1. Making Eigenvector-based Reputation Systems Robust to Collusion
Hui Zhang1, Ashish Goel2, Ramesh Govindan1, Kahn Mason2, Benjamin Van Roy2
1University of Southern California
2Stanford University

2. Outline Research motivation.
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Outline
Research motivation.
PageRank algorithm : a brief introduction.
Study of PageRank’s robustness to collusion.
Adaptive-resetting: make PageRank robust to collusion.
Conclusion & future works.
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3. Research motivation Build reputation in large-scale systems
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Research motivation
Build reputation in large-scale systems
P2P file sharing systems
Blogging communities
Networked gaming, …, etc.
Collusion-proofness is an essential criterion in evaluating a rating scheme.
Not different from other research works on P2P rating, our research goal
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PageRank [Brin1998]
An eigenvector-based rating scheme to rank hypertext documents on the WWW.
An iterative algorithm to calculate the importance of a web page based on the importance of its parent pages.
Can be applied to other systems than WWW.
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5. PageRank: random walk model
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PageRank: random walk model
With prob. (1-), I will continue the walk to a random successor node.
: resetting probability
node
With prob. , I will restart the walk at a random node.
: resetting probability
referential link
The walker X
1/2
1/3 Y Z
As time goes on, the expected percentage of steps the walker is at each node v converges to the PageRank weight PR(v).
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6. PageRank: is it collusion-proof?
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PageRank: is it collusion-proof?
Can a node easily boost its rank by manipulating its out-going links with others’?
I’m not colluding!
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7. Amp(G): a metric on group collusion
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Amp(G): a metric on group collusion x y G G’ i j
: resetting probability
WG(G’) =PR(i)+PR(j)
real group weight
PR(x) 3
(1-)
PR(y) 2 4 +
(1-)
Win(G’) = + 2 N
(1-W(G’))
“actual” group weight
In the system of node group G, for a subgroup G’,
the amplification factor Amp(G’) =
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8. Theorem on Amp In the original PageRank system,
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Theorem on Amp
In the original PageRank system,
where  is the resetting probability.
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9. Two experimental topologies
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Two experimental topologies
W, a Web link topology
Contains the link structure of upwards of 80 million URLs.
Source: the Stanford WebBase.
B, a weblog blogrolling topology
Contains the blogrolling structure of upwards of 72,000 blogs.
Source: the XML-RPC webblog service.
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10. Experiment 1: Collusion200
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Experiment 1: Collusion200
Model a small number of web pages simultaneously colluding.
Methodology:
100 colluding groups of 200 nodes;
Each colluding group has the circle topology consisting of two nodes with adjacent ranks;
Arbitrarily chose node pairs originally ranked around 1000th, 2000th, …, th.
 = 0.15.
(100th, 200th, …, 10000th for B due to the smaller graph size)
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11. Experiment result of Collusion200 (I)
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Experiment result of Collusion200 (I)
Figure 1: W - Amplification factors of the colluding groups in Collusion200.
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12. Experiment result of Collusion200 (III)
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Experiment result of Collusion200 (III)
Figure 2: W – new PR rank after Collusion200.
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13. There is a long flat portion…
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There is a long flat portion…
Figure 3: The PR weight distribution of 4 topologies.
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14. Next step: how to detect collusions?
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Next step: how to detect collusions?
Theorem on Hardness.
Max G’G Amp(G’) is a NP-Hard problem.
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15. An observation on collusion behaviors
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An observation on collusion behaviors
To increase their PR weight, i.e., the stationary weight in the random walk, the colluding nodes will stall the random walk. G G’
When the resetting probability  increases, the colluding nodes must suffer a significant drop in PR weight.
Therefore, we expect the PR weight of colluding nodes to be highly correlated with 1/  (the average walk length), while that of non-colluding nodes is relatively insensitive to the change in .
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16. An intuitive example node referential link 11/27/2018 11/27/2018
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17. An intuitive example node referential link A colluding group
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An intuitive example
node
referential link
A colluding group
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An intuitive example
A colluding node x: PR(x) = , and co-co(PR(x), 1/ )  1. (co-co: correlation coefficient)
A non-colluding node y: PR(x) = , and co-co(PR(y), 1/ )  0. x y
N: the system size; K: the colluding group size; K << N.
node
referential link
A colluding group
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19. Adaptive-resetting scheme
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Adaptive-resetting scheme
Part I – collusion detection:
Given the topology, calculate the PR vector under different  values.
{} = {0.0375, 0.05, 0.075, 0.15, 0.3, 0.45, 0.6}, default = 0.15.
Calculate the correlation coefficient between the curve of each node x's PR weight and the curve of 1/ . Label it as co-co(x).
Part II –  personalization:
Calculate each node x's out-link personalized- = F(default, co-co(x)).
Exponential function FExp=
Linear function FLinear= default+(0.5-default)*co-co(x)
The final PR weight vector is calculated with these personalized resetting values.
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20. Experiment result of Collusion200 (IV)
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Experiment result of Collusion200 (IV)
Figure 5: W - Amplification factors of the colluding groups in Collusion200.
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21. Experiment result of Collusion200 (VI)
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Experiment result of Collusion200 (VI)
Figure 6: W – new PR rank after Collusion200.
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22. Experiment 2: Collusion22
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Experiment 2: Collusion22
Model various colluding subgraphs.
Methodology:
3 colluding groups:
node
referential link
(100th, 200th, …, 10000th for B due to the smaller graph size)
G1: 10-node ring
G2: 10-node star topology
G3: 2-node ring
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23. Experiment result of Collusion22 (I)
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Experiment result of Collusion22 (I)
Figure 7: Amplification factors of the 3 colluding groups in Collusion22.
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24. Experiment result of Collusion22 (II)
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Experiment result of Collusion22 (II)
Figure 8: W – new PR weight after Collusion22.
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25. New top-25 URL list in W Dropped out Dropping New 11/27/2018
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26. Conclusion & future works
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Conclusion & future works
A collusion-proof rating scheme based on PageRank algorithm.
Future works:
Formal analysis of the adaptive-resetting scheme.
Study of Web link structure evolution under PageRank within the framework of game theory.
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27. Backup slides
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28. Reputation systems [Okita2003]
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Reputation systems [Okita2003]
A means of describing social trust networks.
The basic concept is a democratic meritocracy.
A rating system is used to evaluate individual members, and those results are then collated to produce a consensus about the merit of any given member.
Examples:
Livejournal, Friendster, eBay, Advogato
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29. PageRank algorithm [Brin1998]
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PageRank algorithm [Brin1998]
Assume N pages.
Assign all pages the initial value 1/N
Let Nu be the out-degree of Page u, Rank(v) the importance of Page v, Bv the set of pages pointing to v.
Basic algorithm
v Rank(v) =
Enhanced algorithm against rank sinks
v Rank(v) =
: damping factor
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30. Co-co distribution in real-world graphs
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Figure 4: the co-co PDF distribution in W and B: the [0, 0.1] range actually corresponds to [-1, 0.1] range.
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31. Experiment result of Collusion200 (II)
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Experiment result of Collusion200 (II)
Figure A: W – new PR weight after Collusion200.
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32. Experiment result of Collusion200 (VII)
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Experiment result of Collusion200 (VII)
Figure B: B – new PR rank after Collusion200
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33. Experiment result of Collusion200 (X)
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Experiment result of Collusion200 (X)
Figure C: B – new PR weight after Collusion200
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34. Experiment result of Collusion200 (V)
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Experiment result of Collusion200 (V)
Figure 6: W – new PR weight after Collusion200.
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35. Correlation coefficient
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Correlation coefficient
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36. Experiment result of Collusion22 (III)
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Experiment result of Collusion22 (III)
Figure D: W – new PR rank after Collusion22.
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37. How about using finer statistics of the random walk
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How about using finer statistics of the random walk
The revisit intervals of the random walk on a colluding node will likely to have a large variance compared to its expectation.
Figure E:
A counterexample: a star+dangling circle topology 1 2 N
N+1
N-1
N-2
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