=Paper=
{{Paper
|id=Vol-2215/paper7
|storemode=property
|title=Effective Group Formation in Agent Societies
|pdfUrl=https://ceur-ws.org/Vol-2215/paper_7.pdf
|volume=Vol-2215
|authors=Antonio Liotta,Fabrizio Messina,Domenico Rosaci,Giuseppe M.L. Sarné
|dblpUrl=https://dblp.org/rec/conf/woa/LiottaMRS18
}}
==Effective Group Formation in Agent Societies==
https://ceur-ws.org/Vol-2215/paper_7.pdf
Effective Group Formation in Agent Societies
Antonio Liotta∗ , Fabrizio Messina† , Domenico Rosaci‡ , Giuseppe M. L. Sarné §
∗ Data Science Centre, University of Derby, Lonsdale House, Quaker Way Derby DE1 3HD U.K., a.liotta@derby.ac.uk
† Department of Mathematics and Informatics, University of Catania, Viale Andrea Doria Catania, Italy, messina@dmi.unict.it
∗ Department DIIES, University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Cal., Italy, domenico.rosaci@unirc.it
‡ Department DICEAM, University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Cal., Italy, sarne@unirc.it
Abstract—In this paper we address the problem of measuring opinions). Moreover, the updated social values could be un-
the overall effectiveness of group formation in virtual commu- known for one or more members. In other word, the Ek index
nities. Group formation is often driven by the combination of allows us to evaluate the effectiveness of a group formation
similarity and trust measures which are usually exploited with
the recommendations provided by all the community members process once the group is formed and cannot be used to obtain
(global reputation). In this work propose a specific index to mea- a set of groups having a high Ek index value or for evaluating
sure the effectiveness of group formation, and to exploit the local a newcomer request.
reputation in place of the global one. The use of local reputation In this work we also propose to form groups by exploiting
will allow group administrators to save a significant amount of local reputation [3], [4], in place of the global one. The local
computationally and/or communicational tasks. We designed an
algorithm to form effective groups in virtual communities and reputation considers opinions only coming from the neigh-
tested it on real data. boring agent [5], assumed as more reliable than unreferenced
Index Terms—Group formation, Virtual Communities, Repu- opinions. This is particularly useful in a distributed architec-
tation, Trust ture, where each member can manage local information with
a limited consumption of resources, instead of processing the
I. I NTRODUCTION global reputation for which the agent is needed to process all
the community members. However, similarly to real societies,
Group formation in virtual communities have been widely if the individual experience is insufficient to trust another
studied in the last years [1]. Novel affiliations are allowed member and the number of friends (or friends of friends and
when the members of a group give a positive assessment so on), then further members’ opinions are required (although
towards the incoming agent, i.e. when the joining of the new it is needed to decide how to weight their trustworthiness).
member will not decrease the social capital (i.e., effectiveness) Moreover, in order to perform the best choice about poten-
of the group itself [2]. In this context, an important question tial newcomers, trust values must be appropriately combined
is how to measure the overall effectiveness of a group. and evaluated within each community. To this purpose, in vir-
To this end, let us suppose that i) each agent belonging to tual communities different strategies have been adopted but all
the community is characterized by a social value v (i.e., its of them deeply differ from the processes taking place in human
quantitative utility for the community) and ii) to classify the societies. They are mainly based on several different voting
members of a community in n classes Ci (with i ∈ 1 · · · , n) mechanisms [6] which gives the advantages deriving from
on the basis of their social value. Whenever the composition a democratic approach and the disadvantage due to possible
of a group changes – starting from a certain distribution of the manipulations [7] (that we consider as an orthogonal issue with
social values – it causes a social variation (∆V ). For example, respect to our goals). In this context, we propose the formation
when the percentage of agents belonging to the class Ci of effective groups with respect to the adopted group formation
assumes the value ηi∗ , with η1 representing the previous value, strategy by using a weighted voting mechanism (where each
then ∆V = |η1 −η1∗ |. The social variation ∆Vg associated with vote is represented by a trust value obtained by a suitable
∑n n components
the ∗
of the group g can be defined as the average combination of reliability and local reputation). In particular,
i=1 |ηi −ηi |
n where 0 is the value related to the best group, in our contribution is mainly represented by the development
terms of social value, and vice versa, 1 represents the worst of an algorithm, called Effective Group Formation (EGF ),
scenario. To this aim, we define the Ek index as the percentage aimed at computing individual trust by combining reliability
of the groups having a social variation less or equal than and local reputation information in order to accept or refuse
k/100. Moreover, in this paper, in order to test our approach, a newcomer affiliation request by using a voting mechanism.
we will use the E10 index to evaluate the effectiveness of a The algorithm has been tested on the real data derived by the
group. CIAO [8] community.
Note that the formation of a group can not be “driven” by The paper is organized as follows: In Section II the related
the members’ social values, that are known only a posteriori literature is presented and Section III describes the adopted
and at a global level (based on all the community members’ trust measures and the voting procedure. Section IV discusses
39
the EGF algorithm, while Section V presents the experiments III. T HE T RUST-VOTING P ROCESS
we carried out. Finally, in Section VI some conclusions are Let us denote with A the agent community and with a
drawn. directed unlabeled graph G = ⟨N , L⟩ the agents relationships
in A, where N is a set of nodes (e.g., the node n ∈ N and
the agent an ∈ A represent the same entity) and L is a set of
II. R ELATED W ORK
arcs, where li,j ∈ L represents a trust relationship occurring
between the agents ai , aj ∈ A. Below some definitions about
To form groups within social communities, some re-
trust and local trust will be provided.
searchers proposed to adopt similarity measures as in [9], [10].
a) Trust: Let: i) t̂ : A × A → [0, 1] be an agent trust re-
Nevertheless, similarity does not guarantee the existence of
lationship, where 0/1 represents the minimum/maximum trust
good interactions among users. Recent studies [11] witness
degree; ii) rn,k be the reliability measure of the direct trust that
that the larger the mutual members’ trust, the larger their
an has in ak , derived by his/her direct past experiences with
interest for mutual interactions [12]. Therefore, to improve
ak ; and iii) wk be the global reputation measure of the trust
the group effectiveness similarity and trust measures can
perceived by the whole community about ak ∈ A by averaging
be combined, as in [13], but the computation of similarity
all the reliability values rx,k , for each ax ∈ A. Then, for each
measures in huge communities could be too expensive [14],
agent an ∈ A the global trust t̂n,k that an has about ak can
impracticable/unreliable [15]. Differently, forming group tech-
be computed by weighting reliability and global reputation in
niques only based on trust measures have been proposed [16],
the unique measure t̂n,k = α · rn,k + (1 − α) · wk . Note that
but if direct knowledge of a member (i.e., reliability) gives an
t̂ is an asymmetric measure because it includes r.
inadequate knowledge of trust in a community, also opinions
The measure t̂n,k can be used to derive the measure t̂n,g
of other community members (i.e., reputation) must be used.
(where g ⊂ A is an agent group) to determine the “trustwor-
In particular, the computation of the global reputation (i.e.,
thiness” of g as perceived by an and computed by averaging
based on the opinions of all the members) could be difficult in
all the values t̂n,k for all the agents ak ∈ g. Similarly, t̂g,n
presence of unreliable opinions, often due to malicious behav-
represents a synthetic measure of the trust that the whole group
iors [17]. As a consequence the evaluation of the recommender
g has in an and computed by averaging all the ∑ trust values
/
trustworthiness assumes a certain relevance [18], [19]. This
t̂k,n for all the agents ak ∈ g. Formally, t̂g,n = k∈g t̂k,n |g|,
leads to realize complex group formation processes dissimilar
∀k ∈ g, where |g| is the size of g.
from those realized in real user societies. b) Compactness: The compactness combines the similar-
To aggregate trust information we propose using voting ity degree between two agents, or an agent and a group, and
to manage individual opinions and interests [20], [21] by their trust levels [13]. The similarity sn,k is usually computed
reducing conflicts [22] or maximizing the social utility [23]. by comparing some “features” of the an and ak agents’ profile
In the context of huge communities, global voting procedures (e.g., interests, item categories and so on), while the similarity
can be inefficient or unfeasible while a local approach, de- sn,g between an agent an and a group g by weighting the
composing the vote in more local votes successively joined, similarities existing between an and all the agents of g. More
should be desirable [24]. Another aspect is represented by in detail, the compactness measures cn,k (between agents an
the risks of manipulation due to strategic vote [25], [26]. In and ak ), cn,g (between an agent an and a group g) and cg,n
particular, software agent societies are more exposed to voting (between a group g and an agent an ) are obtained as:
manipulations for the agent aptitude to easily explore different
strategies [27]. cn,k = γ · sn,k + (1 − γ) · t̂n,k
Our proposal adopts trusts to support voting in virtual cn,g = γ · sn,g + (1 − γ) · t̂n,g
communities where local trust and local voting approaches are
cg,n = γ · sg,n + (1 − γ) · t̂g,n
usually preferred in presence of great population, mobility,
lack in infrastructure, communications or limited computa- The measure cn,g can be used by any agent to evaluate the
tional and/or storage capabilities. To this regard, a local trust- goodness of joining with g, while the measure cg,n is useful
voting mechanism is applied in a mobile wireless network to a the agent administrator of g for evaluating if accepting
context in [28] to establish whether or not a node should be an into the group.
included in a transmission path; the evaluation is based on c) Local trust: Let t : A × A → [0, 1] be the local trust,
its trustworthiness as it is perceived by the other nodes. The where 0/1 represents the minimum/maximum trust level. The
theory of semi-rings is used in [29] to model trust in Ad-Hoc local trust for an agent an ∈ A arises by all the agents ak
Networks by a graph where links represent trust relationships linked to an by a path (an , . . . , ak ) and by all the oriented
on the basis of second-hand information, even though this paths connecting an with all the agents of such sub-set (i.e.,
information is weighted differently from that derived by direct sub-graph). For each pair of agents an , ak the local trust tn,k
experiences. The authors of [30] discuss a group affiliation of an about ak is given by the combination of the reliability
procedure where any group joining request is evaluated by before defined and a local reputation (i.e., wn,k ) computed by
means of a democratic group trust-voting mechanism, where summing the contributions of how much the agents, belonging
each group member exploits an individual local trust-engine. to the ego-network of an , trusts ak .
40
Let D(n, k) be the set of agents belonging to the ego- ta,c = 0.5; 1
network of an directly connected with ak . Let s(n, k) be the f g h ta,e = 1; 1
sum of the contributions, in term of indirect trust, given by ta,g = 1; 1
the agents ah ∈ D(n, k) and let l(n,k) be the shortest path a b tc,b = 0.5; 0.5
between an and ak . Then the (normalized) local reputation tc,d = 0.25; 0.5
wn,k is defined as: te,d = 1; 0.5
∑ e c
tg,b = 0.75; 1
h∈D(n,k),h̸=n,k 2(l(n,h) −1) · th,k
1
wn,k = ∑ 1 (1) tg,h = 1; 1
h∈D(n,k),k̸=n,k 2(l(n,h) −1) th,b = 0.75; 0.5
d
the contribution in (1) given by ah to wn,k is raised by ra,b = 1; 1
1/2(l(n,h) −1) so that less importance is given to the trust
Fig. 1. An example of agent community (the labels report the trust/reliability
relationships (h, k) which are “far” from an . Finally, the local values and their weights).
trust tn,k combines reliability and local reputation:
tn,k = α · rn,k + (1 − α) · β · wn,k (2) and ad (depicted in yellow) be the nodes asking to join with
the group. The voting mechanism proposed above requires that
where the real parameters α, β ∈ [0, 1]. The former parameter all the group members compute their local trust in ab and
weights reliability and local reputation to give relevance to ad . With respect to the node aa (depicted in orange), its ego-
one or other. The parameter β considers the dependability of network consists of all the green nodes and of the yellow node
wn,k by the number of agents in D(n, k) that contributed to ab . Note that ra,b = 1 and ra,d = 0 because any edge exists
compute wn,k . Specifically, β yields 1.0 if ∥D(u, x)∥ ≥ N between aa and ad . Moreover, in Figure 1 the nodes giving
−1
or ∥D(u, x)∥ · N if ∥D(u, x)∥ < N , where N specifies their contribution to compute the local reputation measures
how many agents of an ego-network are necessary to compute wa,b and wa,d are respectively ⟨ag , ac , ah ⟩ and ⟨ac , ae ⟩. In
a reliable value of the local reputation. Indeed, for a small computing wa,b , the contributions of the nodes ag and ac ,
number of nodes in ∥D(n, k)∥ then an will not have sufficient directly connected with aa , are weighted by 1, while the
information about ak from his ego-network and the local contribution of ah is weighted by 0.5, since it is 2 the shortest
reputation measure will not be suitably relevant. path with aa . Therefore, wa,b = (1 · 0.75 + 1 · 0.75 + 0.5 ·
Note that the capability to provide reliable opinions is 0.5)/(1+1+0.5) = 0.6. Similarly, in computing wa,d both the
unrelated to other aspects and, therefore, it needs a specific contributions of ac and ae are weighted by 1 and in this way
trust/reputation measure [17]. For this reason, in computing wa,d = (0.5·1+0.5·0.25)/(0.5+0.5) = 0.625. Furthermore, if
our local reputation we prefer to tune its relevance in comput- we adopt α = 0.5 and β = 1 for ab and ad , then the two mea-
ing t by means of the parameters α and β above defined. sures of the local trust are τa,b = 0.5·1+(1−0.5)·1·0.6 = 0.8
d) The Local Trust-Voting Mechanism: Voting is the and τa,d = 0.5 · 0 + (1 − 0.5) · 1 · 0.625 = 0.31, respectively.
main approach used in deliberative assemblies to assume a Finally, if Tg = 0.5, the voting result will be that ab is admitted
decision [31]. The voting mechanism adopted here exploits the (i.e., va,b = 1) and ad is not admitted (i.e., va,d = 0) into the
local trust above defined to decide whether an agent belonging group.
to A can join with a group. In particular, each member gives
a vote based on its local trust measures with respect to the IV. T HE DISTRIBUTED G ROUP F ORMATION PROCEDURE
agent presented the joining request to the group. For instance, In this Section we present the distributed algorithm EGF
the agent an may express a vote vn,k to accept an or not to form groups in an agent community by using local trust
the requester agent ak in the group g whether the local trust information and a voting procedure. This algorithm consists
measure tn,k is greater or equal to a threshold Tg ∈ [0, 1]. In of two parts executed by the software agents that operate in
the former case, vn,k = 1, otherwise it is 0. More formally: behalf of their users. The former part is executed on the agent
requester side, while the second part of the algorithm will be
0 if τn,k < Tg
executed by the agent managing the group.
vn,k = (3)
1 if τn,k ≥ Tg A. The EGF algorithm running on the requester agent side.
We assume that the result of the voting process of a group g In Figure 2-A is listed the EGF pseudocode running on the
for a potential new member ak and a particular voting criterion an side, where Xn is the set of the groups to which the agent
v (like that in (3)) is the output of a function V (v, g, ak ). For an belongs to and N M AX is the maximum number of groups
instance, the requester will be accepted into the group only if that an agent can analyse by fixing that N M AX ≥ |Xn |.
the majority of its members has voted for its acceptance. Besides, the generic agent an stores the profile of each group
e) Discussion: In Figure 1 we represent a simple ex- gj contacted in the past and the time elapsed dj from the last
ample of community of 8 agents in order to explain the EGF execution for that group. Moreover, let δn be a timestamp
computation of the local trust and the voting procedure. Let ab threshold and ψn ∈ [0, 1] be a threshold fixed by an . The agent
41
Trust model
an tries to improve its benefits when joining with a group and, A The virtual community
to this aim, the values of c are recalculated when older than N The number of agents of the community
a threshold δi (lines 1-4). Then, candidate groups are sorted α Weighting reliability vs reputation
γ Weighting trust vs similarity in computing compactness
in a decreasing order with respect to the compactness c (see β Scaling factor for the local reputation
the previous section) and the NM ax groups are selected in the L(n, k) Local network of an with respect to ak
loop of lines 7-16. If some groups in the set Lok are not in ωn,k Local reputation of an in L(n, k).
τn,k Local trust of an about ak
Xn , then an could improve the overall compactness by joining τ̂n,k Global trust of the agent an about the agent ak
with those groups within the maximum number of groups that ηn,k Compactness on the agent an and ak
an can join with. ηn,g Compactness on the agentan and group g
ηg,n Compactness on the group g and the agent an
EGF Procedure, executed by the agent an Group formation
Input: Nmax Maximum number of agents a group is able to host
Xn , NM AX , δn , ψn ; Kmax Maximum number of groups a agent can join with
Y = {g ∈ G} a set∩of groups randomly selected C1 Class of agents h ≤ 2
∪ : Class of agents 2 < h ≤ 3
|Y | ≤ NM AX , Xn Y = {0}, Z = (Xn Y ) C2
C3 Class of agents h > 3
1: m ← 0;
Tg Trust threshold for the voting mechanisms
2: for gj ∈ Z : dg > δi do p1 , p2 , p3 Probability that a agent of class Ci will join a group
3: Send a message to âgj to retrieve the profile Pj . TABLE I
4: Compute ci,gj S YMBOL TABLE
5: end for
6: Let be Lok = {g ∈ Z : cn,gj ≥ ψn }, with |Lok | ≤
N M AX
7: k → 0 B. The EGF algorithm running on the group agent.
8: for gj ∈ Lok ∧ gj ̸∈ Xi do
9: send a join request to âgj In Figure 2-B is listed the EGF pseudocode running on the
10: if âgj accepts the request then group manager side, where Kj is the set of the agents affiliated
11: m ← m+1 with the group gj belongs to and KM AX is the maximum
12: end if number of agents to join with the group gj , with ||Kj || ≤
13: end for
KM AX . Suppose that the group administrator âgj stores the
14: for gj ∈ {Xi − Lok } ∧ m > 0 do
15: Sends a leave message to gj profile Pi of each agent ai and the timestamp di of its retrieval.
16: m ← m−1 Then, âgj , fixed the time threshold wj , actives the procedure
17: end for each time that an agent an sends a request to join with gj . In
lines 1 − 5, âgj asks the updated profile of the components
of the group itself. By line 6 of the algorithm, a request is
EGF Procedure, executed by the gi admin agent âj sent at all the agents belonging to the group gj to send their
∪
Input: Kj , KM AX , an , wj , Z = Kj {n}; preferences (i.e., a vote) about the possible joining of an with
1: for am ∈ Kj do the group gj by adopting the strategy specified in the previous
2: if di ≥ wj then section. After the voting, different choices exist, namely:
3: ask to am its updated profile
4: end if • if the agents of gj voted to refuse an in their group, then
5: end for the procedure ends with an out by the group gj (line 7);
6: if (V (v, gj , an ) == 0) then • if the agents of gj voted to accept an in their group; if
7: Send a reject message to an the number of agents already present in gj is less than
8: else
KM AX then an is accepted into gj , otherwise an is not
9: if |Z| ≤ KM AX then
10: Send an accept message to an accepted into gj (line 8 − 10);
11: else • if the agents of gj voted to accept an in their group and
12: for am ∈ Z do the number of agents into the group is already equal to
13: compute cgj −{am },am KM AX then for an and all the agents belonging to the
14: end for
group is updated the value of their compactness (lines
15: Let S = {s1 , s2 , . . . , sKM AX +1 }, with si ∈ Z and
cgj −{si } ≤ cgj −{sk } iff i ≥ k 12 − 14) then for the agent (denoted by m) having the
16: if S[KM AX + 1] == an then worst value of the compactness c (line 16):
17: Send a reject message to an – if m is the same agent an then it is not admitted into
18: else gj (line 17);
19: Send a leave message to the node S[KM AX +1]
20: Send an accept message to an – if m is not the agent an , then an will take the place
21: end if of m into gj (lines 19 and 20).
22: end if
23: end if V. E XPERIMENTS
Fig. 2. EGF algorithm. Top A) - Member Agent. Bottom B) - Group Agent The results of some tests on the EGF algorithm are
shown in this section. To this aim, a publicly available
42
K max = 100 Nmax = 10 S1 . S2 . S3 K max = 100 = 0.5 S1
100 100
90 90
80 80
70 70
60 60
E 10
50 50
E 10
40 40
30 30
20 20
10 10
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 40
Nmax
Fig. 3. Configurations S1 , S2 and S3 with Nmax = 10 and Kmax = 100 Fig. 4. Configuration S1 with Kmax = 100 and α = 0.5
Nmax = 10 = 0.5 S1
dataset extracted from the social network CIAO [8] has 100
90
been used. It stores data of reviewed items, referred to 80
12, 375 users, about user-item ratings and user-trust relation- 70
ships stored into the matrices EM and T M . In particular, 60
10
50
each EM row consists of ⟨userID, productID, categoryID,
E
40
rating, helpf ulness, timestamp⟩ data, where the first three 30
terms identify a user, the product category and the rated 20
10
product itself, the fourth term is the rate (i.e., helpfulness) 0
assigned to the review by the other members and, finally, the 100 200 400
K max
last term is the review publishing data (unused in these tests).
Individual trust networks are built using the helpfulness values. Fig. 5. Configuration S1 with Nmax = 10 and α = 0.5
In our experiments we assumed the helpfulness as a social
value and the group formation activity has been addressed to
obtain different groups configurations in terms of distribution VI. C ONCLUSIONS
of social values. To this aim, CIAO members have been par- Group formation in social communities requires the com-
titioned into three classes (C) characterized by the following putation of the mutual trustworthiness among their members
helpfulness values C1 : h1 ≤ 2, C2 : < h2 ≤ 3 and on the basis of their reputation, a form of social information
C3 : h3 > 3, and defined the three scenarios described in provided by the community. We observed that the effectiveness
Table II. of a group depends on the capability of its members to satisfy
The results obtained by EGF, in term of the E10 index, mutual expectancies. Then, we proposed an index called Ek in
for different α, Nmax , and Kmax values are depicted in order to measure the groups effectiveness with respect to both
Figures 3, 4 and 5, where: i) Figure 3 shows the results for the the desired composition computed and a specific objective.
three configurations for different values of α, fixed Nmax = 10 We also proposed a distributed algorithm to form groups in
and Kmax = 100; ii) Figure 4 shows the results for S1 and virtual communities by improving the effectiveness of the
for different values of Nmax , fixed α = 0.5 and Kmax = 100; group formation activity in terms of E10 index by a weighted
iii) Figure 5 presents the results for S1 and for different values voting mechanism, where each vote is based on a combination
of Kmax , fixed α = 0.5 and Nmax = 10. of reliability and local reputation. The approach has been
In detail, Figures 3 highlights that for α > 0.3 the E10 value tested on real data extracted by the social network CIAO.
decreases, i.e. a greater relevance of reliability with respect to
reputation in forming groups. Moreover, the EFG performance ACKNOWLEDGMENT
for the configurations S2 and S3 decreases with respect to S1 This study has been supported by NeCS Laboratory
for a higher difficulty to obtain the desired configurations. The (DICEAM, University Mediterranea of Reggio Calabria).
influence of Kmax and Nmax on E10 is not significant and
this confirms the trend shown by the results obtained for S1 . R EFERENCES
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