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From complex systems to networks:
discovering and modelign the higher order network
Nitesh Chawla
Frank M. Freimann Profes...
2
Our world is complex
Ship 1 Shanghai à Singapore à Los Angeles à …
Ship 2 Tokyo à Singapore à Seattle à …
Ship 3 Shangha...
3
Our world is complex
Ship 1 Shanghai à Singapore à Los Angeles à …
Ship 2 Tokyo à Singapore à Seattle à …
Ship 3 Shangha...
4
Our world is complex
User 1 Company ranking à Job listing à Applyà …
User 2 Weather à Homepage à News à …
User 3 News à ...
5
Our world is complex
User 1 Company ranking à Job listing à Applyà …
User 2 Weather à Homepage à News à …
User 3 News à ...
6
Complex systems
Trajectories	of	vehicles
Flow	of	information
Spread	of	disease
7
Data
• Ship movements
• Web clickstreams
• Phone call cascades
• … …
Network
representation
• Global shipping
network
• ...
8
Complex systems: representation
How to best represent such big data,
and reveal the intrinsic connections
concisely and ...
9
• Ignore higher order
• Modify existing network analysis algorithms
10
Global shipping movements
11
Global shipping movements à network
12
Goals
Network
representation
Accuracy
Compatibility
Scalability
13
Enriching the network
Conventionally: every node
represents a single entity
(location, state, etc.)
( )
( )
1
1 1( | ) ...
14
Enriching the network
Conventionally: every node
represents a single entity
(location, state, etc.)
Now: break down nod...
15
Enriching the network
Conventionally: every node
represents a single entity
(location, state, etc.)
Now: break down nod...
16
Enriching the network
Conventionally: every node
represents a single entity
(location, state, etc.)
Now: break down nod...
17
Fixed-order Variable-order
Assuming a fixed order
beyond the second order
becomes impractical
because “higher-order
Mar...
18
Fixed-order Variable-order
19
Variable orders in HON
Scalable for big data
20
How to construct HON?
Raw data
• Sequential data
Rule
extraction
• Which nodes need to
be split into higher-
order node...
21
Rule extraction
22
Network wiring
A
• Convert all first-order rules into edges
B
• Convert higher-order rules
• Add higher-order nodes whe...
Effectiveness
24
Higher-order dependencies revealed by HON
Data # Records
Dependencies
revealed
Similar observations
Ship movement 3,415...
Application: clustering
Controlling species invasion through the global shipping network
26
Invasive species
Zebra mussels @ Great Lakes
Clogging water pipes, attach to boats
Photos: Great Lakes Environmental Re...
27
Ship-borne species invasion
Picture from GloBallast Programme 2002
28
Clustering: first-order network
29
Clustering: higher-order network
30
Arctic port connections
31
Arctic port connections
Norway
Alaska
Greenland
Iceland
Russia &
others
Application: ranking
Web page access behaviors for server optimization and advertising
33
Ranking on clickstream network
User 1 Company ranking à Job listing à Applyà …
User 2 Weather à Homepage à News à …
Use...
34
Ranking on clickstream network
35
Ranking on clickstream network
• 26% pages show more
than 10% changes in
ranking
• More than 90% pages lose
PageRank sc...
Visualization & interactive exploration
37
Summary
Higher-order
network
Accuracy
Compatibility
Scalability
38
Visualization & interactive exploration
39
Broad Applicability
Trajectories	of	vehicles
Flow	of	information
Spread	of	disease
40
Summary
Data
• Ship movements
• Web clickstreams
• Phone call cascades
• … …
Network
representation
• Global shipping
n...
41
Full paper
• Jian Xu, Thanuka L. Wickramarathne, and Nitesh V. Chawla.
"Representing Higher-order Dependencies in Netwo...
42
Acknowledgements: Funding
Thank you!
Nitesh V. Chawla
nchawla@nd.edu
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From complex Systems to Networks: Discovering and Modeling the Correct Network"

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From complex Systems to Networks: Discovering and Modeling the Correct Network" by Nitesh Chawla as part of the Cognitive Systems Institute Speaker Series
Nitesh Chawla is the Frank M. Freimann Professor of Computer Science and Engineering, and  director of the research center on network and data sciences (iCeNSA) at the University of Notre Dame.

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From complex Systems to Networks: Discovering and Modeling the Correct Network"

  1. 1. From complex systems to networks: discovering and modelign the higher order network Nitesh Chawla Frank M. Freimann Professor of Computer Science and Engineering Director, iCeNSA 3/2/17 11:17 AM
  2. 2. 2 Our world is complex Ship 1 Shanghai à Singapore à Los Angeles à … Ship 2 Tokyo à Singapore à Seattle à … Ship 3 Shanghai à Singapore à Hong Kong à … Ship 4 Hong Kong à Singapore à Seattle à … … … … … Ship trajectories
  3. 3. 3 Our world is complex Ship 1 Shanghai à Singapore à Los Angeles à … Ship 2 Tokyo à Singapore à Seattle à … Ship 3 Shanghai à Singapore à Hong Kong à … Ship 4 Hong Kong à Singapore à Seattle à … … … … … Ship trajectories Global shipping network
  4. 4. 4 Our world is complex User 1 Company ranking à Job listing à Applyà … User 2 Weather à Homepage à News à … User 3 News à Sports à Scores à … User 4 Events à Homepage à Weather à … … … … … Web page clickstreams
  5. 5. 5 Our world is complex User 1 Company ranking à Job listing à Applyà … User 2 Weather à Homepage à News à … User 3 News à Sports à Scores à … User 4 Events à Homepage à Weather à … … … … … Web page clickstreams Web traffic network
  6. 6. 6 Complex systems Trajectories of vehicles Flow of information Spread of disease
  7. 7. 7 Data • Ship movements • Web clickstreams • Phone call cascades • … … Network representation • Global shipping network • Web traffic network • Social network • … … Network analysis • Clustering • Ranking • Link prediction • Anomaly detection • … …
  8. 8. 8 Complex systems: representation How to best represent such big data, and reveal the intrinsic connections concisely and accurately?
  9. 9. 9 • Ignore higher order • Modify existing network analysis algorithms
  10. 10. 10 Global shipping movements
  11. 11. 11 Global shipping movements à network
  12. 12. 12 Goals Network representation Accuracy Compatibility Scalability
  13. 13. 13 Enriching the network Conventionally: every node represents a single entity (location, state, etc.) ( ) ( ) 1 1 1( | ) t t t t t t tj W i i P X i X i W i j + + + ® = = = ®å
  14. 14. 14 Enriching the network Conventionally: every node represents a single entity (location, state, etc.) Now: break down nodes into higher-order nodes that carry different dependency relationships ( ) ( ) 1 1 1( | ) t t t t t t tj W i i P X i X i W i j + + + ® = = = ®å
  15. 15. 15 Enriching the network Conventionally: every node represents a single entity (location, state, etc.) Now: break down nodes into higher-order nodes that carry different dependency relationships ( ) ( ) 1 1 1( | ) t t t t t t tj W i i P X i X i W i j + + + ® = = = ®å ( )1 ( | ) | ( | ) ( | ) t t k W i h j P X j X i h W i h k + ® = = = ®å
  16. 16. 16 Enriching the network Conventionally: every node represents a single entity (location, state, etc.) Now: break down nodes into higher-order nodes that carry different dependency relationships ( ) ( ) 1 1 1( | ) t t t t t t tj W i i P X i X i W i j + + + ® = = = ®å ( )1 ( | ) | ( | ) ( | ) t t k W i h j P X j X i h W i h k + ® = = = ®å Compatible with existing tools!
  17. 17. 17 Fixed-order Variable-order Assuming a fixed order beyond the second order becomes impractical because “higher-order Markov models are more complex” due to combinatorial explosion --- Rosvall et al. (Nature Comm. 2014)
  18. 18. 18 Fixed-order Variable-order
  19. 19. 19 Variable orders in HON Scalable for big data
  20. 20. 20 How to construct HON? Raw data • Sequential data Rule extraction • Which nodes need to be split into higher- order nodes, and how high the orders are Network wiring • Connecting nodes representing different orders of dependency HON • Use HON like the conventional network for analyses
  21. 21. 21 Rule extraction
  22. 22. 22 Network wiring A • Convert all first-order rules into edges B • Convert higher-order rules • Add higher-order nodes when necessary C • Rewire edges • The edge weights are preserved D • Rewire remaining edges
  23. 23. Effectiveness
  24. 24. 24 Higher-order dependencies revealed by HON Data # Records Dependencies revealed Similar observations Ship movement 3,415,577 Up to 5th order N/A Clickstream 3,047,697 Up to 3rd order “… appear to saturate at k = 3 for Yahoo… browsing behavior across websites is definitely not Markovian but can be captured reasonably well by a not-too-high order Markov chain.” --- Chierichetti et al. (2012) Retweet 23,755,810 N/A
  25. 25. Application: clustering Controlling species invasion through the global shipping network
  26. 26. 26 Invasive species Zebra mussels @ Great Lakes Clogging water pipes, attach to boats Photos: Great Lakes Environmental Research Lab; TIME & LIFE Images, Getty Images $120 billion / year damage & control costs
  27. 27. 27 Ship-borne species invasion Picture from GloBallast Programme 2002
  28. 28. 28 Clustering: first-order network
  29. 29. 29 Clustering: higher-order network
  30. 30. 30 Arctic port connections
  31. 31. 31 Arctic port connections Norway Alaska Greenland Iceland Russia & others
  32. 32. Application: ranking Web page access behaviors for server optimization and advertising
  33. 33. 33 Ranking on clickstream network User 1 Company ranking à Job listing à Applyà … User 2 Weather à Homepage à News à … User 3 News à Sports à Scores à … User 4 Events à Homepage à Weather à … … … … …
  34. 34. 34 Ranking on clickstream network
  35. 35. 35 Ranking on clickstream network • 26% pages show more than 10% changes in ranking • More than 90% pages lose PageRank scores, while a few pages gain significant scores No changes to the ranking algorithm
  36. 36. Visualization & interactive exploration
  37. 37. 37 Summary Higher-order network Accuracy Compatibility Scalability
  38. 38. 38 Visualization & interactive exploration
  39. 39. 39 Broad Applicability Trajectories of vehicles Flow of information Spread of disease
  40. 40. 40 Summary Data • Ship movements • Web clickstreams • Phone call cascades • … … Network representation • Global shipping network • Web traffic network • Social network • … … Network analysis • Clustering • Ranking • Link prediction • Anomaly detection • … …
  41. 41. 41 Full paper • Jian Xu, Thanuka L. Wickramarathne, and Nitesh V. Chawla. "Representing Higher-order Dependencies in Networks." Science Advances 2, e1600028 (2016) • Jun Tao, Jian Xu, Chaoli Wang, and Nitesh V. Chawla. ”HonVis: Visualizing and Exploring Higher Order Networks." IEEE PacificViz, 2017.
  42. 42. 42 Acknowledgements: Funding
  43. 43. Thank you! Nitesh V. Chawla nchawla@nd.edu

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