Trust Propagation Models in Social Networks

1. Propagation Models for Trust and Distrust in Social Networks C. Ziegler, G. Lausen, Information Systems Frontiers, Vol. 7, Issue 4/5, Springer Science + Business Media, Inc., 2005 석사 3 차 지 애 띠

2. Correlation between Trust & Similarity • Credibility and attack-resistance • Product-user matrix sparseness • Computational complexity & scalability

3. OUTLINE • INTRODUCTION • TRUST in SOCIAL NETWORKS • LOCAL GROUP TRUST METRICES • ADVOGATO vs. APPLESEED • PARAMETERIZATION & EXPERIMENTS • IMPELEMENTATION & EXTENTIONS • DISTRUST • DISCUSSION

4. INTRODUCTION • 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.

5. TRUST in SOCIAL NETWORKS • Classification of Trust Metrics • Network Perspective • Global scope –All peers based on complete trust graph information. • Local scope –Personal bias based on partial trust graph information. • Computation Locus • Local approaches • Centralized approaches • Link Evaluation • Scalar metrics analyze trust assertions independently, • Group metrics evaluate groups of assertions “ in tandem”.

6. TRUST in SOCIAL NETWORKS • Classification of Trust Metrics

7. TRUST in SOCIAL NETWORKS • Semantic of Web Trust • Most presented metrics and trust models have been proposed for scenario other than the Semantic 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 ranging 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.)

8. TRUST in SOCIAL NETWORKS • Semantic of Web Trust • Trust Model • Agent set V = {a1, …, an}, a ∈ V is represented and uniquely identified by the URI of their machine-readable personal homepages. • Partial trust function set T = {Wa1, …, Wan}. Every agent a associated with one partial trust function Wa : V  [0, 1]⊥. • The higher the value of Wai(aj), the more trustworthy ai deems aj.

9. TRUST in SOCIAL NETWORKS • 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

10. LOCAL GROUP TRUST METRICES • 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 boolean value indicating trustworthiness

11. Advogato maxflow • 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 level 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.

12. Advogato maxflow • Maximum integer network flow computation (convergence)

13. Advogato maxflow • Algorithm 1. Trust graph conversion functiontransform (G = (V, E, CV) ){ set E’  0, V’  0; for allx ∈ Vdo add node x+ to V’ ; add node x- to V’ ; ifCV(x) >= 1 then add edge (x-, x+ ) to E’ ; set CE’(x-, x+)  CV(x) – 1; for all(x, y) ∈ Edo 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 returnG’ = (V’, E’, CE’) ; }

14. Advogato maxflow • Convergence

15. Advogato maxflow • Example

16. LOCAL GROUP TRUST METRICES • 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 source s, the more paths leading from s to x, the higher energy flowing to x.

17. Appleseed Trust Metric • Algorithm 2. Recursive energy propagation procedureenergize (e∈R0+, s ∈V ){ energy(s)  energy(s) + e ; e’  e / ∑(s, n) ∈ EW(s, n) ; ife > Tthen all (s, n) ∈ E : energize (e’ ∙ W(s, n), n) ; end if }

18. Appleseed 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

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

20. Appleseed Trust Metric • Rank normalization • Serious interferences occur when edges are weighted.

21. Appleseed Trust Metric • Backward trust propagation • Additional “virtual” edges (x, s) from every 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,

22. Appleseed Trust Metric • 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

23. Appleseed Trust Metric • 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 computation 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.

24. Appleseed Trust Metric • Algorithm 3 Appleseed trust metric.

25. LOCAL GROUP TRUST METRICES • Comparison of advogato and appleseed • Advogato has already proven its efficiency in practical usage scenarios 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

26. PARAMETERIZATION & EXPERIMENTS • Web crawling of the Advogato community web site, extracting trust assertions stated by more than 8,000 members. • Four different levels of peer certification, “Observer”, “Apprentice”, “Journeyer”, “Master” are mapped each quantitative trust W(x, y). • Computed trust ranks may not be absolute value, just ranks. Trust injection 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 fewer node accesses. • Convergence rate is very fast no matter how huge the number of trust nodes, large the trust injection.

27. PARAMETERIZATION & EXPERIMENTS • Spreading factor impact

28. PARAMETERIZATION & EXPERIMENTS • Convergence of appleseed

29. PARAMETERIZATION & EXPERIMENTS • Algorithm 4 Adding weight alignment heuristics.

30. IMPLEMENTATION & EXTENTIONS • Appleseed was implemented in JAVA with an architectural cushion 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.

31. DISTRUST • 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

32. DISTRUST • Network impact of distrust

33. DISCUSSION • 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.