Propagation of Trust and Distrust

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Propagation of Trust and Distrust

• Authors R. Guha, R. Kumar, P. Raghavan,
• A. Tomkins
• Presented by Willie Milnor
• Large Scale Distributed Information Systems
  (LSDIS) Lab

2
Outline

• Motivation
• Related Work
• Framework
• Algorithms
• Data
• Experiments
• Results

3
Motivation

• information sharing
• products, employment, reality, etc
• economic motivation to spread information
• open standards
• possible exploitations
• solution web of trust
• users rate users
• web helps users assess users
• e-commerce and recommendation systems

4
Approaches to Trust

• natural aggregation of opinions
• coalition of users with biased opinions
• trust relationships
• built over time
• recursive trust
• benefits
• individually tailored data
• encourage trustworthy behavior
• social networks and economics

5
Distrust

• recent mathematical approaches to trust
• distrust not considered
• users can distrust users
• Epinions and EBay
• challenges
• zero value or no opinion
• negative value unreal eigenvector
• chain of distrust
• unscrupulous users

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Summary of Work

• typically spare networks
• non explicit trust relationships
• taxonomy of schemes for propagation
• web of trust from Epinions
• empirical study on large data set
• ranked by predictive accuracy
• accuracy vs. response time

7
Related Work

• non computational
• affects on beliefs and decision making
• trust in political science
• cryptography and authentication
• PGP1 used web of trust
• The Tipping Point2
• information flow mediation
• business management Ackerlof3
• sellers trustworthiness on quality of a product
• game theoretic approach4
• authenticating third party

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Framework

• n users
• n x n matrices T and D
• tij is trust in j
• 0 lt tij lt 1
• same for D - distrust
• predict unknown values from T and D
• M generic belief matrix

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Atomic Propagation

• basis set of techniques
• direct propagation M
• A trusts B trust(A) propagates to B
• co-citation MTM
• A trusts B,C trust(B) propagates to C
• transpose trust MT
• A trusts B trust(B) propagates to A
• trust coupling MMT
• A,B trust C trust(A) propagates to B

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Propagation of Distrust

• weight and sum each matrix RM
• matrix P(k)
• pij propagation from i to j after k applications
  of the basis set
• 3 models based on distrust
• trust-only M T P(k) RkM
• one-step distrust M T P(k) RkM (T D)
• propagated distrust M T D P(k) RkM

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Iterative Propagation

• final matrix F
• each P(k) propagation via paths of length k
• suitably chosen integer K
• eigenvalue propagation
• F P(K)
• weighted linear propagation
• constant y
• F sum((yk) (P(k)))

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Rounding

• Should i trust j?
• global rounding
• align trust/distrust ratio in F to that in M
• based on a threshold overall relative fraction
• local rounding
• take into account trust/distrust behavior of I
• threshold based on i
• majority rounding
• unknown value is that of the smallest majority of
  a local neighborhood
• capture original local structure

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Distrust Transitivity

• trust transitivity
• i trusts j, j trusts k
• i trusts k
• i distrusts j, j distrusts k
• multiplicative does i trust k ?
• additive does i strongly distrust k ?
• if mij is not 0, mij exp(mij)
• otherwise, mij 0

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Experimental Data

• Epinions
• taxonomy of reviewable objects
• users review on 2-5 axes
• overall ratings
• users review other users
• indicate trust/distrust
• users rate reviews of other users
• reviewers paid royalties
• efforts to rig system
• distrust

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Trust Graph

• directed graph
• 131829 nodes
• 841372 edges
• indegree and outdegree
• large strongly connected component (SCC)
• 41441 nodes
• bowtie structure5
• undirected
• giant weak connected component
• 119130 nodes

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Experiments

• multiplicative distrust only
• 81 experimental categories
• based on algorithmic framework
• does i trusts j ?
• remove single (i,j) from graph
• run algorithm on each category
• Lanczos style matrix operation
• matrix vector multiplication
• overall low errors

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Results

• basis elements
• weighted propagation
• distrust
• one-step
• rounding
• majority clustering
• iteration
• EIG with one-step distrust (usually)
• path length K
• most dramatic for direct propagation

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Conclusions

• trust propagation fundamental to ecommerce
• formal framework of trust propagation
• introduction of distrust
• evaluate schemes on real-world data
• predictive system
• effects of various phenomena

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• Questions Comments

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References

• 1 B. Yu and M. P. Singh. A Social Mechanism of
  Reputation Management in electronic commerce.
  Cooperative Information Agents, pages 154-165,
  2000
• 2 M. Gladwell. The Tipping Point, How Little
  Things Can Make a Big Difference. Little Brown,
  February 2000.
• 3 G. Ackerlof. The Market of Lemons Quality,
  Uncertainty and the Market Mechanism. Quarterly
  Journal of Economics, 84488-500, 1970.
• 4 S. Ba, A. B. Whinston, and H. Zhang.
  Building Trust in Online Auction Markets Through
  an Economic Interative Mechanism. Decision
  Support Systems, 2002.
• 5 A. Z. Broder, R. Kumar, F. Maghoul, P.
  Raghavan, S. Rajagopalan, R. Stata, A. Tomkins,
  and J. Wiener. Graph Structure in the Web.
  WWW9/Computer Networks, 33(1-6)309-320, 2000.