L23: PageRankjeffp/teaching/cs5140/L23-notes.pdf · collection of websites. ... ↳ truthfulness of...
Transcript of L23: PageRankjeffp/teaching/cs5140/L23-notes.pdf · collection of websites. ... ↳ truthfulness of...
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L23: PageRank
Je↵ M. Phillips
April 13, 2020
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Final Report
At most 4 pages/student. Don’t cram in too much!
I Succinct title (and names)
I Problem definition and motivation.
I Explain your Data.
I key idea
I What did you do (which techniques, an implementation, acomparison, an extension)
I What did you learn? Artifacts (charts, plots, examples, math)and Intuition (in words, did it work?)
I ← Same ten Posters
o
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webpage-simia.it( Search ). InvertedIndex
year ;i¥¥ . .
bout→ page 't
, P ?,"
car"
→¥pQgirl)
-
Define most relevantwebpages-
D- d-'
ne'EE¥÷÷÷÷:÷:i:smarm :÷÷÷i÷"¥xE÷÷g÷÷:X
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Crawlers : program ; that walksaround web : ① read page
update fentwiuecfor
② follow random
inverting hyperlinks
use hyperlink infoL a hired "
www.pie.com" )pie
- 3
Spammersbuild fleet pages i link to your
Page w/ hyperlink tag .
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studies : Alternative to search Engine
Yahoo ! and Look Smart
Built an organized , curatedcollection of websites
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pageR-ankfslpjiturml-fktytg.fi?ggignhspiddeieafe
•
1ttqitlinkedto
balanceboth pages .
•
page is important ifa
random MCMC' ' random surfer "
were
to fond it.
-
Web is a big graph G- L V,
E)
V = I set do all pages }
F- = l Ei ; = link pi → B- 3
Petone ML → g* ⇐ converged to vectordistribution
q*Lj ) says how important page ; is .
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Compute q* of lwepgraph-
• Keep truck of crawlers : how frequentreturn .
• Buy bag computer : Compute eigcp )← probtra.ca)
• Precompute P#
=P - P - p .
. . ..
. p
← too big°
q*= go ←last night
a :÷÷÷o÷÷÷t÷÷¥power
method
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Anatomy of Web
Strongly ConnectedComponent
IN
OUTTubes
tendrilsOUT
tendrilsIN
disconnected
ANATOMY of WEB
is this G ergodic
÷ . . Is•
i'④ yo
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Anatomy of Web
0
O
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canwemaheGergodi.ci#• Teleportation ,/ taxation
→ about once every I steps
→ jumpto randomnode
.
P prob trans (G)13--0-15 p
R= a - is ) Pepe Q¥fIf¥¥Z
↳ dense
Rq . - Ul - B) Ptp'
G)ginLt B) Pain + qt nxt vector- -
→
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Spam Farms
÷ .
Google counter
^seafhs¥at
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Trust ( noes ? )
only teleport to trustedpages .
r ← qx , pagerank
t ← get trusted teleport
rts ) - ft ; ) if l arse → spam
↳ truthfulness of webpage
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Word CountConsider as input all of English Wikipedia stored in DFS. Goal is tocount how many times each word is used.
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Inverted IndexConsider as input all of English Wikipedia stored in DFS. Goal is tobuild an index, so each word has a list of pages it is in.
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PhrasesConsider as input all of English Wikipedia stored in DFS. Goal is tobuild an index, on 3-grams (sequence of 3 words) that appears onexactly one page, with link to page.
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Label Propagation (Graph)Consider a large graph G = (V ,E ) (e.g., a social network), with asubset of notes V 0 ⇢ V with labels (e.g., {pos, neg}). Each nodestores its label (if any) and edges.Assign a vertex a label if (a) unlabled, (b) has � 5 labeledneighbors, (c) based on majority vote.
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Label Propagation (Embedding)Consider a data set X ⇢ Rd , with a subset of points X 0 ⇢ X withlabels (e.g., {pos, neg}). Implicitly defines graph with V = X andE using k = 20 nearest neighbors.Assign a vertex a label if (a) unlabled, (b) has � 5 labeledneighbors, (c) based on majority vote.
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Example PageRank
M =
2
664
0 1/2 0 01/3 0 1 1/21/3 0 0 1/21/3 1/2 0 0
3
775
Stripes:
M1 =
2
664
01/31/31/3
3
775 M2 =
2
664
1/2001/2
3
775 M3 =
2
664
0100
3
775 M4 =
2
664
01/21/20
3
775
These are stored as�1 : (1/3, 2), (1/3, 3), (1/3, 4)
�,�
2 : (1/2, 1)(1/2, 4)�,�3 : (1, 3)
�, and
�4 : (1/3, 1), (1/2, 2)
�.
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Example PageRank
M =
2
664
0 1/2 0 01/3 0 1 1/21/3 0 0 1/21/3 1/2 0 0
3
775
Stripes:
M1 =
2
664
01/31/31/3
3
775 M2 =
2
664
1/2001/2
3
775 M3 =
2
664
0100
3
775 M4 =
2
664
01/21/20
3
775
These are stored as�1 : (1/3, 2), (1/3, 3), (1/3, 4)
�,�
2 : (1/2, 1)(1/2, 4)�,�3 : (1, 3)
�, and
�4 : (1/3, 1), (1/2, 2)
�.
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Example PageRank
M =
2
664
0 1/2 0 01/3 0 1 1/21/3 0 0 1/21/3 1/2 0 0
3
775
Blocks:
M1,1 =
0 1/2
1/3 0
�M1,2 =
0 01 1/2
�M2,1 =
1/3 01/3 1/2
�M2,2 =
0 1/20 0
�
These are stored as�1 : (1/2, 2)
�,�2 : (1/3, 1)
�, as�
2 : (1, 3), (1/2, 4)�, as
�3 : (1/3, 1)
�,�4 : (1/3, 1), (1/2, 2)
�, and
as�3 : (1/2, 4)
�.