Effectveness of Informaton on Cndy Hu, Malk Magdon-Ismal, Mark Goldberg and Wllam A. Wallace Department of Industral and Systems Engneerng Rensselaer Polytechnc Insttute Troy, New York Emal: huc@rp.edu, wallaw@rp.edu Department of Computer Scence Rensselaer Polytechnc Insttute Troy, New York Emal: magdon@cs.rp.edu, goldberg@cs.rp.edu Abstract In ths work, we study the effectveness of nformaton retracton n stuatons where nformaton beng spread requres recpents to make a decson or take an acton. Consder the scenaro where nformaton s ntroduced nto a network, advsng recpents to take an acton. If at a later tme, the nformaton s found to be naccurate and the acton s unnecessary, t becomes a concern to cease the nformaton from spreadng any further and stop people from takng the acton. The spread of naccurate nformaton can lead to confuson and mstrust, and therefore t s mportant to be able to quckly mpede or retract naccurate nformaton, f needed to at a later tme. We nvestgate the dea of ntroducng counter messages nto a network to nterfere wth an ongong dffuson and stop the acton that was prescrbed by the prevous messages. These counter messages are dffusve themselves and may spread through the network based on the recpent s evaluaton of the nformaton. We present an emprcal framework for modelng the spread of actonable nformaton and nformaton retracton. Usng the framework, we perform prelmnary experments to nvestgate strateges for broadcastng the counter message, n partcular, how to dentfy ndvduals that should receve the counter message drectly from the nformaton source. There s a trade off between a fast effectve spread of actonable nformaton and the ablty to retract the nformaton. Fndngs also suggest that alternate strateges wll have to be explored to ncorporate group structures and the dstrbuton of trust n desgnng a useful abort mechansm. Index Terms agent-based smulaton, nformaton dffuson, nformaton retracton, socal networks I. INTRODUCTION Consder the scenaro where nformaton s ntroduced nto a network, advsng recpents to take an acton. If at a later tme, the nformaton s found to be naccurate and the acton s unnecessary, t becomes a concern to cease the nformaton from spreadng any further and stop people from takng the acton. The spread of naccurate nformaton can lead to confuson and mstrust, and therefore t s mportant to be able to quckly mpede or retract naccurate nformaton, f needed to at a later tme. We nvestgate the dea of ntroducng counter messages nto a network to nterfere wth an ongong dffuson and stop the acton that was prescrbed by the prevous messages. These counter messages are dffusve themselves and may spread through the network based on the recpent s evaluaton of the nformaton. The nterest of ths study s to compare the spread of the actonable nformaton wth the spread of the counter messages. We present an emprcal framework for modelng the spread of actonable nformaton and counter messages. The nature n whch peces of nformaton spread and how ndvduals evaluate the nformaton would depend on the characterstcs of the nformaton and the understandng of the context. II. RELATED WORK Whether the case s to prevent dsease spreads, protect computer networks from vruses, or control the spread of bad gossp or nformaton, a common goal s to acheve the best possble mmunzaton effect wth the mnmum amount of necessary resources. The assumpton s that resources, e.g. vaccnaton, ant-vrus software, advertsement target, can be costly and lmted. Much lterature looks at mmunzaton strateges for epdemcs on socal networks as well as vruses on computer networks. In both contexts, there s a vrus or dsease s beng spread n a network and the mmunzaton strategy s mnmze the spread of the vrus or dsease by mmunzng certan nodes n the network. Immunzaton strateges focus on selectng whch nodes to mmune, to prevent the spread of dsease n varous complex network structures. The selecton of nodes to vaccnate are often determned from a statc network structure and s often done before the vrus or dsease spread occurs [], [2], [3]. Some research also consdered the case where the mmunzaton and the vrus or dsease spread through the network concurrently [4], [5]. Related research have also looked at ths problem as the spread of competng nformaton n networks, where there s a good campagn (mmunzaton) and a bad campagn (vrus). Budak et al. [6] nvestgated the problem of lmtng the spread of msnformaton by fndng optmal methods for dssemnatng good nformaton. The authors looked at dentfyng a subset of ndvduals n the network that needs to be convnced to adopt a good nformaton campagn so that the number of ndvduals that adopt the bad nformaton campagn s mnmzed.
III. EXPERIMENTAL FRAMEWORK Frst, we descrbe a dffuson framework for smulatng the spread of actonable nformaton and counter messages through a network. The purpose of the counter message s to nterfere wth an ongong dffuson and to stop the acton that was prescrbed earler. To avod confuson, the message beng dffused wll be referred to as the Acton message. The acton assocated wth the Acton message s to spread the nformaton and leave the network after a perod of tme,.e. ndvdual may remove themselves from the network. The counter message wll be referred to as the Abort message. The acton assocated wth the Abort message s to not leave the network. A. Dffuson model The dffuson model defnes how nformaton flows through the socal network and how ndvdual nodes process the nformaton from ncomng messages and determne ther behavors. The messages are ntroduced through external source nodes. Each message s classfed nto one of two types: Acton or Abort and s characterzed by a source-value par (S, V ), whch specfes the orgnal source and a correspondng nformaton value. The messages are propagated when nodes nteract and the nformaton value of the message may change as t s pass from node to node. When the message s passed from a sender to a recpent, the nformaton value of the message at the recpent s a functon of the socal relatonshp between the sender the recpent. We model ths by placng a trust weght on the edge whch defnes the lkelhood that a message wll be beleved as t s passed from one node to another. ) Informaton propagaton: If (S, V ) s a source-value par at node a whch s propagated to node b then the source-value par at node b s (S, α(a, b) V ), where α(a, b) < s the propagaton loss from a to b, quantfed by the socal relatonshp between nodes a and b. Each node has an Acton set and an Abort set. The Acton set contans the source-value pars (S, V )... for messages relatng to message type Acton whle the Abort set stores the messages (S, V )... relatng to Abort. At the end of each tme step, each node wll merge all of the nformaton they receved and update ther propertes based on the fused nformaton value. The process n whch nformaton s fused s descrbed by the followng steps. 2) Informaton fuson: The frst step s to combne the nformaton values of messages that orgnated from the same source. For each message type, when the same source appears n multple messages, the combned nformaton value for that source at the recever node s at least the maxmum of the nformaton values for the source over all the messages and at most the sum of all the nformaton values of the source. The next step s to combne the fused nformaton value at the node for each type of message,.e. the Acton messages n the Acton set are fused nto one value, Acton fused and the Abort messages n the Abort set are fused nto one value, Abort f used. For each type of message, we combne the nformaton values from each source by takng a weghted convex combnaton of the sum and maxmum of the values accordng to a parameter λ, where λ [, ]. Suppose that node k has source-value pars (S k, V k ), (S k 2, V k 2 ),... for message type Acton and (S k, V k ), (S2 k, V2 k ),... for message type Abort then the fused nformaton value at node k s computed as follows: Acton fused k = λ. Smlarly, V k + ( λ) max V k () Abort fused k = λ (V k ) + ( λ ) max(v k ) (2). The last step s to merge the fused values of the Acton messages wth the fused values of the Abort messages to determne a total fused value. For any node k, we compute the nformaton fused value fused k by takng the dfference between ts Acton message fused value and ts Abort fused value. fused k = Acton fused k Abort fused k, fused k R (3) 3) Node states and behavor: After computng the fused nformaton value, the node wll determne ts state and behavor based on whether the nformaton value exceeds certan thresholds. Intally, all the nodes are Unnformed. When nodes become exposed to nformaton, they can enter nto one of three states: Dsbeleved, Undecded, or Beleved. Each node has two thresholds, a lower bound LB and an upper bound UB such that LB UB (4) Dependng on whch threshold ts fused nformaton value exceeds, the node would undertake a state change: If fused k > UB, then the node wll enter Beleved state. If LB < fused k < UB, then node wll enter Undecded state. If fused k < LB, then node wll enter Dsbeleved state. Each node state has a correspondng behavor as descrbed n Table I. Snce Abort nformaton s also dffusve, t s possble for a Dsbeleved node to take the acton of propagatng Abort nformaton. We ntroduce a σ threshold, where σ <= LB, that determnes whether the Dsbeleved node wll perform such an acton. If Acton fused Abort fused <= σ, then the node wll spread Abort nformaton. Otherwse, the node wll exhbt no acton. If σ =, then the node would requre that ts Abort fused value to be at least as large as the Acton fused value, n order to spread the Abort nformaton. If σ <, then the node wll need more Abort nformaton than Acton nformaton before t s wllng to propagate the nformaton. If < σ <= LB, then the node s more eager to spread the Abort nformaton. In addton to spreadng nformaton, nodes may also seek nformaton. A node n Undecded state wll query ts neghbors n the network for addtonal nformaton. Snce there
State Descrpton Behavor Unnformed Node has not receved any messages No acton Dsbeleved Node has receved an Acton message but does not No acton beleve the message Dsbeleved Node has receved an Abort message and possbly an If fused k < σ then spread Abort message to ts Acton message neghbors, else no acton Undecded Node has receved an Acton message, or receved Query neghbors n the network both Acton and Abort messages, and s uncertan of what to do Beleved Node has receved an Acton message, or receved both Acton and Abort messages, and beleves the Spread the Acton message to ts neghbors and s removed from the network after x tme steps value of the Acton message Removed Node s no longer n the network No acton TABLE I DESCRIPTION OF NODE STATES AND CORRESPONDING BEHAVIORS are two types of messages, t s necessary to defne what nformaton s requested when a node queres ther neghbors and what nformaton ther neghbors wll share. When the Undecded node queres for nformaton, they wll request for any pece of nformaton that s avalable from ther neghbors, regardless of ther own message sets. When the quered node receves a request for nformaton, they wll determne what messages to share based on ther node state and send the message set wth some probablty p. If the quered node s Unnformed, then nothng s sent or receved Dsbeleved, then only Abort set s sent Undecded, then both Acton set and Abort set are sent Beleved, then only the Acton set Removed, then nothng s sent or receved. B. Prelmnary experments The followng experments looks at the the effect of the followng parameters on the effectveness of the abort dffuson. ) Seed selecton for broadcastng Abort nformaton, and 2) Dstrbuton of trust values on the edges n the network. In these set of experments, there are two sources of Acton nformaton and two sources of Abort nformaton. The followng assumptons are made. The ntal broadcast of Acton messages reaches s = 2, seed nodes. The subsequent broadcast of Abort messages also reaches s = 2, seed nodes. The seeds are dvded equally among the sources. The Acton and Abort messages from the sources wll reach all ther recpents wth probablty =..The nodes n the network have the same trust n the sources for both Acton nformaton and Abort nformaton and the nformaton value of Acton nformaton s the same as Abort nformaton,.e. same mportance. Unless otherwse specfed, the node parameters are lsted below. Informaton fuson parameters for Acton set and Abort set: λ =. and λ 2 = Nodes threshold (LB =, UB = ) Edge probablty (p=5) Threshold for spreadng Abort nformaton: sgma =. Tme steps between enterng Beleved state and Removed state (5) Tme steps for spreadng Abort () When a node enters Beleved state, t wll contact ther neghborng nodes and try to spread the Acton nformaton for 5 tme steps. If they reman n Beleved state for the entre duraton, they wll then be removed from the network and enter Removed state. When the node s removed, all the ncomng and outgong edges from the node are removed as well. Note that t s possble for a Beleved node to receve Abort nformaton and change to an Undecded or Dsbeleved state. If ths occurs and the node enters Beleved state at a future tme step, the node wll once agan spread Acton nformaton for 5 tme steps. The experments smulate the dffuson process of Acton and Abort nformaton on a random group model network wth, nodes and densty.4. The random group model conssts of two groups of equal szes, where the edge probablty between nodes from dfferent groups s p d and the edge probablty between nodes from the same group s p s = 2 p d. IV. EXPERIMENTAL RESULTS AND DISCUSSION In analyzng the expermental results, we compare the followng the followng two cases. Frst, we smulate the spread of the Acton messages and record the proporton of nodes that, enter Removed state,.e. depart the network, for each network structure and model confguratons. Next, we smulate the spread of Acton messages followed by Abort messages and record the proporton of nodes that depart the network. We compare the two proportons to evaluate the effectveness of the spread of Abort nformaton. A. Seed selecton for broadcastng Abort nformaton One strategy s to perform a retracton where the Abort messages are delvered to the same set of nodes that ntally receved the Acton messages. In ths case, the Abort nformaton tres to catch up to the Acton nformaton to stop the spread. Another strategy s to select a dfferent set of nodes to propagate the Abort nformaton, ether randomly or targeted, e.g. hghest degree nodes. In these experments, the same number of nodes are selected for broadcastng Acton messages as well as Abort messages. Fgure shows the smulaton results usng varous seedng strateges for Acton and Abort nformaton on the group
Proporton of Evacuated Nodes Proporton Proporton of Evacuated of Evacuated Nodes Nodes. Acton_ Acton 2 3 4 5 6 7 8 9 Tme step Acton_Domnatng Abort message was Set broadcast Acton_Independent Acton Acton.. 2 3 4 5 6 7 8 9 Tme step Abort message was broadcast 2 3 4 5 6 7 8 9 Tme step Abort message was broadcast Proporton of Evacuated Nodes Proporton Proporton of Evacuated of Evacuated Nodes Nodes. Acton_ Acton 2 3 4 5 6 7 8 9 Tme step Abort Acton_K message center was broadcast Acton_Modfed Acton Acton.. 2 3 4 5 6 7 8 9 Tme step Abort message was broadcast 2 3 4 5 6 7 8 9 Tme step Abort message was broadcast Fg.. Smulaton results Group model network. Average trust of the network s. Trust n source s and the nformaton value of the messages s 5. model network. The red lne dsplays the proporton of evacuated nodes as the result of the dffuson of the Acton nformaton and serves as the benchmark for comparson for the presented seed selecton strateges. The results show that under these confguratons, a retracton s only effectve f the Abort messages are broadcast soon after the Acton nformaton. The trust n the nformaton source s relatvely hgh and the nformaton value of Acton messages s also hgh. Along wth the predefned node thresholds, the fused value of the nformaton at the seed node wll easly exceed the upper bound threshold and the selected seeds nodes would enter Beleved state upon recevng the Acton message broadcast drectly from the source and mmedately propagate the Acton nformaton. The Abort message becomes neffectve f t s delvered at tme step 7 or later. The more effectve the Acton dffuson s the more dffcult t s to retract the spread. In most of the cases, broadcastng the Abort nformaton after 2 tme steps s most effectve n mnmzng the number of evacuated nodes when the messages are sent to the set of nodes wth hghest degrees. However, when the Acton nformaton spreads from hghest degree nodes, sendng Abort nformaton s randomly selected nodes s more effectve n mmunzng the Acton messages. B. Dstrbuton of trust and Effects of Groups The followng experments looks at the effects of the dstrbuton of trust and groups n the model for the varous seedng strateges. The trust values between nodes are assgned dependng on the sender and recever s socal group membershp and the average trust of the network t avg s kept constant. Hgh trust s defned wth the value t hgh = t avg + ɛ and low trust wth value t low = t avg ɛ, where ɛ s the trust dfferental from the average trust t avg. Here, ɛ s equal to.5. The followng two scenaros are compared. In the frst scenaro, nodes have equal trust n each other. There are essentally no groups and no dfferences n trust between nodes,.e. ɛ = and t hgh = t low = t avg. In the second scenaro, edges connectng nodes who belong to the same group have wth a hgher trust value of t hgh and edges between nodes from dfferent groups have a lower trust value of t low. Proporton of Evacuated Nodes. Acton_ Equal trust 2 3 4 5 6 7 8 9 Tme step of Abort message broadcast Proporton of Evacuated Nodes Hgher trust n same group. 2 3 4 5 6 7 8 9 Tme step of Abort message broadcast Fg. 2. Smulaton results for the Group model network where the Acton messages are broadcast to hghest degree nodes. Average trust of the network was. Trust n source s 5 and the nformaton values of the Acton and Abort messages are 5 Proporton of Evacuated Nodes. Acton_ Equal trust 2 3 4 5 6 7 8 9 Tme step of Abort message broadcast Proporton of Evacuated Nodes Hgher trust n same group. 2 3 4 5 6 7 8 9 Tme step of Abort message broadcast Fg. 3. Smulaton results for the Group model network where the Acton messages are broadcast to hghest degree nodes. Average trust of the network was 5. Trust n source s and the nformaton values of the Acton and Abort messages are 5. We look at the effects of the dstrbuton of trust and groups n the model for two contexts. In the frst context, when the Acton message s propagated from the nformaton source, the fused value of the nformaton just about exceeds the node s upper bound threshold. The seed nodes wll enter Beleved state upon recevng the Acton nformaton drectly from the nformaton source. In the second context, seed nodes wll entered Undecded state upon recevng the Acton nformaton drectly from the nformaton sources. Smulaton results for the two contexts are shown n Fgures 2 and 3. The Acton nformaton s broadcast to the set of nodes wth hghest degrees. The green lne dsplays the results of the retracton, where Abort messages are broadcast to the same hghest degree nodes. The blue lne dsplays the case where Abort messages are broadcast to a random set of nodes. An nterestng observaton s that n these settngs, the retracton strategy for spreadng Abort nformaton s effectve n the equal trust scenaro but not as effectve n the hgher trust n same group scenaro. V. CONCLUSION AND FUTURE WORK The prelmnary experments presented some nterestng observatons. The Abort message should be sent out as soon as possble after the Acton message n order for the Abort nformaton to have any effect n the network. In addton, the Abort message must have characterstcs so that t wll dffuse more rapdly than the Acton message, e.g. hgh nformaton value. However, ths mples that there s a tradeoff between a
rapd spread of the Acton message and the possble need to Abort because of new nformaton. If the Acton nformaton spreads so effectvely through the network and changes the structure of the network,.e. large proportons of nodes are removed from the network, t would make an Abort stuaton very dffcult and possbly neffectve. The experments also showed that for the case of spreadng hgh valued nformaton from hgh trusted sources, retracton s only effectve f Abort messages are broadcast soon after the Acton nformaton. Afterwards, an alternatve strategy s needed for sendng Abort nformaton. Under other crcumstances, when the fused value of the nformaton only slghtly exceeds the node s threshold to act, retracton s stll a possble strategy n a network wth homogeneous trust. However, when we ntroduce trust dfferentals and groups, retracton s no longer a useful mechansm. Ths suggests that alternate strateges wll have to be explored to ncorporate trust varants and the dstrbuton of trust n desgnng a useful mechansm for spreadng Abort messages. ACKNOWLEDGMENT Ths materal s based upon work sponsored by the Army Research Laboratory and was accomplshed under Cooperatve Agreement Number W9NF-9-2-53. The vews and conclusons contaned n ths document are those of the authors and should not be nterpreted as representng the offcal polces, ether expressed or mpled, of the Army Research Laboratory or the U.S. Government. The U.S. Government s authorzed to reproduce and dstrbute reprnts for Government purposes notwthstandng any copyrght notaton here on. REFERENCES [] R. Cohen, S. Havln, and D. ben Avraham, Effcent mmunaton strateges for computer networks and populatons, Physcal Revew Letters, vol. 9, no. 24, 23. [2] Z. Dezső and A.-L. Barabás, Haltng vruses n scale-free networks, Phys. Rev. E, vol. 65, no. 5, p. 553, May 22. [3] R. Pastor-Satorras and A. Vespgnan, Immunzaton of complex networks, Phys. Rev. E, vol. 65, no. 3, p. 364, Feb 22. [4] L. Chen and K. Carley, The mpact of countermeasure propagaton on the prevalence of computer vruses, IEEE Trans. on Systems, Man, and Cybernetcs - Part B: Cybernetcs, vol. 34, no. 2, pp. 823 833, 24. [5] H.-H. Jo, H.-T. Moon, and S. K. Baek, Immunzaton dynamcs on a 2-layer network model, Physca A: Statstcal Mechancs and ts Applcatons, vol. 36, no. 2, pp. 534 542, March 26. [6] C. Budak, D. Agrawal, and A. E. Abbad, Lmtng the spread of msnformaton n socal networks, Department of Computer. Scence, UCSB, Tech. Rep., 2.