The PageRank Citation Ranking:The PageRank Citation Ranking:Bringing Order to the WebBringing Order to the Web

Larry Page etc.Stanford University, Technical Report 1998

Presented by:Ratiya Komalarachun

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ContentsContents

Motivation Related work Background Knowledge Page Rank & Random Surfer Model Implementation Application Conclusion

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MotivationMotivation

Web: heterogeneous and unstructured

Free of quality control on the web

Commercial interest to manipulate ranking

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Related WorkRelated Work Academic citation analysis

Link based analysis

Clustering methods of link structure

Hubs & Authorities Model based on an eigenvector calculation

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hubs

Hubs & Authorities ModelHubs & Authorities Model

authorities

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Hubs & Authorities ModelHubs & Authorities Model

Mutually reinforcing relationship

“A good hub is a page that points to many good authorities”

“A good authority is a page that is pointed by many good hub”

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Link Structure of the WebLink Structure of the Web Forward links (outedges) Backlinks (inedges) Approximation of importance /

quality

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PageRankPageRank A page has high rank if the sum of

the ranks of its backlinks is high

Backlinks coming from important pages convey more importance to a page

Problem: Dangling Links, Rank Sink

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Dangling LinksDangling Links

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PageRank CalculationPageRank Calculation

uBv vN

vRcuR

)()(

Given: R(u) = Rank of u, R(v) = Rank of v,

c < 1 (used for normalization) Nv = number of link from v

Bu = the set of pages that point to u

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PageRank CalculationPageRank Calculation

100 50

50

9

3

3

3

53

50

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Page cycles pointed by some incoming link

Problem: Ranking increase, don’t effect any rank outside

Rank SinkRank Sink

.6

.6

.6

.6

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Escape TermEscape Term Solution: Rank Source

E(u) is some vector over the web pages– uniform, favorite page etc.

)()(

)( ucEN

vRcuR

uBv v

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R is the dominant eigenvector and c is the dominant eigenvalue of because c is maximized

Matrix NotationMatrix Notation

ReEAcR TT )(

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Computing PageRankComputing PageRank - initialize vector over web pages Loop: - new ranks sum of normalized backlink ranks

- compute normalizing factor

- add escape term

- control parameter

While - stop when converged

SR 0

iT

i RAR 1

111 ii RRd

dERR ii 11

ii RR 1

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Page Rank vs. Random Surfer Model

E(u) = “the random surfer gets bored periodically and jumps to a different page and not kept in a loop forever”

Random Surfer ModelRandom Surfer Model

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ImplementationImplementation Computing resources — 24 million pages — 75 million URLs

— Process 550 pages/sec Memory and disk storage

Weight Vector (4 byte float)

Matrix A (linear access)

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ImplementationImplementation

Assign a unique integer ID Sort and Remove dangling links Rank initial assignment Iteration until convergence Add back dangling links and Re-

compute

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Convergence PropertiesConvergence Properties

Using theory of random walks on graphs

O(log(|V|)) due to rapidly mixing graph G of the web.

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Convergence PropertiesConvergence Properties

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Searching with PageRankSearching with PageRank

Using title search

Comparing with Altavista

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Sample ResultsSample Results

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Some Applications Some Applications

Estimate web traffic

Backlink predictor

User Navigation

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ConclusionConclusion PageRank is a global ranking based

on the web's graph structure PageRank uses backlinks

information to bring order to the web

PageRank can separate out representative pages as cluster center

A great variety of applications