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 Time Series Prediction and ChemoInformatics Group Adaptive Informatics Research Centre Helsinki University of Technology

Outline Background Background Algorithms Algorithms –Atomic propagation –Propagation methods –Rounding –Transitivity issues Experimental results Experimental results Antti Sorjamaa - TSPCi - AIRC - HUT2/27

Background Trust  Valid information Trust  Valid information Distrust  Disinformation or no information Distrust  Disinformation or no information Increasing flow of information makes it necessary to validate the information Increasing flow of information makes it necessary to validate the information Opinion of a single user is always right, but is it trustworthy? Opinion of a single user is always right, but is it trustworthy? eBay, Epinions, huuto.net, etc. eBay, Epinions, huuto.net, etc. Antti Sorjamaa - TSPCi - AIRC - HUT3/27

Background (2) Problems of disinformation Problems of disinformation –Stock manipulation by bogus postings on investment boards –Marketers posing as customers –Search engine link spamming –Online relationships, dating Web of Trust Web of Trust –Does not apply directly to Distrust Antti Sorjamaa - TSPCi - AIRC - HUT4/27

Origin of Trust Collect opinions of several users Collect opinions of several users –One user can use several accounts –Group of users agree and perform spoofing IRL Trust is built and maintained over long time periods IRL Trust is built and maintained over long time periods –Trust relationships –Good basis for the propagation of Trust –More individual view of the Web of Trust Antti Sorjamaa - TSPCi - AIRC - HUT5/27

Problems of Distrust ”Negative Trust” ”Negative Trust” Shifting the already existing Trust scores distort the results Shifting the already existing Trust scores distort the results Algorithmic complications Algorithmic complications –Negative eigenvalues –Negative probabilities What is Distrust propagation? What is Distrust propagation? Antti Sorjamaa - TSPCi - AIRC - HUT6/27

Notation Antti Sorjamaa - TSPCi - AIRC - HUT n = number of users T = Trust matrix, n x n, values from 0 to 1 D = Distrust matrix, as Trust matrix B = Beliefs matrix, typically T or T - D C B, α = Combined atomic propagation matrix P (k ) = Propagation matrix using k steps F = Final beliefs 7/27

Atomic Propagation Basic propagation techniques, ”atoms” Basic propagation techniques, ”atoms” Matrix operations, multiplying B with appropriate matrix operator Matrix operations, multiplying B with appropriate matrix operator 4 basic atoms 4 basic atoms –Direct Propagation –Co-citation –Transpose Trust –Trust coupling Antti Sorjamaa - TSPCi - AIRC - HUT

Atomic Propagation (2) Direct Propagation, B Direct Propagation, B Co-citation, B T B Co-citation, B T B Transpose Trust, B T Transpose Trust, B T Trust coupling, BB T Trust coupling, BB T Antti Sorjamaa - TSPCi - AIRC - HUT , = /27

Trust Coupling, BB T Antti Sorjamaa - TSPCi - AIRC - HUT = = /27

Atomic Propagation (3) Direct Propagation, B Direct Propagation, B Co-citation, B T B Co-citation, B T B Transpose Trust, B T Transpose Trust, B T Trust coupling, BB T Trust coupling, BB T Antti Sorjamaa - TSPCi - AIRC - HUT11/27

Notation Antti Sorjamaa - TSPCi - AIRC - HUT n = number of users T = Trust matrix, n x n, values from 0 to 1 D = Distrust matrix, as Trust matrix B = Beliefs matrix, typically T or T - D C B, α = Combined atomic propagation matrix P (k ) = Propagation matrix using k steps F = Final beliefs 12/27

Propagation Methods Trust only: B = T Trust only: B = T One-step Distrust: B = T One-step Distrust: B = T Propagated Distrust: B = T - D Propagated Distrust: B = T - D Antti Sorjamaa - TSPCi - AIRC - HUT13/27

Iterative Propagation Eigenvalue Propagation Eigenvalue Propagation Weighted Linear Combinations (WLC) Weighted Linear Combinations (WLC) Antti Sorjamaa - TSPCi - AIRC - HUT14/27

Rounding Binary decision of Trust (±1) Binary decision of Trust (±1) –Global Rounding Order F according to Trust values Order F according to Trust values Fraction of Trust in the whole F Fraction of Trust in the whole F –Local Rounding Order F according to Trust values Order F according to Trust values Fraction of Trust in the corrent row of F Fraction of Trust in the corrent row of F –Majority Rounding Smallest local well-defined neighborhood Smallest local well-defined neighborhood Antti Sorjamaa - TSPCi - AIRC - HUT15/27

, ,7 000 Transitivity Direct Propagation of Trust Direct Propagation of Trust –If 1 trusts 2 and 2 trusts 3 then 1 trusts 3 Does not apply to Distrust directly Does not apply to Distrust directly ”Enemy of my enemy is my friend”  Multiplicative Trust Propagation Antti Sorjamaa - TSPCi - AIRC - HUT = , , /27

Transitivity (2) Multiplicative Distrust creates problems Multiplicative Distrust creates problems –As seen on previous slide: ”Enemy of my enemy is my friend” –Directed cycle with negative values can lead to the user to distrust himself! Additive Distrust Propagation Additive Distrust Propagation –Transform the basic propagation atom –For example exp(b ij )  b ij Antti Sorjamaa - TSPCi - AIRC - HUT17/27

Experimental Results Epinions dataset from Epinions.com Epinions dataset from Epinions.com Users write and read reviews from many different topics Users write and read reviews from many different topics Users can also rate the reviews and other reviewers Users can also rate the reviews and other reviewers Review reading creates royalties Review reading creates royalties –Distrust system to decrease abuse Similar systems: Amazon, Slashdot Similar systems: Amazon, Slashdot Antti Sorjamaa - TSPCi - AIRC - HUT18/27

Epinions Dataset nodes with edges nodes with edges Edges either Trust (+1) or Distrust (-1) Edges either Trust (+1) or Distrust (-1) 85 percent of edges are Trust edges 85 percent of edges are Trust edges Large Strongly Connected Component (SCC) of over nodes Large Strongly Connected Component (SCC) of over nodes Bowtie: In almost nodes and out more than nodes Bowtie: In almost nodes and out more than nodes Antti Sorjamaa - TSPCi - AIRC - HUT19/27

Methodology Propagation of Distrust Propagation of Distrust –Trust, One-step and Propagated Distrust Iteration Methods: EIG and WLC Iteration Methods: EIG and WLC Rounding: Global, Local and Majority Rounding: Global, Local and Majority Atomic Propagations: Atomic Propagations: –Direct, Co-sitation and all combined  81 different combinations Antti Sorjamaa - TSPCi - AIRC - HUT20/27

Experiments Each combination of methods get the same treatment Each combination of methods get the same treatment Validation using Leave-One-Out (LOO) Validation using Leave-One-Out (LOO) –Total of 3250 random edges  prediction error ε –About 500 Distrust and 500 Trust edges  prediction error ε S Naive errors: ε = 0,15 and ε S = 0,5 Naive errors: ε = 0,15 and ε S = 0,5 Antti Sorjamaa - TSPCi - AIRC - HUT21/27

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

Results (2) Antti Sorjamaa - TSPCi - AIRC - HUT23/27

Results (3) Antti Sorjamaa - TSPCi - AIRC - HUT24/27

Results (4) Antti Sorjamaa - TSPCi - AIRC - HUT25/27

Conclusions Web of Trust and Distrust is important part of many e-commerce related sites Web of Trust and Distrust is important part of many e-commerce related sites –Distrust stabilizes the propagation of opinions in the network –Distrust decreases the effect of abuse Rounding is surprisingly important Rounding is surprisingly important Small number of expressed Trust scores lead to accurate prediction Small number of expressed Trust scores lead to accurate prediction Antti Sorjamaa - TSPCi - AIRC - HUT26/27

27/27 Questions?