Combating Web Spam with TrustRank
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1 Combating Web Spam with rustrank Authors: Gyöngyi, Garcia-Molina, and Pederson Published in: Proceedings of the 0th VLDB Conference Year: 00 Presentation by: Rebecca Wills Date: April, 00
2 Questions we will answer today include Why should we care about this paper? What is rustrank? Is rustrank mathematically sound?
3 Why should we care about this paper? Image captured: week of March -
4 Why should we care about this paper? Image captured: week of March -
5 Why should we care about this paper? Google registered the trademark for rustrank on March, 00. he algorithm receives human assistance. he authors state, We believe that our work is a first attempt at formalizing the problem and at introducing a comprehensive solution to assist in the detection of Web spam.
6 What is Web spam? he term refers to hyperlinked webpages that are created to mislead search engines. Example : webpages containing numerous words having nothing to do with the webpage using text invisible to humans but observed by search engines Example : webpages receiving links from numerous other real or phony webpages for the sole purpose of increasing PageRank
7 Research Goal of the Authors Our research goal is to assist the human experts who detect web spam. In particular, we want to identify pages and sites that are likely to be spam or that are likely to be reputable.
8 What is rustrank? An algorithm that creates a personalization vector to be used in the PageRank computation for the purpose of combating Web spamming
9 Example Web Graph V = {,,,,,, } E = {(,), (,), (,), (,), (,), (,), (,), (,)}
10 Example Web Graph H = Basic PageRank ( ) ( α) r = α r H + e n ( ) 0 α <, n = V, and e =...
11 Example Web Graph H = Basic PageRank ( ) ( α) r = α r H + e n Note: he authors do not directly address the dangling node issue. hey do mention the biased PageRank definition, where v is any probability vector, but they compare their results to the regular PageRank definition.
12 Why is the definition okay? Biased PageRank ( H ) ( α) r = α r + v Class Definition of PageRank (with dangling node fix v ) π ( α) ( α H av ev ) = π + + ( π H ) ( π a) ( ) = α + α + α v Scalar ( I αh ) = ( ) ( ) α π a + α v ( π a) ( ) v ( I αh ) So, π π = α + α
13 Why is the definition okay? Biased PageRank ( H ) ( α) r = α r + v Class Definition of PageRank (with dangling node fix v ) ( I αh ) = α( π a) ( α) + α( π a) ( α) v ( I αh ) So, π = + π ( I α ) x H = βv, π = x, β > 0 x e produces the PageRank vector. v [Langville & Meyer, 00, h m..., pages - ]
14 Example Web Graph H = r rustrank ( r H ) ( α) = α + v where v is formed to combat Web spam
15 Overall Idea r rustrank ( r H ) ( α) = α + v Step : Select a small seed set of webpages. Step : Identify good webpages from the seed set. Step : Create personalization vector based on identification of good webpages.
16 Step : Select a small seed set of webpages. V = {,,,,,, } E = {(,), (,), (,), (,), (,), (,), (,), (,)} E = {(,), (,), (,), (,), (,), (,), (,), (,)}
17 Step : Select a small seed set of webpages U = Inverse PageRan k ( ) ( α) s = α s U + e n Note: he authors emphasize that Inverse PageRank (named based on E ) works well in practice.
18 Step : Select a small seed set of webpages. Function: SelectSeed Initial iterate: s 0 = e While: k M ( s ) k U ( α) Do: sk = α + e, k n his is based on the belief that trust flows out of good seed webpages. It gives preference to webpages from which many other webpages can be reached. See Maple file for implementation of SelectSeed for this example.
19 Step : Select a small seed set of webpages. Function: SelectSeed Initial iterate: s 0 = e While: k M ( s ) k U ( α) Do: sk = α + e, k n Note: his algorithm is the Jacobi Method applied to r (I αu) = ( α) / n e. he diagonal part of (I αu) is I, and the sum of the upper and lower triangular parts is αu. See Maple file for implementation of SelectSeed for this example.
20 Step : Select a small seed set of webpages. Function: SelectSeed Initial iterate: s While: k M For α = 0.8 and M = 0, we obtain s 0 0 ( s ) k U ( α) Do: sk = α + e, k n ( ) Suppose we want to check the top webpages (in blue above). {,, } hen, our seed set is S =. = e
21 Step : Identify good webpages from seed set. V = {,,,,,,}. S = { },,. Back to the original graph Oracle function:, if webpage i is good Oi () = 0, if webpage i is bad. his is the step requiring human involvement, and it is, to some extent, subjective.
22 Step : Identify good webpages from seed set. V = {,,,,,,}. S = { },,. Oracle function:, if webpage i is good Oi () = 0, if webpage i is bad. S = {,} and S = {}. +
23 Step : Create personalization vector based on identification of good webpages. S = {,} and S = {}. + v = ( ) Comment: I think it s interesting that the authors go through the trouble of making the personalization vector a probability vector even though the PageRank vector will not be a probability vector. Also, they do not use a probability vector to initialize the Inverse PageRank algorithm.
24 Compute rustrank Function: rustrank Initial iterate: r 0 = v While: k M ( ) k H ( α) Do: r = α r + v, k k Note: his M and α can be different from the ones used for Inverse PageRan k.
25 Compute rustrank Function: rustrank Initial iterate: r 0 = v While: k M ( ) k H ( α) Do: r = α r + v, k k Note: his algorithm is the Jacobi Method applied to r (I αh) = ( α)v. he diagonal part of (I αh) is I, and the sum of the upper and lower triangular parts is αh. See Maple file for implementation of rustrank for this example.
26 Compute rustrank Function: rustrank Initial iterate: r 0 = v While: k M ( ) k H ( α) Do: r = α r + v, k k For α = 0.8 and M = 0, we obtain r 0 ( ). See Maple file for implementation of rustrank for this example.
27 Compute rustrank Interestingly, for the whole Web graph, the authors identified: Good webpages, V + = {,,, }, and Bad webpages, V = {,, }. he Basic PageRank algorithm ranked good webpage higher than bad webpage, but the rustrank algorithm did not. (Perhaps, they should have identified good and bad webpages differently for the example.) For α = 0.8 and M = 0, we obtain 0 ( ) ( ) rustrank: r Basic PageRank: x See Maple file for implementation of PageRank for this example.
28 Experiments Web data Entire AltaVista index (August 00) Site-level Web graph Seed set million vertices million without inlinks,000 candidates reduced to,900 then,0 8 selected high-quality sites Evaluation sample 000 manually tagged sites Oracle: Gyöngyi (the first author of the paper)
29 Experiments Manual evaluation took weeks Compared Inverse PageRank to other options for selecting the seed set (such as using webpages with high Basic PageRank scores) Observed that websites with highest inverse PageRank scores showed a heavy bias toward spam Removed all websites not listed in any major web directories Final filter only selected websites with a clearly identifiable authority
30 Experiments Section.: Seed Set he authors indicate that they compare inverse PageRank to high PageRank (seed set made up of pages with highest basic PageRank scores). hey state: We describe these experiments in []. Due to space limitations, here we just note that inverse PageRank turned out to be slightly better at identifying useful seed sets. hus, for the rest of our experiments, we relied on the inverse PageRank method. I searched the Web and never found []. he above statement reminds me of Fermat s comment about his last theorem.
31 Experiments Each bucket represents % of the total PageRank score. here are 0 buckets. rustrank buckets have the same number of websites as PageRank buckets. Picture of graph available at:
32 Experiments Picture of graph available at:
33 Also discussed: Assessing rust Oracle Function:, O( i) = 0, if if webpage i is good webpage i is bad. rust function: For webpage i, (i) = Pr[O(i) = ]. hreshold trust property: For webpage i, (i) > δ O(i) =. Signal function: I, ( i) ( j) and O( i) < O( j), =, ( i) ( j) and O( i) > O( j) 0, otherwise. ( O, i, j)
34 Assessing rust Suppose X V with m randomly selected elements. Let P = {(i, j) X X: i j}. hen, P = m(m ). Pairwise Orderedness: pairord (, O, P) = P ( i, j) I P (, O, i, j) P Precision: prec (, O) = { i X : ( i) > δ and O( i) = } { i X : ( i) > δ} Recall: rec (, O) = { i X : ( i) > δ and O( i) = } { i X : O( i) = }
35 Assessing rust Seed set: S V with L elements. S + = {i S: O(i) = } and S = {i S: O(i) = 0}. Ignorant trust function: = +., 0,, ) ( 0 S V i S i S i i M-step trust function: > = + +., 0, ), ( and ), ( s.t. and or, ) ( S V i S i S k M k i d M j i d S j S i S i i M
36 Back to Example Suppose S = {,, }. hen, S + = {, } and S = {}. Vertex i Oracle O(i) Ignorant rust 0 (i) -step rust (i) -step rust (i) -step rust (i)
37 Back to Example Suppose S = {,, }. hen, S + = {, } and S = {}. Vertex i Oracle O(i) Ignorant rust 0 (i) -step rust (i) -step rust (i) -step rust (i) 0 0 0
38 Back to Example Suppose S = {,, }. hen, S + = {, } and S = {}. Vertex i Oracle O(i) Ignorant rust 0 (i) -step rust (i) -step rust (i) -step rust (i) / / / 0 / / / / / / /
39 Back to Example Now, suppose X = V. hen, P = () =. M pairoid( M, O, P) prec( M, O) if δ = / rec( M, O) if δ = / 0 ( 8)/ / = / ( )/ / = 9/ ( 0)/ = ( 8)/ / = /
40 Summary of Paper Formalizes the problem of Web spam and spam detection algorithms Introduces Inverse PageRank to select seed sets First use of an oracle to assess webpages Introduces the rustrank algorithm (which is the PageRank algorithm with a carefully chosen personalization vector) Provides empirical results Defines trust assessing metrics
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