generalizing pagerank (pisa)

DampingFunctions forLink Ranking

R Baeza-YatesP Boldi andC Castillo

Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

The Choice of a Damping Function forPropagating Page Importance

in Link-Based Ranking

Ricardo Baeza-Yates1 Paolo Boldi2 and Carlos Castillo3

1 Yahoo Research ndash Barcelona Spain2 Universita di Milano ndash Italy

3 Universita di Roma ldquoLa Sapienzardquo ndash Italy

February 6th 2005



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

1 Notation

2 Rewriting PageRank

3 Functional Rankings

4 Algorithms

5 Comparison

6 Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Let PNtimesN be the normalized link matrix of a graph

Row-normalized

No ldquosinksrdquo



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Definition (PageRank)

Stationary state of

αP +(1minus α)

N1NtimesN

Follow links with probability α

Random jump with probability 1minus α



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Rewriting PageRank [Boldi et al 2005]

r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Definition (Branching contribution of a path)

Given a path p = 〈x1 x2 xt〉 of length t = |p|

branching(p) =1

d1d2 middot middot middot dtminus1

where di are the out-degrees of the members of the path



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Explicit formula for PageRank [Newman et al 2001]

ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)

Path(minus i) are incoming paths in node i

General functional ranking

ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Distribution of shortest paths

it (40M pages) uk (18M pages)

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

euint (800K pages) Synthetic graph (100K pages)

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght

Length of the path (t)

damping(t) with α=08damping(t) with α=07

Exponential damping = PageRank

damping(t) = α(1minus α)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght


damping(t) with L=15damping(t) with L=10

Linear damping

damping(t) =

2(Lminust)L(L+1) t lt L

0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


For calculating LinearRank we use

LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt

However we cannot hold the temporary Pt in memory



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

We have to rewrite to be able to calculate

R(0) =2

L + 1

R(k+1) =(Lminus k minus 1)

(Lminus k)R(k)P

LinearRank =Lminus1sumk=0

R(k)

Now we can give the algorithm



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquorsaquo

1 for i 1 N do Initialization2 Score[i] larr R[i] larr 2

L+13 end for

4 for k 1 Lminus 1 do Iteration step5 Aux larr 06 for i 1 N do Follow links in the graph7 for all j such that there is a link from i to j do8 Aux[j] larr Aux[j] + R[i]outdegree(i)9 end for

10 end for11 for i 1 N do Add to ranking value12 R[i] larr Aux[i] times (Lminuskminus1)

(Lminusk)

13 Score[i] larr Score[i] + R[i]14 end for15 end for16 return Score



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for4 for k 1 Lminus 1 do Iteration step5 Aux larr 0

6 for i 1 N do Follow links in the graph7 for all j such that there is a link from i to j do8 Aux[j] larr Aux[j] + R[i]outdegree(i)9 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for4 for k 1 Lminus 1 do Iteration step5 Aux larr 06 for i 1 N do Follow links in the graph7 for all j such that there is a link from i to j do8 Aux[j] larr Aux[j] + R[i]outdegree(i)9 end for

10 end for

11 for i 1 N do Add to ranking value12 R[i] larr Aux[i] times (Lminuskminus1)

(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquorsaquo

Other functions studied in the paper

Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquorsaquo

How to approximate one functional ranking with another

Analysis (in the paper) match the first few levels of theirdamping functions

In practice the orderings can be very similar



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquorsaquo

Experimental comparison 18-million nodes in the UK WebGraph

Calculated PageRank with α = 01 02 09

Calculated LinearRank with L = 5 10 25

For certain combinations of parameters the rankings arealmost equal



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquorsaquo

Experimental Comparison in the UK Web Graph

05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullrsaquorsaquorsaquo

Prediction of Best Parameter Combinations (Analysis)

5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α

Actual optimumPredicted optimum with length=5



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullrsaquorsaquo

What have we done

Separate the damping from the calculation

Show that different damping functions can provide thesame ranking

Analysis and experiments in the paper



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullrsaquo

What can we do with this

Fast approximation of PageRank using linear damping

Fast calculation of other link-based rankings (eg HITS)

Spam detection (eg cut the first levels of links)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull

Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

Baeza-Yates R Boldi P and Castillo C (2005)The choice of a damping function for propagating importance in link-basedrankingTechnical report Dipartimento di Scienze dellrsquoInformazione Universit degliStudi di Milano

Boldi P Santini M and Vigna S (2005)Pagerank as a function of the damping factorIn Proceedings of the 14th international conference on World Wide Webpages 557ndash566 Chiba Japan ACM Press

Newman M E Strogatz S H and Watts D J (2001)Random graphs with arbitrary degree distributions and their applicationsPhys Rev E Stat Nonlin Soft Matter Phys 64(2 Pt 2)

Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions

1 Notation

2 Rewriting PageRank

3 Functional Rankings

4 Algorithms

5 Comparison

6 Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Row-normalized

No ldquosinksrdquo



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Row-normalized

No ldquosinksrdquo



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Stationary state of

αP +(1minus α)

N1NtimesN





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



r(α) =(1minus α)

N

infinsumt=0

(αP)t



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




branching(p) =1





Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



ri (α) =sum

pisinPath(minusi)

(1minus α)α|p|

Nbranching(p)



ri (α) =sum

pisinPath(minusi)

damping(|p|)N

branching(p)



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance


00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance

00

01

02

03

5 10 15 20 25 30

Freq

uenc

y

Distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


000

010

020

030

1 2 3 4 5 6 7 8 9 10

Wei

ght



Linear damping

damping(t) =


0 t ge L



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



LinearRank =1

N

infinsumt=0

damping(t)Pt

=1

N

Lminus1sumt=0

2(Lminus t)

L(L + 1)Pt




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



R(0) =2

L + 1


(Lminus k)R(k)P


R(k)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



L+13 end for



(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions






(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




10 end for


(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions





(Lminusk)




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



Hyperbolic damping

Empirical damping

02

03

04

05

06

07

1 2 3 4 5

Ave

rage

text

sim

ilari

ty

Link distance



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions







Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



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05 06 07 08 09

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05 06 07 08 09

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080085090095100

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05 06 07 08 09

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080085090095100

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05 06 07 08 09

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Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



05 06

07 08

09

5 10

15 20

25

080085090095100

τ

τ ge 095

αL



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions



5

10

15

20

25

05 06 07 08 09

L th

at m

axim

izes

Ken

dallrsquo

s τ

Exponent α




Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


What have we done






Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions








Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions


Thank you



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions



Notation

RewritingPageRank

FunctionalRankings

Algorithms

Comparison

Conclusions




Notation

Rewriting PageRank

Functional Rankings

Algorithms

Comparison

Conclusions

generalizing pagerank (pisa)

Technology

boldi andc

path pagerank

pagerank newman

functional rankings1

dampingfunctions for0

branchingp pagerank

notation1 p rewriting

p rewritingri