page rank - users.cs.fiu.edugiri/teach/5768/f19/lecs/unitx8-pagerank.pdfpagerank! essential...
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Page Rank
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PageRank & Link AnalysisLawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. ”The PageRank citation ranking: Bringing order to the web.” 1999.
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CAP 5510 / CGS 5166
Early Search Engines
! Crawl the web, collect terms, build inverted index (term to URL mapping)
! Spammers found tricks to beat the system ❑ Add irrelevant terms to URL (Term Spam) ❑ Copy top hit URL to your page
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CAP 5510 / CGS 5166
Importance of Web Pages
! If more links into X, then X is important ! If important pages link to X, then X is important
❑ Chicken and Egg problem for importance
! Random Walk Idea ❑ Simulate random walk & count # of recurring visits ❑ Spam farm problem to trap random walker
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CAP 5510 / CGS 5166
Random Walks & PageRank
! Perform random walks ! Importance of page is proportional to how often you visit a node ! During web search, prefer to report important pages
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CAP 5510 / CGS 5166
Example
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CAP 5510 / CGS 5166
Example
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CAP 5510 / CGS 5166
Example
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CAP 5510 / CGS 5166
Random Walks
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CAP 5510 / CGS 5166
Computing the Stationary Prob
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CAP 5510 / CGS 5166
Random Walks w/ Dead Ends
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CAP 5510 / CGS 5166
Rand Walks w/o Dead Ends
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CAP 5510 / CGS 5166
Rand Walk w/ Teleporting (0.8)
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PageRank
! Essential component of Google search engine ! PageRank allows efficient and stable prioritization of search results ! Vote of Confidence Principle
❑ PageRank of a web page will be high if it is linked to other highly ranked pages
! Random Walk / Markov Chain Analogy ❑ Which pages are most visited on a random walk?
! Teleportation Analogy ❑ Models when a user jumps next to an unlinked page
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Random Walk + Teleportation Analogy
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CAP 5510 / CGS 5166
Implementing PageRank
! Even v may not fit in memory ! Use MapReduce
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CAP 5510 / CGS 5166
Partitioning for MapReduce
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Impact of teleportation parameter
10 Wikipedia pages with highest PageRank [Gleich, ‘09]
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Applications of PageRank
! Clustering [Andersen ‘06] [reset to same page] ! Sports Ranking [Govan ‘08] ! Bioinformatics – GeneRank [Morrison ‘05], ProteinRank [Freschi ‘07] ! Network Alignment [Singh ‘07] ! Literature – BookRank; Bibliometrics – CiteRank, AuthorRank, TimedPageRank; ! Information Systems – PopRank, FactRank, ObjectRank, FolkRank ! Recommender Systems – ItemRank ! Social Networks – BuddyRank, TwitterRank ! Web – HostRank, DirRank, TrustRank, BadRank, VisualRank
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Mathematics of PageRank
! Given: Pij = prob of transition from j to i ! PageRank is given by solution x to equation
❑ (αP + (1-α)veT)x = x ❑ Thus x is eigenvector of a certain matrix ❑ Alternative equation: (I-αP)x = (1-α)v ❑ Eigenvectors can be computed using ❑ ge et al. used an iterative powering method:
▪ x(k+1) = αPx(k) + (1-α)v ❑ Convergence in 3656 iterations to within 10-16 error
Random Walk Teleportation
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Variants of PageRank: Localized
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CAP 5510 / CGS 5166
Topic-Sensitive PageRank
! Teleport to a URL with same topic
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CAP 5510 / CGS 5166
Variants of PageRank
! Hubs & Authorities ❑ Authorities are nodes with information
▪ E.g., Course webpage
❑ Hubs provide links to authorities ▪ E.g., list of courses offered
! Good Authorities linked from Good Hubs ! Good Hubs link to Good Authorities
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CAP 5510 / CGS 5166
Computing h and a
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Variants of PageRank
! Reverse PageRank (follow inlinks, not outlinks) ! Dirichlet PageRank (fix importance of subset) ! Weighted PageRank ! Undirected PageRank ! Timed PageRank ! PageTrust