Effective Group Formation in Agent Societies

Abstract

-In this paper we address the problem of measuring the overall effectiveness of group formation in virtual communities. Group formation is often driven by the combination of similarity and trust measures which are usually exploited with the recommendations provided by all the community members (global reputation). In this work propose a specific index to measure the effectiveness of group formation, and to exploit the local reputation in place of the global one. The use of local reputation will allow group administrators to save a significant amount of computationally and/or communicational tasks. We designed an algorithm to form effective groups in virtual communities and tested it on real data. Index Terms-Group formation, Virtual Communities, Reputation, Trust

I. INTRODUCTION

Group formation in virtual communities have been widely studied in the last years [ 1 ]. Novel affiliations are allowed when the members of a group give a positive assessment towards the incoming agent, i.e. when the joining of the new member will not decrease the social capital (i.e., effectiveness) of the group itself [ 2 ]. In this context, an important question is how to measure the overall effectiveness of a group.

To this end, let us suppose that i) each agent belonging to the community is characterized by a social value v (i.e., its quantitative utility for the community) and ii) to classify the members of a community in n classes Ci (with i 2 1 ; n) on the basis of their social value. Whenever the composition of a group changes – starting from a certain distribution of the social values – it causes a social variation (∆V ). For example, when the percentage of agents belonging to the class Ci assumes the value i , with 1 representing the previous value, then ∆V = j 1 1 j. The social variation ∆Vg associated with the n components of the group g can be defined as the average ∑in=1 jn i i j where 0 is the value related to the best group, in terms of social value, and vice versa, 1 represents the worst scenario. To this aim, we define the Ek index as the percentage of the groups having a social variation less or equal than k=100. Moreover, in this paper, in order to test our approach, we will use the E10 index to evaluate the effectiveness of a group.

Note that the formation of a group can not be “driven” by the members’ social values, that are known only a posteriori and at a global level (based on all the community members’ opinions). Moreover, the updated social values could be unknown for one or more members. In other word, the Ek index allows us to evaluate the effectiveness of a group formation process once the group is formed and cannot be used to obtain a set of groups having a high Ek index value or for evaluating a newcomer request.

In this work we also propose to form groups by exploiting local reputation [ 3 ], [ 4 ], in place of the global one. The local reputation considers opinions only coming from the neighboring agent [ 5 ], assumed as more reliable than unreferenced opinions. This is particularly useful in a distributed architecture, where each member can manage local information with a limited consumption of resources, instead of processing the global reputation for which the agent is needed to process all the community members. However, similarly to real societies, if the individual experience is insufficient to trust another member and the number of friends (or friends of friends and so on), then further members’ opinions are required (although it is needed to decide how to weight their trustworthiness).

Moreover, in order to perform the best choice about potential newcomers, trust values must be appropriately combined and evaluated within each community. To this purpose, in virtual communities different strategies have been adopted but all of them deeply differ from the processes taking place in human societies. They are mainly based on several different voting mechanisms [ 6 ] which gives the advantages deriving from a democratic approach and the disadvantage due to possible manipulations [ 7 ] (that we consider as an orthogonal issue with respect to our goals). In this context, we propose the formation of effective groups with respect to the adopted group formation strategy by using a weighted voting mechanism (where each vote is represented by a trust value obtained by a suitable combination of reliability and local reputation). In particular, our contribution is mainly represented by the development of an algorithm, called Effective Group Formation (EGF ), aimed at computing individual trust by combining reliability and local reputation information in order to accept or refuse a newcomer affiliation request by using a voting mechanism. The algorithm has been tested on the real data derived by the CIAO [ 8 ] community.

The paper is organized as follows: In Section II the related literature is presented and Section III describes the adopted trust measures and the voting procedure. Section IV discusses the EGF algorithm, while Section V presents the experiments we carried out. Finally, in Section VI some conclusions are drawn.

II. RELATED WORK

To form groups within social communities, some researchers proposed to adopt similarity measures as in [ 9 ], [ 10 ]. Nevertheless, similarity does not guarantee the existence of good interactions among users. Recent studies [ 11 ] witness that the larger the mutual members’ trust, the larger their interest for mutual interactions [ 12 ]. Therefore, to improve the group effectiveness similarity and trust measures can be combined, as in [ 13 ], but the computation of similarity measures in huge communities could be too expensive [ 14 ], impracticable/unreliable [ 15 ]. Differently, forming group techniques only based on trust measures have been proposed [ 16 ], but if direct knowledge of a member (i.e., reliability) gives an inadequate knowledge of trust in a community, also opinions of other community members (i.e., reputation) must be used. In particular, the computation of the global reputation (i.e., based on the opinions of all the members) could be difficult in presence of unreliable opinions, often due to malicious behaviors [ 17 ]. As a consequence the evaluation of the recommender trustworthiness assumes a certain relevance [ 18 ], [ 19 ]. This leads to realize complex group formation processes dissimilar from those realized in real user societies.

To aggregate trust information we propose using voting to manage individual opinions and interests [ 20 ], [ 21 ] by reducing conflicts [ 22 ] or maximizing the social utility [ 23 ]. In the context of huge communities, global voting procedures can be inefficient or unfeasible while a local approach, decomposing the vote in more local votes successively joined, should be desirable [ 24 ]. Another aspect is represented by the risks of manipulation due to strategic vote [ 25 ], [ 26 ]. In particular, software agent societies are more exposed to voting manipulations for the agent aptitude to easily explore different strategies [ 27 ].

Our proposal adopts trusts to support voting in virtual communities where local trust and local voting approaches are usually preferred in presence of great population, mobility, lack in infrastructure, communications or limited computational and/or storage capabilities. To this regard, a local trustvoting mechanism is applied in a mobile wireless network context in [ 28 ] to establish whether or not a node should be included in a transmission path; the evaluation is based on its trustworthiness as it is perceived by the other nodes. The theory of semi-rings is used in [ 29 ] to model trust in Ad-Hoc Networks by a graph where links represent trust relationships on the basis of second-hand information, even though this information is weighted differently from that derived by direct experiences. The authors of [ 30 ] discuss a group affiliation procedure where any group joining request is evaluated by means of a democratic group trust-voting mechanism, where each group member exploits an individual local trust-engine.

III. THE TRUST-VOTING PROCESS

Let us denote with A the agent community and with a directed unlabeled graph G = ⟨N ; L⟩ the agents relationships in A, where N is a set of nodes (e.g., the node n 2 N and the agent an 2 A represent the same entity) and L is a set of arcs, where li;j 2 L represents a trust relationship occurring between the agents ai; aj 2 A. Below some definitions about trust and local trust will be provided.

a) Trust: Let: i) t^ : A A ! [0; 1] be an agent trust relationship, where 0=1 represents the minimum/maximum trust degree; ii) rn;k be the reliability measure of the direct trust that an has in ak, derived by his/her direct past experiences with ak; and iii) wk be the global reputation measure of the trust perceived by the whole community about ak 2 A by averaging all the reliability values rx;k, for each ax 2 A. Then, for each agent an 2 A the global trust t^n;k that an has about ak can be computed by weighting reliability and global reputation in the unique measure t^n;k = rn;k + (1 ) wk. Note that t^ is an asymmetric measure because it includes r.

The measure t^n;k can be used to derive the measure t^n;g (where g A is an agent group) to determine the “trustworthiness” of g as perceived by an and computed by averaging all the values t^n;k for all the agents ak 2 g. Similarly, t^g;n represents a synthetic measure of the trust that the whole group g has in an and computed by averaging all the trust values t^k;n for all the agents ak 2 g. Formally, t^g;n = ∑k2g t^k;n/jgj, 8k 2 g, where jgj is the size of g.

b) Compactness: The compactness combines the similarity degree between two agents, or an agent and a group, and their trust levels [ 13 ]. The similarity sn;k is usually computed by comparing some “features” of the an and ak agents’ profile (e.g., interests, item categories and so on), while the similarity sn;g between an agent an and a group g by weighting the similarities existing between an and all the agents of g. More in detail, the compactness measures cn;k (between agents an and ak), cn;g (between an agent an and a group g) and cg;n (between a group g and an agent an) are obtained as: cn;k = cn;g = cg;n = sn;k + (1 sn;g + (1 sg;n + (1 ) t^n;k ) t^n;g ) t^g;n

The measure cn;g can be used by any agent to evaluate the goodness of joining with g, while the measure cg;n is useful to a the agent administrator of g for evaluating if accepting an into the group.

c) Local trust: Let t : A A ! [0; 1] be the local trust, where 0/1 represents the minimum/maximum trust level. The local trust for an agent an 2 A arises by all the agents ak linked to an by a path (an; : : : ; ak) and by all the oriented paths connecting an with all the agents of such sub-set (i.e., sub-graph). For each pair of agents an; ak the local trust tn;k of an about ak is given by the combination of the reliability before defined and a local reputation (i.e., wn;k) computed by summing the contributions of how much the agents, belonging to the ego-network of an, trusts ak.

Let D(n; k) be the set of agents belonging to the egonetwork of an directly connected with ak. Let s(n; k) be the sum of the contributions, in term of indirect trust, given by the agents ah 2 D(n; k) and let l(n;k) be the shortest path between an and ak. Then the (normalized) local reputation wn;k is defined as: wn;k = ∑

1 h2D(n;k);h̸=n;k 2(l(n;h) 1) th;k ∑ 1 h2D(n;k);k̸=n;k 2(l(n;h) 1) (1) the contribution in (1) given by ah to wn;k is raised by 1=2(l(n;h) 1) so that less importance is given to the trust relationships (h; k) which are “far” from an. Finally, the local trust tn;k combines reliability and local reputation: tn;k = rn;k + (1 ) wn;k (2) where the real parameters ; 2 [0; 1]. The former parameter weights reliability and local reputation to give relevance to one or other. The parameter considers the dependability of wn;k by the number of agents in D(n; k) that contributed to compute wn;k. Specifically, yields 1:0 if ∥D(u; x)∥ N or ∥D(u; x)∥ N 1 if ∥D(u; x)∥ < N , where N specifies how many agents of an ego-network are necessary to compute a reliable value of the local reputation. Indeed, for a small number of nodes in ∥D(n; k)∥ then an will not have sufficient information about ak from his ego-network and the local reputation measure will not be suitably relevant.

Note that the capability to provide reliable opinions is unrelated to other aspects and, therefore, it needs a specific trust/reputation measure [ 17 ]. For this reason, in computing our local reputation we prefer to tune its relevance in computing t by means of the parameters and above defined.

d) The Local Trust-Voting Mechanism: Voting is the main approach used in deliberative assemblies to assume a decision [ 31 ]. The voting mechanism adopted here exploits the local trust above defined to decide whether an agent belonging to A can join with a group. In particular, each member gives a vote based on its local trust measures with respect to the agent presented the joining request to the group. For instance, the agent an may express a vote vn;k to accept an or not the requester agent ak in the group g whether the local trust measure tn;k is greater or equal to a threshold Tg 2 [0; 1]. In the former case, vn;k = 1, otherwise it is 0. More formally: vn;k = 8 0 < : 1 if n;k < Tg if n;k

Tg

We assume that the result of the voting process of a group g for a potential new member ak and a particular voting criterion v (like that in (3)) is the output of a function V (v; g; ak). For instance, the requester will be accepted into the group only if the majority of its members has voted for its acceptance.

e) Discussion: In Figure 1 we represent a simple example of community of 8 agents in order to explain the computation of the local trust and the voting procedure. Let ab f e a d g c b (3) and ad (depicted in yellow) be the nodes asking to join with the group. The voting mechanism proposed above requires that all the group members compute their local trust in ab and ad. With respect to the node aa (depicted in orange), its egonetwork consists of all the green nodes and of the yellow node ab. Note that ra;b = 1 and ra;d = 0 because any edge exists between aa and ad. Moreover, in Figure 1 the nodes giving their contribution to compute the local reputation measures wa;b and wa;d are respectively ⟨ag; ac; ah⟩ and ⟨ac; ae⟩. In computing wa;b, the contributions of the nodes ag and ac, directly connected with aa, are weighted by 1, while the contribution of ah is weighted by 0:5, since it is 2 the shortest path with aa. Therefore, wa;b = (1 0:75 + 1 0:75 + 0:5 0:5)=(1+1+0:5) = 0:6. Similarly, in computing wa;d both the contributions of ac and ae are weighted by 1 and in this way wa;d = (0:5 1+0:5 0:25)=(0:5+0:5) = 0:625. Furthermore, if we adopt = 0:5 and = 1 for ab and ad, then the two measures of the local trust are a;b = 0:5 1+(1 0:5) 1 0:6 = 0:8 and a;d = 0:5 0 + (1 0:5) 1 0:625 = 0:31, respectively. Finally, if Tg = 0:5, the voting result will be that ab is admitted (i.e., va;b = 1) and ad is not admitted (i.e., va;d = 0) into the group.

IV. THE DISTRIBUTED GROUP FORMATION PROCEDURE In this Section we present the distributed algorithm EGF to form groups in an agent community by using local trust information and a voting procedure. This algorithm consists of two parts executed by the software agents that operate in behalf of their users. The former part is executed on the agent requester side, while the second part of the algorithm will be executed by the agent managing the group.

A. The EGF algorithm running on the requester agent side.

In Figure 2-A is listed the EGF pseudocode running on the an side, where Xn is the set of the groups to which the agent an belongs to and N MAX is the maximum number of groups that an agent can analyse by fixing that N MAX jXnj. Besides, the generic agent an stores the profile of each group gj contacted in the past and the time elapsed dj from the last EGF execution for that group. Moreover, let n be a timestamp threshold and n 2 [0; 1] be a threshold fixed by an. The agent an tries to improve its benefits when joining with a group and, to this aim, the values of c are recalculated when older than a threshold i (lines 1-4). Then, candidate groups are sorted in a decreasing order with respect to the compactness c (see the previous section) and the NMax groups are selected in the loop of lines 7-16. If some groups in the set Lok are not in Xn, then an could improve the overall compactness by joining with those groups within the maximum number of groups that an can join with.

EGF Procedure, executed by the agent an

Input:

Xn; NMAX ; n; n; Y = fg 2 Gg a set of groups randomly selected : jY j NMAX , Xn ∩ Y = f0g, Z = (Xn ∪ Y ) 1: m 0; 2: for gj 2 Z : dg > i do 3: Send a message to a^gj to retrieve the profile Pj . 4: Compute ci;gj 5: end for 6: Let be Lok = fg 2 Z : cn;gj

N MAX 7: k ! 0 8: for gj 2 Lok ^ gj ̸2 Xi do 9: send a join request to a^gj 10: if a^gj accepts the request then 11: m m + 1 12: end if 13: end for 14: for gj 2 fXi Lokg ^ m > 0 do 15: Sends a leave message to gj 16: m m 1 17: end for ng, with jLokj EGF Procedure, executed by the gi admin agent a^j Input:

Kj ; KMAX ; an; wj ; Z = Kj ∪fng; 1: for am 2 Kj do 2: if di wj then 3: ask to am its updated profile 4: end if 5: end for 6: if (V (v; gj ; an) == 0) then 7: Send a reject message to an 8: else 9: 10: 11: else 12: 13: 14: 15: if jZj KMAX then

Send an accept message to an for am 2 Z do

compute cgj famg;am end for

Let S = fs1; s2; : : : ; sKMAX +1g, with si 2 Z and cgj fsig cgj fskg iff i k if S[KMAX + 1] == an then

Send a reject message to an

A N L(n; k) !n;k n;k ^n;k n;k n;g g;n Nmax Kmax C1 C2 C3 Tg p1; p2; p3

Trust model The virtual community The number of agents of the community Weighting reliability vs reputation Weighting trust vs similarity in computing compactness Scaling factor for the local reputation Local network of an with respect to ak Local reputation of an in L(n; k).

Local trust of an about ak Global trust of the agent an about the agent ak Compactness on the agent an and ak Compactness on the agentan and group g Compactness on the group g and the agent an

Group formation Maximum number of agents a group is able to host Maximum number of groups a agent can join with Class of agents h 2 Class of agents 2 < h 3 Class of agents h > 3 Trust threshold for the voting mechanisms Probability that a agent of class Ci will join a group

TABLE I

SYMBOL TABLE B. The EGF algorithm running on the group agent.

In Figure 2-B is listed the EGF pseudocode running on the group manager side, where Kj is the set of the agents affiliated with the group gj belongs to and KMAX is the maximum number of agents to join with the group gj , with jjKj jj KMAX . Suppose that the group administrator a^gj stores the profile Pi of each agent ai and the timestamp di of its retrieval. Then, a^gj , fixed the time threshold wj , actives the procedure each time that an agent an sends a request to join with gj . In lines 1 5, a^gj asks the updated profile of the components of the group itself. By line 6 of the algorithm, a request is sent at all the agents belonging to the group gj to send their preferences (i.e., a vote) about the possible joining of an with the group gj by adopting the strategy specified in the previous section. After the voting, different choices exist, namely: if the agents of gj voted to refuse an in their group, then the procedure ends with an out by the group gj (line 7); if the agents of gj voted to accept an in their group; if the number of agents already present in gj is less than KMAX then an is accepted into gj , otherwise an is not accepted into gj (line 8 10); if the agents of gj voted to accept an in their group and the number of agents into the group is already equal to KMAX then for an and all the agents belonging to the group is updated the value of their compactness (lines 12 14) then for the agent (denoted by m) having the worst value of the compactness c (line 16): – if m is the same agent an then it is not admitted into gj (line 17); – if m is not the agent an, then an will take the place of m into gj (lines 19 and 20).

V. EXPERIMENTS The results of some tests on the EGF algorithm are shown in this section. To this aim, a publicly available

0.1 0.2 0.3 0.4 0.5 0.6 dataset extracted from the social network CIAO [ 8 ] has been used. It stores data of reviewed items, referred to 12; 375 users, about user-item ratings and user-trust relationships stored into the matrices EM and T M . In particular, each EM row consists of ⟨userI D; productI D; categoryI D; rating; helpf ulness; timestamp⟩ data, where the first three terms identify a user, the product category and the rated product itself, the fourth term is the rate (i.e., helpfulness) assigned to the review by the other members and, finally, the last term is the review publishing data (unused in these tests). Individual trust networks are built using the helpfulness values.

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 of social values. To this aim, CIAO members have been partitioned into three classes (C) characterized by the following helpfulness values C1 : h1 2, C2 : < h2 3 and C3 : h3 > 3, and defined the three scenarios described in Table II.

The results obtained by EGF, in term of the E10 index, for different , Nmax, and Kmax values are depicted in Figures 3, 4 and 5, where: i) Figure 3 shows the results for the three configurations for different values of , fixed Nmax = 10 and Kmax = 100; ii) Figure 4 shows the results for S1 and for different values of Nmax, fixed = 0:5 and Kmax = 100; iii) Figure 5 presents the results for S1 and for different values of Kmax, fixed = 0:5 and Nmax = 10.

In detail, Figures 3 highlights that for > 0:3 the E10 value decreases, i.e. a greater relevance of reliability with respect to reputation in forming groups. Moreover, the EFG performance for the configurations S2 and S3 decreases with respect to S1 for a higher difficulty to obtain the desired configurations. The influence of Kmax and Nmax on E10 is not significant and this confirms the trend shown by the results obtained for S1. S 1

Fig. 5. Configuration S1 with Nmax = 10 and = 0:5

VI. CONCLUSIONS

Group formation in social communities requires the computation of the mutual trustworthiness among their members on the basis of their reputation, a form of social information provided by the community. We observed that the effectiveness of a group depends on the capability of its members to satisfy mutual expectancies. Then, we proposed an index called Ek in order to measure the groups effectiveness with respect to both the desired composition computed and a specific objective. We also proposed a distributed algorithm to form groups in virtual communities by improving the effectiveness of the group formation activity in terms of E10 index by a weighted voting mechanism, where each vote is based on a combination of reliability and local reputation. The approach has been tested on real data extracted by the social network CIAO.

ACKNOWLEDGMENT

This study has been supported by NeCS Laboratory (DICEAM, University Mediterranea of Reggio Calabria).

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