The Efficacy of Collusions in Web Ranking and the Countermeasurements Hui Zhang University of Southern California

Outline Problem Statement. PageRank algorithm : a brief introduction. 10/14/2018 Outline Problem Statement. PageRank algorithm : a brief introduction. Study of PageRank’s robustness to collusion. Adaptive-resetting: make PageRank robust to collusion. Conclusions. 10/14/2018 USC CS599 P2Peco

Search Engine Optimization (SEO) 10/14/2018 Search Engine Optimization (SEO) Not different from other research works on P2P rating, our research goal 10/14/2018 USC CS599 P2Peco

Web spam [Gyongyin et al. 2004] 10/14/2018 Web spam [Gyongyin et al. 2004] Web spamming refers to actions intended to mislead search engines and give some pages higher ranking than they deserve. A spammer will play with two factors which decide the rank score of a page in a query: Relevance – textual similarity between the query and a page. Importance – the global popularity of a page, which is query-independent. Not different from other research works on P2P rating, our research goal 10/14/2018 USC CS599 P2Peco

Collusion in Web ranking 10/14/2018 Collusion in Web ranking A manipulation of the hyperlink structure by a group of users with the intention of improving the rating one or more users in the group. Not different from other research works on P2P rating, our research goal 10/14/2018 USC CS599 P2Peco

10/14/2018 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. 10/14/2018 USC CS599 P2Peco

PageRank: random walk model 10/14/2018 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). 10/14/2018 USC CS599 P2Peco

PageRank: is it collusion-proof? 10/14/2018 PageRank: is it collusion-proof? Can a node easily boost its rank by manipulating its out-going links with others’? I’m not colluding! 10/14/2018 USC CS599 P2Peco

Amp(G): a metric on group collusion 10/14/2018 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’) = 10/14/2018 USC CS599 P2Peco

Answer for (1+1 = ?) in PageRank 10/14/2018 Answer for (1+1 = ?) in PageRank In the original PageRank system, where  is the resetting probability. 10/14/2018 USC CS599 P2Peco

Two experimental topologies 10/14/2018 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: www.blogstreet.com, the XML-RPC webblog service. 10/14/2018 USC CS599 P2Peco

Experiment 1: Collusion200 10/14/2018 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, …, 100000th.  = 0.15. (100th, 200th, …, 10000th for B due to the smaller graph size) 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (I) 10/14/2018 Experiment result of Collusion200 (I) Figure 1: W - Amplification factors of the 100 colluding groups in Collusion200. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (III) 10/14/2018 Experiment result of Collusion200 (III) Old rank: 100009th New rank: 5038th Old rank: 10001th New rank: 450th Old rank: 1005th New rank: 67th Figure 2: W – new PR rank after Collusion200. 10/14/2018 USC CS599 P2Peco

There is a long flat portion… 10/14/2018 There is a long flat portion… Figure 3: The PR weight distribution of 4 topologies. 10/14/2018 USC CS599 P2Peco

Next step: how to detect collusions? 10/14/2018 Next step: how to detect collusions? Identifying colluding groups is unlikely to be computationally tractable. The densest k-subgraph problem[Feige et al. 1997]. The classical CLIQUE problem. The problem of finding hiding large cliques in random graphs[Juels 1998]. 10/14/2018 USC CS599 P2Peco

Hardness on Amp Theorem on Hardness. 10/14/2018 Hardness on Amp Theorem on Hardness. Max G’G Amp(G’) is a NP-Hard problem. 10/14/2018 USC CS599 P2Peco

How about using finer statistics of the random walk 10/14/2018 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 10/14/2018 USC CS599 P2Peco

An observation on collusion behaviors 10/14/2018 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 . 10/14/2018 USC CS599 P2Peco

An intuitive example node referential link 10/14/2018 USC CS599 P2Peco

An intuitive example node referential link A colluding group 10/14/2018 An intuitive example node referential link A colluding group 10/14/2018 USC CS599 P2Peco

10/14/2018 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 10/14/2018 USC CS599 P2Peco

Adaptive-resetting scheme 10/14/2018 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. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (IV) 10/14/2018 Experiment result of Collusion200 (IV) Figure 5: W - Amplification factors of the 100 colluding groups in Collusion200. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (VI) 10/14/2018 Experiment result of Collusion200 (VI) Figure 6: W – new PR rank after Collusion200. 10/14/2018 USC CS599 P2Peco

Experiment 2: Collusion22 10/14/2018 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 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion22 (I) 10/14/2018 Experiment result of Collusion22 (I) Figure 7: Amplification factors of the 3 colluding groups in Collusion22. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion22 (II) 10/14/2018 Experiment result of Collusion22 (II) Figure 8: W – new PR weight after Collusion22. 10/14/2018 USC CS599 P2Peco

New top-25 URL list in W Dropped out Dropping New 10/14/2018 USC CS599 P2Peco

10/14/2018 Conclusions Simple collusions lead to effective Web ranking improvement. A simple scheme based on PageRank algorithm effectively counteracts Web ranking collusions. 10/14/2018 USC CS599 P2Peco

Backup slides 10/14/2018 USC CS599

Reputation systems [Okita2003] 10/14/2018 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 10/14/2018 USC CS599 P2Peco

PageRank algorithm [Brin1998] 10/14/2018 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 10/14/2018 USC CS599 P2Peco

Co-co distribution in real-world graphs 10/14/2018 Figure 4: the co-co PDF distribution in W and B: the [0, 0.1] range actually corresponds to [-1, 0.1] range. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (II) 10/14/2018 Experiment result of Collusion200 (II) Figure A: W – new PR weight after Collusion200. 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (VII) 10/14/2018 Experiment result of Collusion200 (VII) Figure B: B – new PR rank after Collusion200 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (X) 10/14/2018 Experiment result of Collusion200 (X) Figure C: B – new PR weight after Collusion200 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion200 (V) 10/14/2018 Experiment result of Collusion200 (V) Figure 6: W – new PR weight after Collusion200. 10/14/2018 USC CS599 P2Peco

Correlation coefficient 10/14/2018 Correlation coefficient 10/14/2018 USC CS599 P2Peco

Experiment result of Collusion22 (III) 10/14/2018 Experiment result of Collusion22 (III) Figure D: W – new PR rank after Collusion22. 10/14/2018 USC CS599 P2Peco