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INHA UNIVERSITYINCHEON, KOREA

http://eslab.inha.ac.kr

Propagation Models for Trust and DisPropagation Models for Trust and Distrust in Social Networkstrust in Social Networks

C. Ziegler, G. Lausen, Information Systems Frontiers, C. Ziegler, G. Lausen, Information Systems Frontiers, Vol. 7, Issue 4/5, Springer Science + Business Media, Inc., 2005 Vol. 7, Issue 4/5, Springer Science + Business Media, Inc., 2005

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Correlation between Trust & Correlation between Trust & Similarity Similarity

Credibility and attack-resistance Product-user matrix sparseness Computational complexity & scalability



OUTLINEOUTLINE

INTRODUCTION TRUST in SOCIAL NETWORKS LOCAL GROUP TRUST METRICES

• ADVOGATO vs. APPLESEED PARAMETERIZATION &

EXPERIMENTS IMPELEMENTATION & EXTENTIONS DISTRUST DISCUSSION



INTRODUCTIONINTRODUCTION

When supposing huge network, trust judgements based on personal experience and acquaintanceship become unfeasible.

Trust was defined by Mui as the “subjective expectation an agent has about another’s future behavior based on the history of their encounters.”(Mui,2002)

Trust metrics must take into account subtle social and psychological aspects of trust and suffice criteria of computability and scalability.



TRUST in SOCIAL NETWORKSTRUST in SOCIAL NETWORKS

Classification of Trust Metrics• Network Perspective

◦ Global scope – All peersAll peers based on completecomplete trust graph information.

◦ Local scope – Personal biasPersonal bias based on partialpartial trust graph information.

• Computation Locus◦ Local approaches ◦ Centralized approaches

• Link Evaluation◦ Scalar metrics analyze trust assertions independentlyindependently,◦ Group metrics evaluate groups of assertions “ in in

tandemtandem”.




Classification of Trust Metrics




Semantic of Web Trust• Most presented metrics and trust models have been propose

d for scenario other than the Semantic WebSemantic Web.• To define one common trust model,

◦ FOAF (“Friend of a Friend”) aims at enriching personal homepages with machine-readable content encoded in RDF statements and these pages allow their owners to nominate all individuals part of the FOAF universe.

(Dumbill, 2002)◦ Extended FOAF schema to contain trust assertions with value ra

nging from 1 (distrust) to 9 (trust) has been issued. (Golbeck, Parsia and Hendler, 2003)

◦ But they only capture the notation of trust and lack of trust, instead of trust and distrust. (Zero trust and distrust are not same.)




Semantic of Web Trust

• Trust Model◦ Agent set V = {a1, …, an}, a ∈ V is represented and uniquely iden

tified by the URI of their machine-readable personal homepages. ◦ Partial trust function set T = {Wa1, …, Wan}. Every agent a associa

ted with one partial trust function Wa : V [0, 1]⊥.

◦ The higher the value of Wai(aj), the more trustworthy ai deems aj.



Semantic of Web Trust

• Trust metrics for the semantic web

◦ Limitations of some distributed approaches Trust data storage Convergence

◦ Welcome properties of local group trust metrics Partial trust graph exploration Computational scalability




LOCAL GROUP TRUST LOCAL GROUP TRUST METRICESMETRICES

Advogato maxflow (Levien and Aiken,2000)

• To discover which users are trusted by members of an online community and which or not.

• Arbitrary agents compute personalized lists of trusted peers, not one single global ranking.

• Trust computation steps◦ Input : the number of members to trust n, the trust seed s, being

a subset of entire set of users V◦ Output : a characteristic function that maps each member to a b

oolean value indicating trustworthiness



Maximum integer network flow computation (Ford and Fulkerson,1962)

• Capacities CV:V N are assigned to every community members x ∈ V based upon the shortest-path distance from the seed to x.

• The capacity of seed is given by the input n.• The capacity of each successive level is equal to that of previous le

vel l divided by the average outdegree of edges from l.• The old directed graph G = (V, E, CV) is converted to G’ = (V’, E’, CE’)

as single-source/single sink formulation.

Advogato maxflowAdvogato maxflow



Maximum integer network flow computation (convergence)




Algorithm 1. Trust graph conversion function transform (G = (V, E, CV) ){ set E’ 0, V’ 0; for all x ∈ V do

add node x+ to V’ ; add node x- to V’ ; if CV(x) >= 1 then add edge (x-, x+ ) to E’ ; set CE’(x-, x+) CV(x) – 1; for all (x, y) ∈ E do add edge (x-, x+) to E’ ; set CE’(x-, x+) ∞; end do add edge (x-, supersink) to E’ ; set CE’(x-, supersink) 1; end if end do return G’ = (V’, E’, CE’) ; }




Convergence





Example



LOCAL GROUP TRUST LOCAL GROUP TRUST METRICESMETRICES Appleseed Trust Metric

• Being inspired by maximum network flow computation, Appleseed is motivated by spreading activation model(Quillian,1968).

• Searches in contextual network graphs◦ Edges (x, y) ∈ E ⊆ V ⅹ V (x, y ∈ V)◦ Continuous weight W : E [0,1]◦ Source node s is activated through an injection of energy e◦ e is then propagated to other nodes along edges◦ All energy is fully divided among successor nodes wrt. their local

edge weight.◦ Supposing average outdegrees >= 1, the closer node x to the s

ource s, the more paths leading from s to x, the higher energy flowing to x.



Algorithm 2. Recursive energy propagation

procedure energize (e∈R0+, s ∈V ){ energy(s) energy(s) + e ;

e’ e / ∑(s, n) ∈ E W(s, n) ;

if e > T then all (s, n) ∈ E : energize (e’ W∙ (s, n), n) ; end if }

Appleseed Trust MetricAppleseed Trust Metric



Trust propagation• Node chains

◦ Trust decay : people tend to trust individuals trusted by immediate friends more than ones trusted by friends of friends.

• Rank sinks : Infinite trust rank




Spreading factor• in(x) : energy influx into node x.• d : global spreading factor• Energy d in(x)∙ is distributed among the successors, while r

etaining (1-d) in(x)∙ for itself.• For instance, d = 0.85, in(x) = 5.0 energy(x) = 0.75, total

energy distributed to successor 4.25• Suppose that energy(n) =0 for all n ∈ V before injection in0 in

to source s. ∑x∈V energy(x) = in0

• d may also be seen as the ratio between direct trust in x and trust in the ability of x to recommend others as trustworthy peers.




Rank normalization

• Serious interferences occur when edges are weighted.





Backward trust propagation• Additional “virtual” edges (x, s) from ever

y node x ∈ V ＼ {s} to the source s, which are assigned full trust W(x, s)=1, are created.

every node is blindly trust the trust source s.

trust weight “overwritten”

Nonlinear trust normalization • Situations where nodes y with poor ratings from x are awarded high trust ranks, thanks to low outdegree of x,



Algorithm outline

• Input : trust seed s, trust injection e, spreading factor d ∈ [0, 1], accuracy threshold Tc

• Output : rankings of agents wrt. the trust.• Nodes are accessed only when reached by energy flow.• Trust(x), energy(x) are initialized to 0. • Virtual trust edges are added when x is discovered.• In every iteration, the amount of incoming trust is




Algorithm outline• The trust rank of x is updated as follows : trust(x) trust(x) + (1 - d) in(x)∙• Trust network generally contain cycles, hence the computatio

n of in(x) is inherently recursive. A criterion that has to be satisfied for convergence, relying on accuracy threshold Tc, is needed.

◦ Vi ⊆ V : set of nodes that were discovered until step i

◦ trusti(x) : current trust ranks of x for all x ∈ V◦ ∀x ∈ Vi : trusti(x) – trusti-1(x) ≤ Tc

◦ When supposing d > 0, Tc > 0, trust source s part of connected component G’ ⊆ G containing at least two nodes, convergence and termination are guaranteed.





Algorithm 3 Appleseed trust metric.



Comparison of advogato and appleseed• Advogato has already proven its efficiency in practical usage sc

enarios such as the Advogato online community.• Attack resistance

◦ “bottleneck property”,“on the part of bad nodes does not affect the trust value”.

• Trust weight normalization ◦ Advogato encourages agents issuing numerous trust statements,

while Appleseed penalizes overly abundant trust certificates..• Deterministic trust computation

◦ Linear equations allow to characterize the amount of trust assigned to x, as well as the quantity that x accords to its successor nodes.

• Model and output type

LOCAL GROUP TRUST LOCAL GROUP TRUST METRICESMETRICES



PARAMETERIZATION & PARAMETERIZATION & EXPERIMENTSEXPERIMENTS Web crawling of the Advogato community web site, extracting trust asse

rtions stated by more than 8,000 members. Four different levels of peer certification, “Observer”, “Apprentice”, “Jour

neyer”, “Master” are mapped each quantitative trust W(x, y). Computed trust ranks may not be absolute value, just ranks. Trust injec

tion in0 for alignment,

Alignment heuristics - add indicator node i with W(s, i)=1 to tell whether trust injection in0 is “good” or not.

Spreading factor - generally d = 0.85 Accuracy threshold - Tc = 0.01, to make the algorithm terminate after fe

wer node accesses. Convergence rate is very fast no matter how huge the number of trust n

odes, large the trust injection.



PARAMETERIZATION & PARAMETERIZATION & EXPERIMENTSEXPERIMENTS Spreading factor impact



PARAMETERIZATION & PARAMETERIZATION & EXPERIMENTSEXPERIMENTS Convergence of appleseed



PARAMETERIZATION & PARAMETERIZATION & EXPERIMENTSEXPERIMENTS Algorithm 4 Adding weight alignment heuristics.



IMPLEMENTATION & IMPLEMENTATION & EXTENTIONSEXTENTIONS Appleseed was implemented in JAVA with an architectural cushio

n to access “real” RDF homepages. Testbed for local group trust metrics.

• Humans must be able to comprehend why agent a was accorded higher trust rank than b and come to similar results when asked for a personal judgement.

• yFiles library to perform all sophisticated graph drawing.



DISTRUSTDISTRUST

Semantic of distrust• Distrust as negated trust – serious implications resulting from assuming

that trust multiplication and distrust to negated trust. ¬ trust (a, b) ∧ ¬ trust (b, c) trust (a, c)• Propagation of trust Distrust (a, b) ∧ trust (b, c) distrust (a, c)• Incorporating distrust into appleseed



DISTRUSTDISTRUST

Network impact of distrust



DISCUSSIONDISCUSSION

Appleseed can suit other application scenarios, such as group trust in online communities, open rating systems, and ad-hoc and p2p network.

Trust relationships by means of heuristics, an actual policy for eventual boolean decision-taking wrt. Which agents to grant trust and which to deny.

Local group trust metrics will become subject to substantial research for diverse computing domains within the near future.

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