Time Series Prediction and ChemoInformatics Group Adaptive Informatics Research Centre

1. Propagation of Trust and DistrustR. Guha, R. Kumar, P. Raghavan and A. TomkinsNew York, 2004Antti Sorjamaa Time Series Prediction and ChemoInformatics Group Adaptive Informatics Research Centre Helsinki University of Technology

2. Outline • Background • Algorithms • Atomic propagation • Propagation methods • Rounding • Transitivity issues • Experimental results Antti Sorjamaa - TSPCi - AIRC - HUT

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

4. Background (2) • 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 • Does not apply directly to Distrust Antti Sorjamaa - TSPCi - AIRC - HUT

5. Origin of Trust • 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 • Trust relationships • Good basis for the propagation of Trust • More individual view of the Web of Trust Antti Sorjamaa - TSPCi - AIRC - HUT

6. Problems of Distrust • ”Negative Trust” • Shifting the already existing Trust scores distort the results • Algorithmic complications • Negative eigenvalues • Negative probabilities • What is Distrust propagation? Antti Sorjamaa - TSPCi - AIRC - HUT

7. Notation 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 CB,α= Combined atomic propagation matrix P(k ) = Propagation matrix using k steps F = Final beliefs Antti Sorjamaa - TSPCi - AIRC - HUT

8. Atomic Propagation • Basic propagation techniques, ”atoms” • Matrix operations, multiplying B with appropriate matrix operator • 4 basic atoms • Direct Propagation • Co-citation • Transpose Trust • Trust coupling 4 1 1 2 2 3 3 5 Antti Sorjamaa - TSPCi - AIRC - HUT

9. Atomic Propagation (2) • Direct Propagation, B • Co-citation, BTB • Transpose Trust, BT • Trust coupling, BBT 1 2 3 = Antti Sorjamaa - TSPCi - AIRC - HUT

10. Trust Coupling, BBT = 4 1 3 5 = Antti Sorjamaa - TSPCi - AIRC - HUT

11. Atomic Propagation (3) • Direct Propagation, B • Co-citation, BTB • Transpose Trust, BT • Trust coupling, BBT Antti Sorjamaa - TSPCi - AIRC - HUT

12. Notation 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 CB,α= Combined atomic propagation matrix P(k ) = Propagation matrix using k steps F = Final beliefs Antti Sorjamaa - TSPCi - AIRC - HUT

13. Propagation Methods • Trust only: B = T • One-step Distrust: B = T • Propagated Distrust: B = T - D Antti Sorjamaa - TSPCi - AIRC - HUT

14. Iterative Propagation • Eigenvalue Propagation • Weighted Linear Combinations (WLC) Antti Sorjamaa - TSPCi - AIRC - HUT

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

16. Transitivity • Direct Propagation of Trust • If 1 trusts 2 and 2 trusts 3 then 1 trusts 3 • Does not apply to Distrust directly ”Enemy of my enemy is my friend”  Multiplicative Trust Propagation = Antti Sorjamaa - TSPCi - AIRC - HUT

17. Transitivity (2) • 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 • Transform the basic propagation atom • For example exp(bij)  bij Antti Sorjamaa - TSPCi - AIRC - HUT

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

19. Epinions Dataset • 131 829 nodes with 841 372 edges • Edges either Trust (+1) or Distrust (-1) • 85 percent of edges are Trust edges • Large Strongly Connected Component (SCC) of over 41 000 nodes • Bowtie: In almost 40 000 nodes and out more than 30 000 nodes Antti Sorjamaa - TSPCi - AIRC - HUT

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

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

22. Results K = 20 e1 = Direct Only e2 = Co-sitation Only e* = [0,4 0,4 0,1 0,1] Antti Sorjamaa - TSPCi - AIRC - HUT

23. Results (2) Antti Sorjamaa - TSPCi - AIRC - HUT

24. Results (3) Antti Sorjamaa - TSPCi - AIRC - HUT

25. Results (4) Antti Sorjamaa - TSPCi - AIRC - HUT

26. Conclusions • 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 • Small number of expressed Trust scores lead to accurate prediction Antti Sorjamaa - TSPCi - AIRC - HUT

27. Questions? Antti.Sorjamaa@hut.fi http://www.cis.hut.fi/projects/tsp