Propagation of Trust and Distrust Antti Sorjamaa Propagation of Trust and Distrust R. Guha, R. Kumar, P. Raghavan and A. Tomkins New York, 2004 Antti Sorjamaa

Propagation of Propagation of Trust and DistrustTrust and Distrust

R. Guha, R. Kumar, P. Raghavan and A. Tomkins

New York, 2004

Antti SorjamaaAntti Sorjamaa

Time Series Prediction and ChemoInformatics Time Series Prediction and ChemoInformatics GroupGroupAdaptive Informatics Research CentreAdaptive Informatics Research CentreHelsinki University of TechnologyHelsinki University of Technology

OutlineOutline

BackgroundBackground AlgorithmsAlgorithms

– Atomic propagationAtomic propagation– Propagation methodsPropagation methods– RoundingRounding– Transitivity issuesTransitivity issues

Experimental resultsExperimental results

Antti Sorjamaa - TSPCi - AIRC - HUTAntti Sorjamaa - TSPCi - AIRC - HUT 22/27/27

BackgroundBackground

Trust Trust Valid information Valid information Distrust Distrust Disinformation or no Disinformation or no

informationinformation Increasing flow of information makes it Increasing flow of information makes it

necessary to validate the informationnecessary to validate the information Opinion of a single user is always Opinion of a single user is always

right, but is it trustworthy?right, but is it trustworthy? eBay, Epinions, huuto.net, etc.eBay, Epinions, huuto.net, etc.


Background (2)Background (2)

Problems of disinformationProblems of disinformation– Stock manipulation by bogus Stock manipulation by bogus

postings on investment boardspostings on investment boards– Marketers posing as customersMarketers posing as customers– Search engine link spammingSearch engine link spamming– Online relationships, datingOnline relationships, dating

Web of TrustWeb of Trust– Does not apply directly to DistrustDoes not apply directly to Distrust


Origin of TrustOrigin of Trust

Collect opinions of several usersCollect opinions of several users– One user can use several accountsOne user can use several accounts– Group of users agree and perform Group of users agree and perform

spoofingspoofing IRL Trust is built and maintained over IRL Trust is built and maintained over

long time periodslong time periods– Trust relationshipsTrust relationships– Good basis for the propagation of TrustGood basis for the propagation of Trust– More individual view of the Web of TrustMore individual view of the Web of Trust


Problems of DistrustProblems of Distrust

””Negative Trust”Negative Trust” Shifting the already existing Trust Shifting the already existing Trust

scores distort the resultsscores distort the results Algorithmic complicationsAlgorithmic complications

– Negative eigenvaluesNegative eigenvalues– Negative probabilitiesNegative probabilities

What is Distrust propagation?What is Distrust propagation?


NotationNotation

Antti Sorjamaa - TSPCi - AIRC - HUTAntti Sorjamaa - TSPCi - AIRC - HUT

nn = number of users = number of users

T = Trust matrix, T = Trust matrix, nn x x nn, values from 0 to 1, values from 0 to 1

D = Distrust matrix, as Trust matrixD = Distrust matrix, as Trust matrix

B = Beliefs matrix, typically T or T - DB = Beliefs matrix, typically T or T - D

CCB,B,αα = Combined atomic propagation matrix= Combined atomic propagation matrix

PP((k k ) ) = Propagation matrix using = Propagation matrix using kk steps steps

F = Final beliefsF = Final beliefs

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Atomic PropagationAtomic Propagation

Basic propagation techniques, Basic propagation techniques, ”atoms””atoms”

Matrix operations, multiplying B with Matrix operations, multiplying B with appropriate matrix operatorappropriate matrix operator

4 basic atoms4 basic atoms– Direct PropagationDirect Propagation– Co-citationCo-citation– Transpose TrustTranspose Trust– Trust couplingTrust coupling


1 2 3

4

1 2

35

Atomic Propagation (2)Atomic Propagation (2)

Direct Propagation, BDirect Propagation, B Co-citation, BCo-citation, BTTBB Transpose Trust, BTranspose Trust, BTT

Trust coupling, BBTrust coupling, BBTT


1 2 3

0 1 0

0 0 0,7

0 0 0

0 1 0

0 0 0,7

0 0 0=

0 0 0,7

0 0 0

0 0 0

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4

1

35

Trust Coupling, BBTrust Coupling, BBTT


0 0 0 1 0

0 0 0 0 0

0 0 0 1 0

0 0 0 0 0

0 0 1 0 0

=

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 1 0

0 0 0 1 0

0 0 0 0 0

0 0 0 1 0

0 0 0 0 0

0 0 1 0 0

=

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 1 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 1

1 0 1 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

1 0 1 0 0

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Atomic Propagation (3)Atomic Propagation (3)

Direct Propagation, BDirect Propagation, B Co-citation, BCo-citation, BTTBB Transpose Trust, BTranspose Trust, BTT

Trust coupling, BBTrust coupling, BBTT


NotationNotation


nn = number of users = number of users

T = Trust matrix, T = Trust matrix, nn x x nn, values from 0 to 1, values from 0 to 1

D = Distrust matrix, as Trust matrixD = Distrust matrix, as Trust matrix

B = Beliefs matrix, typically T or T - DB = Beliefs matrix, typically T or T - D

CCB,B,αα = Combined atomic propagation matrix= Combined atomic propagation matrix

PP((k k ) ) = Propagation matrix using = Propagation matrix using kk steps steps

F = Final beliefsF = Final beliefs

1212/27/27

Propagation MethodsPropagation Methods

Trust only: B = TTrust only: B = T

One-step Distrust: B = TOne-step Distrust: B = T

Propagated Distrust: B = T - DPropagated Distrust: B = T - D


Iterative PropagationIterative Propagation

Eigenvalue PropagationEigenvalue Propagation

Weighted Linear Combinations Weighted Linear Combinations (WLC)(WLC)


RoundingRounding

Binary decision of Trust (±1)Binary decision of Trust (±1)– Global RoundingGlobal Rounding

Order F according to Trust valuesOrder F according to Trust values Fraction of Trust in the whole FFraction of Trust in the whole F

– Local RoundingLocal Rounding Order F according to Trust valuesOrder F according to Trust values Fraction of Trust in the corrent row of FFraction of Trust in the corrent row of F

– Majority RoundingMajority Rounding Smallest local well-defined neighborhoodSmallest local well-defined neighborhood


0 1 0

0 0 0,7

0 0 0

0 -1 0

0 0 -0,7

0 0 0

TransitivityTransitivity

Direct Propagation of TrustDirect Propagation of Trust– If 1 trusts 2 and 2 trusts 3 then 1 trusts 3If 1 trusts 2 and 2 trusts 3 then 1 trusts 3

Does not apply to Distrust directlyDoes not apply to Distrust directly

””Enemy of my enemy is my friend”Enemy of my enemy is my friend”

Multiplicative Trust PropagationMultiplicative Trust Propagation


=

0 -1 0

0 0 -0,7

0 0 0

0 0 0,7

0 0 0

0 0 0

1616/27/27

Transitivity (2)Transitivity (2)

Multiplicative Distrust creates problemsMultiplicative Distrust creates problems– As seen on previous slide:As seen on previous slide:

””Enemy of my enemy is my friend”Enemy of my enemy is my friend”– Directed cycle with negative values can Directed cycle with negative values can

lead to the user to distrust himself!lead to the user to distrust himself! Additive Distrust PropagationAdditive Distrust Propagation

– Transform the basic propagation atomTransform the basic propagation atom

– For example exp(bFor example exp(bijij) ) b bijij


Experimental ResultsExperimental Results

Epinions dataset from Epinions.comEpinions dataset from Epinions.com Users write and read reviews from Users write and read reviews from

many different topicsmany different topics Users can also rate the reviews and Users can also rate the reviews and

other reviewersother reviewers Review reading creates royaltiesReview reading creates royalties

– Distrust system to decrease abuseDistrust system to decrease abuse Similar systems: Amazon, SlashdotSimilar systems: Amazon, Slashdot


Epinions DatasetEpinions Dataset

131 829 nodes with 841 372 edges131 829 nodes with 841 372 edges Edges either Trust (+1) or Distrust (-1)Edges either Trust (+1) or Distrust (-1) 85 percent of edges are Trust edges85 percent of edges are Trust edges Large Strongly Connected Component Large Strongly Connected Component

(SCC) of over 41 000 nodes(SCC) of over 41 000 nodes Bowtie: In almost 40 000 nodes and Bowtie: In almost 40 000 nodes and

out more than 30 000 nodesout more than 30 000 nodes


MethodologyMethodology

Propagation of DistrustPropagation of Distrust– Trust, One-step and Propagated DistrustTrust, One-step and Propagated Distrust

Iteration Methods: EIG and WLCIteration Methods: EIG and WLC Rounding: Global, Local and MajorityRounding: Global, Local and Majority Atomic Propagations:Atomic Propagations:

– Direct, Co-sitation and all combinedDirect, Co-sitation and all combined

81 different combinations81 different combinations


ExperimentsExperiments

Each combination of methods get the Each combination of methods get the same treatmentsame treatment

Validation using Leave-One-Out (LOO)Validation using Leave-One-Out (LOO)– Total of 3250 random edgesTotal of 3250 random edges

prediction error prediction error εε– About 500 Distrust and 500 Trust edgesAbout 500 Distrust and 500 Trust edges

prediction error prediction error εεSS

Naive errors: Naive errors: εε = 0,15 and = 0,15 and εεSS = 0,5 = 0,5


2222/27/27Antti Sorjamaa - TSPCi - AIRC - HUTAntti Sorjamaa - TSPCi - AIRC - HUT

ResultsResults

Results (2)Results (2)






ConclusionsConclusions

Web of Trust and Distrust is important Web of Trust and Distrust is important part of many e-commerce related part of many e-commerce related sitessites– Distrust stabilizes the propagation of Distrust stabilizes the propagation of

opinions in the networkopinions in the network– Distrust decreases the effect of abuseDistrust decreases the effect of abuse

Rounding is surprisingly importantRounding is surprisingly important Small number of expressed Trust Small number of expressed Trust

scores lead to accurate predictionscores lead to accurate prediction


2727/27/27

Questions?Questions?

[email protected]://www.cis.hut.fi/projects/tsp

Documents

Propagation of Trust and Distrust Antti Sorjamaa Propagation of Trust and Distrust R. Guha, R. Kumar, P. Raghavan and A. Tomkins New York, 2004 Antti Sorjamaa