Link prediction with the linkpred tool

Measuring scholarly impact: Methods and practice
Link prediction with the linkpred tool
Raf Guns
University of Antwerp
raf.guns@uantwerpen.be

If you want to follow along…
Download and install Anaconda Python from
http://continuum.io/downloads
Download the example data from http://bit.ly/1HpZvIa

“A pair of scientists who have five mutual previous
collaborators, for instance, are about twice as likely to
collaborate as a pair with only two, and about 200 times as
likely as a pair with none.” (Newman, 2001; emphasis mine)

Agenda
What is link prediction? (and why?)
Example data
The linkpred tool
Link prediction in practice
Conclusion

Networks in informetrics
 Citation
 Papers
 Journals
 Authors
 Patents
 …
 Collaboration
 Authors
 Institutions
 Countries
 …
 Co-citation
 Bibliographic coupling
 Web links
 And so on

Definitions
A network G = (V, E) consists of:
 A set of nodes or vertices V
 A set of links or edges E
Each link connects two nodes from V
Neighbourhood N(v) of node v: all nodes connected to v
Node degree |N(v)| of v: number of connected nodes =
number of items in set N(v)

Change in networks
Most networks are not static, e.g. in collaboration network:
 New authors appear
 Old authors disappear
 New collaborations are initiated
 Previous collaborators stop collaborating

Change in networks
Some changes are more plausible than others

Change in networks
Different mechanisms have been identified
 Assortativity: similar nodes are more likely to connect
 Preferential attachment: well-connected nodes attract
more new connections
 Cf. cumulative advantage, Matthew effect

The link prediction question
Liben-Nowell and Kleinberg (2003, 2007):
“Given a snapshot of a social network, can we infer which
new interactions among its members are likely to occur
in the near future?”

Link prediction steps
1. Data gathering
2. Preprocessing
3. Prediction
4. Evaluation

Why link prediction?
 You want to know which links will appear in the future
 Recommendation
 Finding missing links
 Finding ‘anomalous’ links (correct or incorrect)
 Evaluating network formation and evolution models

Data
Guns and Rousseau (2013)
 Collaboration between
cities in Africa and
South-Asia
 Topic: malaria
 In three consecutive
time periods
Available as three Pajek
network files:
http://bit.ly/1HpZvIa

About
https://github.com/rafguns/linkpred
Cross-platform (written in Python)
Open source: BSD license
Command-line tool!
Alternative: LPmade
(https://github.com/rlichtenwalter/LPmade)

How and where to get linkpred
1. Install Anaconda Python:
http://continuum.io/downloads
2. Open command-line window
3. Run command:
> pip install
https://github.com/rafguns/linkpred/archive/stable.zip
4. Wait until installation is finished

Basic usage
> linkpred
Should display brief usage instructions
> linkpred --help
Displays more complete help output

Basic usage
> linkpred training-network-file --predictors
predictor --output output-type
Read the network in training-network-file, predict using
predictor and give output of output-type
> linkpred training-network-file test-network-
file --predictors predictor --output output-
type
Read the network in training-network-file, compare with test-
network-file, predict using predictor and give output of
output-type

Preprocessing
Nodes may also appear and disappear
 Restrict to intersection of node sets of training and test
network
 Only where test network is available
Restrict by degree (default: only discard isolate nodes)
Directed networks: not supported
 Convert to undirected first

Prediction: choosing predictors
Local
 AdamicAdar
 AssociationStrength
 CommonNeighbours
 Cosine
 DegreeProduct
 Jaccard
 MaxOverlap
 MinOverlap
 NMeasure
 Pearson
 ResourceAllocation
Global
 GraphDistance
 Katz
 RootedPageRank
 SimRank
Other
 Community
 Copy
 Random

Local predictors
Tendency towards triadic closure
Number of common neighbours is a simple but powerful predictor.

Local predictors
 Common neighbours
 Normalizations of common neighbours
 Jaccard coefficient, cosine measure…
 Adamic/Adar (Adamic & Adar, 2003)
𝑊 𝑢, 𝑣 =
𝑧∈𝑁 𝑢 ∩𝑁(𝑣)
1
log |𝑁 𝑧 |

Weighted networks
In weighted networks, links have weights (e.g. number of
joint papers, number of citations…)
Link weights : often ignored!!
Most predictors in linkpred can use link weights
 General idea: higher link weight (e.g., more common
papers), stronger connection

Global predictors
Graph distance: lowest
number of links needed to
travel from a to b
 problem: small world
phenomenon

Global predictors
Katz (1953):
𝑊 𝑣𝑖, 𝑣𝑗 =
𝑘=1
∞
𝛽 𝑘 𝑎𝑖𝑗
(𝑘)
 𝑎𝑖𝑗 : 1 if i and j are linked, 0 otherwise
 𝑎𝑖𝑗
(𝑘)
: number of walks with length k from i to j
 𝛽: parameter, “probability of effectiveness of a single
link”
 Longer walks: lower effectiveness

Global predictors
Rooted PageRank

Global predictors
SimRank (Jeh & Widom, 2002)
“Objects that link to similar objects are similar
themselves.”
𝑊 𝑢, 𝑣 =
𝑐
|𝑁(𝑢)| ∙ |𝑁(𝑣)|
)𝑝∈𝑁(𝑢 )𝑞∈𝑁(𝑣
)𝑊(𝑝, 𝑞
Starting point: a node is maximally similar to itself:
W(v, v) = 1

Demo
Predict
Save predictions to file  import in e.g. Excel

Evaluation
Step 4: ‘How well does it work?’
How?  compare to ‘known good’ test network
Four groups:
Link Non-link
Predicted True positive False positive
Not predicted False negative True negative

Evaluation
Simply save results to text file:
--output cache-evaluations
Create chart:
 Recall-precision
 ROC

Evaluation: recall-precision
Precision: fraction of
correct predictions
Recall: fraction of correctly
predicted links

Evaluation: ROC
False positive rate:
Fraction of incorrectly
predicted links
True positive rate:
fraction of correctly
predicted links
(= recall)

Profiles
A simple way to save and reuse the configuration of a
complex prediction run (options, predictors, parameters…)
Usage example:
> linkpred network-file --profile profile.yml
Format: YAML, see https://en.wikipedia.org/wiki/YAML

Example profile
predictors:
- name: AdamicAdar
displayname: Adamic/Adar
- name: GraphDistance
displayname: Graph distance
parameters:
weight: weight
- name: SimRank
displayname: SimRank (c=0.4)
parameters:
c: 0.4
- name: SimRank
displayname: SimRank (c=0.8)
parameters:
c: 0.8
output:
- cache-predictions
- recall-precision

About link prediction
Link prediction is possible because link formation is not a
purely random process
Limitations:
 Unaware of social and other circumstantial factors
 Which predictor is ‘best’ for a concrete situation?
 Trade-off between prediction accuracy and non-triviality

About linkpred
Relatively simple but powerful
Limitations:
 Not suitable for very large and/or dense networks
 Does not incorporate more complex setups like predictor
combinations, machine learning etc.
All results can be exported for analysis in other software
(cache-*)
Open source: contributions welcome! 

Link prediction with the linkpred tool

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Editor's Notes