PageRank extensions and a new way to measure scientific impacts

PAGERANK EXTENSIONS AND A NEW

WAY TO MEASURE SCIENTIFIC

IMPACTS

Son NGUYEN KIM

1

OUTLINE

I. Context

II. What is PageRank?

III. PageRank extensions

IV. Pira Algorithm

V. Scientific impact measures

VI. Database

VII. Future works

2

I. CONTEXT

1. SNOW

2. PIRA

3

1. SNOW

Create a pertinent ranking method for a dynamic context (forum, Twitter, Facebook, …)

Example: forum, YouTube

4

2. PIRA (PUBLICATION INDUCED RESEARCH ANALYSES)

Validation project for Snow

Create new PageRank-like method to rank authors and scientific publications

Author paper graph

Author PaperAuthorship

Citation

5

II. WHAT IS PAGERANK?

1. How does Google work?

2. Definition of PageRank

3. Damping factor

6

1. HOW DOES GOOGLE WORK?

Crawling DB

Calcu

late web

site’ score

DB

PageRank

Website PageRank-score

Google 1000000

Yahoo 900000

…

Le Monde 1000

…

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1. HOW DOES GOOGLE WORK?

David Beckham DBDavid + beckham

Websites relative

to keywords

Website Request-score

davidbeckham.com 1000

lequipe.fr 999

…

Ex: Request-score = number of keyword appearance * PR-score8

2. DEFINITION OF PAGERANK

Random surfer model

Score of a website (vertex) is the probability it is visited in an infinite journey

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3. DAMPING FACTOR

Resemblance to Markov chain:

State space = set of vertices

State transition = edge

Irreducibility => Stationary distribution

Irreducibility = connectedness

Graph is strongly connected => Score determined and unique

And if the graph is not strongly connected?

10

A

C

B

D

A

3. DAMPING FACTOR

The probability a web surfer gets bored and decides to jump to a random website

The state transition is non-zero between all pair of vertices

11

A

C

B

D

A

C

B

D

df / 4

1-df

3. DAMPING FACTOR EFFECT

Change score order of two vertices !

Score(V3) > Score(V5)

Score(V3) < Score(V5)

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III. PAGERANK EXTENSIONS

1. Extended graph

2. P-weight

3. C-weight

4. Path Diversity

13

1. EXTENDED GRAPH

Different vertices’ types, different edges’ types

More general: vertices and edges can carry properties

Type is short-cut for property « type »

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Company website----------------------------

AdresseProfit

.....

Personal blog----------------------------

CreatorTheme

.....

Commercial link

Partenariat link

Friend link--------------yearplace

Publicity link-------------------Price

2. P-WEIGHT

Assign different probability weight

(p-weight) to different edges

This value determines the

appreciation of an object towards

another

Ex: in Facebook, “comment” edge

vs. “like” edge

This value is relative

A

B

C

P-weight = 1

P-weight = 2

15

3. C-WEIGHT

V1 V2

e• Increment differently the counter on the journeycounter(V2) = counter(V2) + c-weight(e)

• Represents the appreciation a vertex gives to another

• Example: author

paper

Wrote: c-weight = 0

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C-WEIGHT VS P-WEIGHT

Score(V3) > Score(V5)

Score(V3) = Score(V5)

• Two ways to favor a vertex• Are they equivalent ?

17

4. PATH DIVERSITY

Remember the journey

Add a additional checking process before incrementing counter(w): compare w to previous vertices

Ex: if w appears already in this list, it is probable that the visitor has fallen in a cycle (ex: w --> w1 --> w2 --> w) and so w should not receive any credit

w w1

w218

IV. PIRA ALGORITHM

1. Author paper graph

2. Journey extensions

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1. AUTHOR PAPER GRAPH

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Paper set Author set

cite

wrote

IsWrittenBy

Score of an author/ a paper is the probability it is visited in an infinite journey on the author paper graph

2. JOURNEY EXTENSIONS

a) Choosing type before choosing nodes

b) C-weight

c) P-weight

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2. JOURNEY EXTENSION

A. CHOOSING TYPE BEFORE CHOOSING NODE

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P

AA

A

P

P

1/6

1/6

1/6

1/4

1/4



Score(A2) = score(A1) !

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If « wrote » edge and « cite » edge are treated equally

With the extension « choosing type firstly »

Score(A2) = score(A1) / n

2B. JOURNEY EXTENSION:

C-WEIGHT FOR “WROTE” EDGE

C-weight(wrote) = 0

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An author does not give directly appreciationtowards his papers:

A P

wrote

2B. JOURNEY EXTENSION:

C-WEIGHT FOR “WROTE” EDGE

If no c-weight(wrote)

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Score(P2) > Score(P1)

If c-weight(wrote) = 0 Score(P2) = Score(P1)

2C. JOURNEY EXTENSION

P-WEIGHT FOR “WROTE” EDGE

If no p-weight, then Score(P3) < Score(P4) !

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C-weight(wrote) = 0 => Score(P1) = Score(P2)

Score(P3) = Score(P4)

2C. JOURNEY EXTENSION:

P-WEIGHT FOR “WROTE” EDGE

pe

a

Solution:P-weight(e) = 1 / nbAuthor(p)

P-weight(w1) = P-weight(w2) + P-weight(w3) + P-weight(w4)



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V. SCIENTIFIC IMPACT MEASURES

1. Author measures

a) Classic measures

b) Scenarios

c) Summary

2. Paper measures

a. Classic measures

b. Summary

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1. AUTHOR MEASURES

A. CLASSIC MEASURES

Publication

Citation

H-Index, G-Index

PR-A: PageRank on Author graph

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1A. CLASSIC MEASURES

PUBLICATION

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A

P

P

P

wrote

Publication-score(A) = 3


CITATION

32

A

P

P

P

wrote

Citation-score(A) = 5

P

P

P

cite


H-INDEX

33

A

P

P

P

wrote

HIndex-score(A) = 2

P

P

P

cite


PR-A: PAGERANK ON AUTHOR GRAPH

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• Author graph

• P-weight

p qAB

1

P-weight = 1/6A’

A’’ B’

cite

wrote

1. AUTHOR MEASURES

B. SCENARIOS

Quality of paper

Number of co-authors

Quality of citing papers

Self citation

Score range

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1B. SCENARIO: QUALITY OF PAPER

Quality of paper

score(A1) > score(A2)

Publication No

Citation Yes

H-Index Yes

PR-A Yes

Pira Yes

36Score(A1) > Score(A2)

1C. SCENARIO: NUMBER OF CO-AUTHORS

score(A1) < score(A4)

Publication No

Citation No

H-Index No

PR-A Yes

Pira Yes

Number of co-authors

37Score(A1) < Score(A2)

1D. SCENARIO: QUALITY OF CITING PAPER


Publication No

Citation No

H-Index No

PR-A No …

Pira Yes


38

Score(A1) > Score(A2)

1E. SCENARIO: SELF-CITATION


Publication No

Citation No

H-Index No

PR-A Yes

Pira Yes

Self-citation

39Score(A1) < Score(A2)

1G. SCENARIO: SCORE RANGE

Millions of authors

Score range (in general)

Publication: < 1000

Citation < 20000

H-Index < 100, G-Index < 200

PR-A, Pira: infinity

Sufficient score range

Publication No

Citation No

H-Index No

PR-A Yes

Pira Yes40

1. AUTHOR MEASURES

C. SUMMARY

Criteria/Measures Publication Citation H-Index PR-A Pira

Paper quality No Yes Yes Yes Yes

Number of co-authors No No No Yes Yes

Citing papers' quality No No No No Yes

Self-citation's effect No No No Yes Yes

Domain specific No No No Yes Yes

Score range No No No Yes Yes

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2. PAPER MEASURES

A. CLASSIC MEASURES

Citation

PR-P: PageRank for papers

Papers

Cite

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2B. SUMMARY FOR PAPER MEASURES

Criteria/Measures Citation PR-P Pira

Citing papers' quality No Yes Yes

Self-citation's effect No Yes Yes

Domain specific No Yes Yes

Score range No Yes Yes

Citing authors' quality No No Yes

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VI. DATABASE

Aggregate DBLP and CiteSeerX

246039 authors (73241 in DBLP) and 281207 papers(67772 in DBLP)

The theoretic scenarios have been found

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VII. FUTURE WORKS

Pira

Optimization : >10 times faster than matrix-multiplication algorithm

Apply path diversity

Take into account the content

Create a complete search engine for scientific world

Snow

A lot of work to do …

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Thank you !

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1D. SCENARIO: QUALITY OF CITING PAPER


Publication No

Citation No

H-Index No

PR-A No …

Pira Yes


PR-A vs Pira47



Score(A2) = score(A1) !Score(P2) = Score(A1) + score(A2)

Score (A2) = Score(P2) / 2

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Choose type first !

Score(P2) = Score (A2) + Score(A1) / n

Score(A2) = Score(P2) / 2Score(A2) = Score(A1) / n

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1F. SCENARIO: DOMAIN SPECIFIC

Domain specific: the average number of citations varies from domain to domain.

An average paper is cited about 6 times in life sciences and < 1 times in mathematics

Domain specific

Publication No

Citation No

H-Index No

PR-A Yes

Pira Yes

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PR-P VS PIRA

Quality of citing authors

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VII. SNOW ON FORUM

1. Forum graph

2. Algorithm

3. Demonstration

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1. FORUM GRAPH

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2. ALGORITHM

Post User

wasWrittenBy, p-weight = 5

Wrote, c-weight = 0

Positive, c-weight = 2

Negative, c-weight = -2

• Path diversity = 6

• C-weight & P-weight

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3. DEMONSTRATION

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3. DAMPING FACTOR

The probability df a web surfer gets bored and decides to jump to a random website

In practice, Google set df to 0.15

The score of a website is the probability it is visited in a infinite journey on the web-graph by following 2 rules:

When a visitor arrives at a website A that has at least one outgoing links (i.e. having links to at least one website)

with probability df, the visitor picks a random website (in the set of all websites) to jump to and restart the journey

with probability 1 - df the visitor picks randomly an outgoing link of A to follow

If this website does not have any outgoing links, then the visitor picks a random website to restart the journey from.

Adaption to Markov chain

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PageRank extensions and a new way to measure scientific impacts

Data & Analytics

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