The document discusses the concept of 'network of networks' (non) and its applications across various domains, particularly in graph mining and biological network analysis. It presents models for cross-network association, ranking, and clustering while exploring motivational frameworks for these methodologies. Additionally, the document highlights recent works related to multi-layered networks, time series analysis, and visual comparisons in brain networks.

1. Arizona State University
Inside the Atoms: Mining
a Network of Networks and Beyond
Hanghang Tong
hanghang.tong@asu.edu
http://tonghanghang.org
- 1 -
@KDD BigMine 16: the 5th International Workshop on Big Data, Streams and Heterogeneous Source Mining

2. Arizona State University
Hospital Networks
US Power Grid
Biological Networks
Collaboration Networks
Observation: Graphs are everywhere!
- 2 -
Traffic Network
Brain Networks

3. Arizona State University
Graph Mining: An Overview
- 3 -
Observation: Mining stops at nodes/links (atom) level.
Q: Is there a level x (x=4, 5, …)? What is it?
graph
subgraph
node/link

4. Arizona State University
A Motivating Example: Cross-Network Association
(e.g., candidate gene prioritization problem)
- 4 -
§ Problem Definition
– Given: (1) two networks P and G,
and (2) their partial association A;
– Find: missing associations in A.
§ Solutions: Graph Ranking
– Given: a green node (disease);
– Find: the most relevant blue nodes (genes).
P
GA
A Powerful Primitive in (A1) drug discovery; (A2) social recommendation; (3) QA post-tagging, etc.
(PPI)
(Phenotype)

5. Arizona State University
A Motivating Example: Cross-Network Association
(e.g., candidate gene prioritization problem)
- 5 -
§ Problem Definition
– Given: (1) two networks P and G,
and (2) their partial association A;
– Find: missing associations in A.
§ Solutions: Graph Ranking
– Given: a green node (disease);
– Find: the most relevant blue nodes (genes).
§ Limitations: Each green node (disease) might
have its own PPI network!
O. Magger, Y. Y. Waldman, E. Ruppin, and R. Sharan. Enhancing the prioritization of disease-causing genes
through tissue specific protein interaction networks. PLoS Computational Biology, 8(9), 2012.
P
GA

6. Arizona State University
A Motivating Example: Cross-Network Association
(e.g., candidate gene prioritization problem)
- 6 -
• A Disease Network P
• A PPI Network G
a
b
c
d
GA
4
5
3
6
7
2
1P
• A Disease Network P
• A set of :ssue-specific PPI
Networks G1 ,…, G7
4
5
3
6
7
2
1P
A G1 a
b
d
c
G2
a
c
db
G7 a
b
d
c
… …
……

7. Arizona State University
A Set of Networks: More Applications
- 7 -
Collaborations
System of Systems
Brain Networks
Cyber-Physics Systems

8. Arizona State University
Roadmap
§ Motivations
§ NoN: A Network of Networks
– NoN Modeling
– NoN Mining
§ Beyond NoN
§ Some of Our Other Recent Work
- 8 -

9. Arizona State University
Modeling NoN
§ Q: How to represent a set of inter-connected
networks (e.g., Tissue-Specific PPI Networks)?
- 9 -
4
5
3
6
7
2
1P
A G1 a
b
d
c
G2
a
c
db
G7 a
b
d
c
… …
……

10. Arizona State University
Introducing the NoN Model
§ A: each green node (disease) itself is a network
- 10 -
NoN (A Network of Networks) := a triplet R = <G, A, θ>
• G: Main Network (the green, disease to disease networks)
• A: Domain Networks (the blue, tissue-specific PPI networks)
• θ: Mapping function (each green, main node à a blue, domain network)
J. Ni, H. Tong, W. Fan, X. Zhang: Inside the atoms: ranking on a network of networks. KDD 2014

11. Arizona State University
NoN Models: Examples
Applications The Main Network (G) Domain Networks (A)
Gene-Pheno Assoc. Disease Sim Network Tissue-specific PPI Nets
LBSN Geo-proximity network Social Networks
Brain Initiative Person-Person Network Brain Networks
Team of Teams Project Dependence Net Team Networks
Scholarly Data Res. Area Sim Network Collaboration Networks
- 11 -
NoN (A Network of Networks) := a triplet R = <G, A, θ>
• G: Main Network (the green, disease to disease networks)
• A: Domain Networks (the blue, tissue-specific PPI networks)
• θ: Mapping function (each green, main node à a blue, domain network)

12. Arizona State University
NoN - Generalizations
§ G1: Multi-layered NoN
– Candidate Gene Prioritization: Disease-tissue-
protein
– Geo-social networks: City-district-person
§ G2: Soft Mapping function θ
– 1-to-many, or many-to-many
- 12 -
• C. Chen, J. He, N. Bliss and H. Tong: “On the Connectivity of Multi-layered Networks: Models, Measures and
Optimal Control” ICDM 2015.

13. Arizona State University
NoN vs. Some Popular Multi-Network Models
§ They are all special case of our NoN model!
– Tensor: a special NoN with
1) A full clique main network (G);
2) All domain networks (A) sharing the same node sets
– Hypergraph: a special NoN with
1) All domain networks (A) being empty
– Multiplex: a special NoN with
1) Two-layers
2) All domain networks (A) sharing the same node sets
- 13 -

14. Arizona State University
Roadmap
§ Motivations
§ NoN: A Network of Networks
– NoN Modeling
– NoN Mining: Ranking and Clustering
§ Beyond NoN
§ Some of Our Other Recent Work
- 14 -

15. Arizona State University
NoN Mining - Ranking
A1: Given a disease (e.g. P1),
what are the most relevant
genes (blue nodes)?
- 15 -
A2: Who is most influential,
considering both the within-
and cross-area influence?

16. Arizona State University
Ranking on a Single Network
- 16 -
Node 4
Node 1
Node 2
Node 3
Node 4
Node 5
Node 6
Node 7
Node 8
Node 9
Node 10
Node 11
Node 12
0.13
0.10
0.13
0.22
0.13
0.05
0.05
0.08
0.04
0.03
0.04
0.02
1
4
3
2
5
6
7
9
10
8
11
12
0.13
0.10
0.13
0.13
0.05
0.05
0.08
0.04
0.02
0.04
0.03
Ranking vector
More red, more relevant
Nearby nodes, higher scores
Background
4r
r
H. Tong, C. Faloutsos, J.-Y. Pan: Fast Random Walk with Restart and Its Applications. ICDM 2006.
(best paper award at 2006, ICDM 2015 10-Yeart Highest Impact Paper Award)

17. Arizona State University
Ranking on a Single Network
- 17 -
Node 4
Node 1
Node 2
Node 3
Node 4
Node 5
Node 6
Node 7
Node 8
Node 9
Node 10
Node 11
Node 12
0.13
0.10
0.13
0.22
0.13
0.05
0.05
0.08
0.04
0.03
0.04
0.02
1
4
3
2
5
6
7
9
10
8
11
12
0.13
0.10
0.13
0.13
0.05
0.05
0.08
0.04
0.02
0.04
0.03
Ranking vector
More red, more relevant
Nearby nodes, higher scores
4r
r
Background
Footnote: “Maxwell Equation” for Web [Soumen Chakrabarti]
ri = c x A x ri + (1-c) x ei

18. Arizona State University
Ranking on a Single Network
- 18 -
Background
An Optimization Viewpoint of “Maxwell Equation” for Web (Symmetric A)
ri = c x A x ri + (1-c) x ei
= argmin cri'(I – A)ri + (1-c) x||ri – ei||2
Network Smoothness Query Preference

19. Arizona State University
Ranking on NoN
§ Optimization Formulation:
§ Intuition:
– Similar ranking scores for an overlapped node, if their
G(i,j) is high.
– A set of correlated g random walks
- 19 -J. Ni, H. Tong, W. Fan, X. Zhang: Inside the atoms: ranking on a network of networks. KDD 2014
#1: within-network smoothness #2: query preference#2: query preference
#3: cross-network consistency

20. Arizona State University
Ranking on NoN
§ Optimization Formulation:
§ Equivalence: J(r) = J(r1,…,rg)
– Intuition: a single R.W. on the integrated graph A
– Property: J(r) is positive-definite!
- 20 -
~
#1: within-network smoothness #2: query preference
#3: cross-network consistency

21. Arizona State University
Ranking on NoN
§ Equivalence: J(r) = J(r1,…,rg)
– Intuition: One single random walk on the integrated
graph A
– Property: J(r) is positive-definite!
§ Algorithms:
– #1: A linear algorithm à the optimal solution
– #2: Any existing fast solution on a single network
– #3: Further Speedup: O(T(m+ng)) à O(T(g log(g) + z))
• g << n; and z << m (key idea: using main network to do pruning)
- 21 -
~

22. Arizona State University
NoN Ranking - Results
- 22 -
A1: Candidate Gene Prioritization
• Which genes are most relevant wrt
disease a?
ROC Curve Comparison
A2: Co-authorship Prediction
• Which DM authors are most likely to
collaborate with a given Med author?
AUC and Accuracy

23. Arizona State University
NoN Mining - Clustering
§ Obj. Function:
- 23 -J. Ni, H. Tong, W. Fan, X. Zhang: Flexible and Robust Multi-Network Clustering. KDD 2015
Similar Intuition ! P-value vs. (biologically
meaningful) clusters
§ Results:

24. Arizona State University
Roadmap
§ Motivations
§ NoN: A Network of Networks
– NoN Modeling
– NoN Mining
§ Beyond NoN: From NoN to NoX
§ Some of Our Other Recent Work
- 24 -

25. Arizona State University
NoT: A Network of Time Series
§ Problem Definition
- 25 -
• Y. Cai, H. Tong, W. Fan and P. Ji: Fast Mining of a Network of Coevolving Time Series. SDM 2015.
• Y. Cai, H. Tong, W. Fan, P. Ji, Q. He:Facets: Fast Comprehensive Mining of Coevolving High-order Time Series. KDD 2015
§ Models &
Algorithms
§ Results
0 50 100 150
200
400
600
800
1000
1200
1400
frame #
coordinate
original
DCMF
DMF
dynaMMo
DCMFdynaMMo
DMF
MARKER PLACEMENT GUIDE
The marker placement in this document is only one of many possible combinations. T his
guide will only show the standard marker placement that’s being used in the motion
capture laboratory. The marker placement in this guide resembles the one that is shown
and explained in the Vicon 512 manual. As such, the Vicon 512 Manual can offer
additional information. The difference with the marker set in this document from the
Vicon 512 Manual is the addition of 4 m arkers, namely RARM, L ARM, RLEG, a nd
LLEG.
Before starting, below are some general rules of thumb one should follow:
• Have the person who’s going to be motion captured wear tight fitting clothes—strap
down any areas of the clothing that is loose. The marker balls’ position should move
as little as possible and should be properly seen.
• Place the marker balls as close to the boneas possible. This follows therule of
having the marker balls stay stationary during movement.

26. Arizona State University
iBall: A Network of Regression Models
- 26 -
• Y. Yao, H. Tong, F. Xu, J. Lu: Predicting long-term impact of CQA posts: a comprehensive viewpoint. KDD 2014
• L. Li, H. Tong: The Child is Father of the Man: Foresee the Success at the Early Stage. KDD 2015.
• “Data Mining Reveals the Secret to Getting Good Answers”, MIT Technology Review, 2013
§ Results
§ Models & Algorithms§ Problem Definition
D1
D3
D2 D4

27. Arizona State University
Fascinate: Cross-Layer Dependence
Inference on Multi-Layered Networks
- 27 -
§ Results
§ Methods§ Problem Definition
Infer Unobserved Cross-Layer Links Cross-Layer Inference = Collective CF
Effectiveness Efficiency
• C. Chen, J. He, N. Bliss and H. Tong: “On the Connectivity of Multi-layered Networks: Models, Measures and Optimal Control” ICDM15.
• C. Chen, H. Tong, L. Xie, L. Ying and Q. He: “FASCINATE: Fast Cross-Layer Dependence Inference on Multi-layered Networks”, KDD16, 3:15pm, Monday, Plaza Room A/B

28. Arizona State University
Conclusion: a Network of X
§ Summary
– NoN: Network + Networks
– NoT: Network + Time Series
– iBall: Network + Regression
– Fascinate: Network + Inference
§ Take Home Messages
– Modeling: `No’ (i.e., a Network of X) as the answer
• Networks as data à as context
– Algorithms: Networks as the contextual regularizer
- 28 -

29. Arizona State University
Roadmap
§ Motivations
§ NoN: A Network of Networks
§ Beyond NoN
§ Some of Our Other Recent Work
– Team Replacement
– TravelModeLogger
– BrainQuest
- 29 -
– Network Alignment
– Optimal Networks
– Visual Influence Sum

30. Arizona State University
Replacing the Irreplaceable:
Team Replacement Recommendation
- 30 -
• L. Li, H. Tong, N. Cao, K. Ehrlich, Y.-R. Lin and N. Buchler: Replacing the Irreplaceable: Fast Algorithms for Team Member
Recommendation, WWW 2015
• N. Cao, Y.-R. Lin, L. Li, H. Tong: g-Miner: Interactive Visual Group Mining on Multivariate Graphs, ACM CHI 2015
• System prototype & video demo: http://team-net-work.org
§ Problem Definition
§ System
§ Sol.
§ Results

31. Arizona State University
Travel Mode Identification w/ Smartphones
- 31 -
§ Prob.Dfn
• X. Su, H. Tong and P. Ji: Accelerometer-based Activity Recognition on Smartphone. CIKM 2014
• X. Su, H. Caceres, H. Tong and Q. He: Travel Mode Identification with Smartphones. TRB 2015
§ Method
§ Results
§ Open Challenges
² Battery Consumption (sampling
rates, sensor selection)
² On-line algorithms
² Adaptive (summer vs. winter;
high-way vs. local)

32. Arizona State University
BrainQuest: Visual Brain Comparison
- 32 -
Quest brains to spot picture diff.
• L. Shi, H. Tong, X. Mu: BrainQuest: Perception-Guided Visual Brain Comparison, ICDM 2015
• L. Shi, H. Tong, M. Daianu, X. Mu and P. Thompson Block-wise Human Brain Network Visual Comparison Using NodeTrix Representation. VIS'16

33. Arizona State University
BrainQuest: Visual Brain Comparison
- 33 -
Quest computers to spot brain diff.
• L. Shi, H. Tong, X. Mu: BrainQuest: Perception-Guided Visual Brain Comparison, ICDM 2015
• L. Shi, H. Tong, M. Daianu, X. Mu and P. Thompson Block-wise Human Brain Network Visual Comparison Using NodeTrix Representation. VIS'16

34. Arizona State University
BrainQuest: Visual Brain Comparison
- 34 -
Quest computers to spot brain diff.
AD group (n1) Control group (n2)
• L. Shi, H. Tong, X. Mu: BrainQuest: Perception-Guided Visual Brain Comparison, ICDM 2015
• L. Shi, H. Tong, M. Daianu, X. Mu and P. Thompson Block-wise Human Brain Network Visual Comparison Using NodeTrix Representation. VIS'16

35. Arizona State University
BrainQuest: Visual Brain Comparison
- 35 -
§ VAFramework
§ Model & Algorithm
§ ProblemDfn.
§ Results
Spot structural diff. between
two groups of brain networks
• L. Shi, H. Tong, X. Mu: BrainQuest: Perception-Guided Visual Brain Comparison, ICDM 2015
• L. Shi, H. Tong, M. Daianu, X. Mu and P. Thompson Block-wise Human Brain Network Visual Comparison Using NodeTrix Representation. VIS'16

36. Arizona State University
Query-Specific Optimal Networks
- 36 -
L. Li, Y. Yao, J. Tang, W. Fan, H. Tong: QUINT: On Query-Specific Optimal Networks. KDD 2016.
10:00am, Monday, Plaza Room A/B
§ Goal: Optimal Networks
– Query-Specific
– Optimal Topology + Weights
– On-line Learning
§ + Error Estimation
§ Results
§ Methods: VERY efficient
way to estimate
Accuracy(MAP)Scalabilitys x
ij
Query node
Positive node
@Q(x, s)
@As(i, j)
Q(j, s) ⇥ Q(x, i)
/
Neighbor of Neighbor ofs x

37. Arizona State University
Attributed Network Alignment
• D. Koutra, H. Tong, D. Lubensky:BIG-ALIGN: Fast Bipartite Graph Alignment. ICDM 2013.
• S. Zhang and H. Tong: Final: Fast Attributed Network Alighnment. KDD 2016, 3:15pm, Monday, Plaza Room A/B
§ Formulation
§ Algorithms
§ ProblemDfn.
§ Results
Accuracy vs. Time Accuracy vs. Noise
• Iterative Alg.
• Global Optimal
• Same Complexity as
ISORANK
• Further Speed-up
• Low-Rank Approximation
• On-Query Alignment (Linear)

38. Arizona State University
Vegas: Influence Graph Visual Summarization
- 38 -
• L. Shi, H. Tong, J. Tang and C. Lin: Flow-based Influence Graph Visual Summarization, ICDM 2014
• L. Shi, H. Tong, J. Tang, C. Lin: VEGAS: Visual influEnce GrAph Summarization on Citation Networks. TKDE 2015
§ Solution
§ Results
“Stochastic High-Level Petri Net and Applications”
§ Prob. Dfn.
Who/What How/Why

39. Arizona State University
Q&A
Inside the atom is a whole new world!
- 39 -
• “A whole new world
• Every turn a surprise
• With new horizons to pursue
• Every moment red-letter
……”

40. Arizona State University
§ Collaborators:
– Norbou Buchler, Nan Cao, Madelaine Daianu, Kate Ehrlich, Wei
Fan, Qing He, Ping Ji, Yu-ru Lin, Lei Shi, Chuang Lin, Jie Tang,
Paul M. Thompson, Lei Xie, Yuan Yao, Lei Ying, Xiang Zhang
§ Students:
– Liangyue Li
– Chen Chen
– Yongjie Cai (now at Google)
– Xing Su
– Si Zhang
Acknowledgement
- 40 -