher the incidence of the ness (W s < 1). (ii) (Sim) Groups formed by the A2G-Sim
component cM in computing the similarity, in other words algorithm are driven by the similarity criterion (W s = 1).
cM is an “uncorrelated component”. Furthermore, the higher The computation of the measures are performed by follow-
the value of W s, the lower the impact of the trust relationship ing the steps described below: (i) Rows of the matrix EM
in computing the compactness γ. are arranged in an increasing order, basing on the database
In this perspective, the M AC (Mean Average Compactness) timestamp. (ii) The matrix EM is divided into a number of
and M AS (Mean Average Similarity) measures have been time-windows of equal size. The first time-window is for the
used to perform experiments, in dependence of wI and W s. training set and the remaining for the tests. (iii) The trust
network is built by loading the matrix T M and for all. (iv)
The training is performed by executing the algorithm A2G-
Data: au : an agent, H the current set of groups of au , m: an integer Comp (resp. A2G-Sim) on the first time-window, in order
in [0, n], kMAX : the number of groups au can join with to form groups of agents. (v) The training is stopped when
Result: The new set S of groups of au [ “stable” values of M AC for A2G-Comp (M AS for A2G-
Y = a set of m random groups extracted from DF; Z = H Y;
Sim) are reach, i.e. the difference between two steps is less
for (g ∈ Z) {au sends a message to ag and let pg be the profile of g};
S = the set of kMAX groups of Z with the highest compactness values; than a given threshold (in our case it was 5%). (vi) Data of
for (g ∈ S) do the remaining time-windows is loaded in sequence for each of
if (g ∈/ H) then {au sends a join request with its profile to ag }; them and M AS is computed without executing the algorithm
else {au left g};
end A2G, such that group composition remains the same as in the
return S end of the training phase. This technique allows us to study the
variation of M AS due to the addition of events representing
Algorithm 1: The User Agent Task
the execution of some further actions by the agents.
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5

TABLE II 1
PARAMETERS USED IN EXPERIMENTS ON THE CIAO DATASET. Quartiles
Median
0.95
Parameter Value Parameter Value
Number of Groups 50 kMAX 10
kMIN 0 NREQ 5 0.9
kMAX 50 Size of the Training Set 10, 000

MAS
nMIN 0 Size of the Test Set 26, 065 0.85

0.8
VII. E XPERIMENTS
0.75
Experiments exploited the described framework on a dataset
extracted from the social network CIAO [12]3 referred to 0.7
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
12, 375 users and consisting of two matrices (i.e., EM, T M ).
WI
Rows of matrix EM have the form {userID, productID,
Fig. 3. MAS vs parameter wI achieved by the A2G-Sim (Ws = 0.1).
categoryID, rating, helpfulness, timestamp}, where categoryID
is the commercial category of the item identified by productID
which received the rating by the reviewer identified by userID, 0.98
and helpfulness represents the level of satisfaction of the Quartiles
Median
0.96
other member for that rating (it has not been used in our
experiments). Table VII contains the parameters used to carry 0.94

out the experiments. The training set is made by the first 0.92
10, 000 events. The software used for the experiments can be 0.9

MAS
downloaded at https://github.com/fmes/simU2G. 0.88

0.86
0.94
Quartiles 0.84
Median
0.92 0.82

0.9 0.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
WI
0.88
MAS

Fig. 4. MAS vs. parameter wI achieved by the A2G-Comp (W s = 0.5).
0.86

0.84

A. Results
0.82

0.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Experiments were performed by varying weights wI and
Ws W s in the range [0.1 − 0.9]. Figures 1 and 2 report the
Fig. 1. MAS vs parameter W s achieved by the A2G-Comp (wI = 0.1). execution of A2G-Comp for wI = 0.1 and wI = 0.5 and
W s in the range [0.1 − 0.9]. In Figure 1 the values of the
M AS are relevant also when the weight of the trust component
0.94
is low (i.e., W s > 0.5). In particular, values of MAS are
Quartiles
Median larger than 0.8 (e.g., median is 0.82 for W s = 0.8), giving
0.92 a good time-stability with a visible bias around the median
0.9
value, if compared to the results shown in Figure 2, on which
the uncorrelated component starts to assume a less significant
0.88 weight. Figures 3-4 show the results for the 1st, 2nd, and 3rd
MAS

quartile, minimum and maximum values of M AS computed
0.86
after the training for the remaining time windows. Figure 3
0.84 shows the behavior of A2G-Sim for different values of wI ,
while Figure 4 represents the different values of M AS for
0.82
A2G-Comp with W s = 0.5. From these Figures we note
0.8 that the lower the value of wI , the lower the value of overall
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Ws
similarity at the end of the test for A2G-Sim (Figure 3), while
for A2G-Comp the values of M AS are higher of about 10%.
Fig. 2. MAS vs parameter W s achieved by the A2G-Comp (wI = 0.5).
This first set of results say us of driving groups formation
by compactness when the weight wM is of at least 25% to
3
Data used in our experiments are publicly available at http://www.public. obtain homogeneous time-stable groups in terms of average
asu.edu/∼jtang20/datasetcode/truststudy.htm similarity.
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