1. Jie Tang Computer Science, Tsinghua University @WWW’2017
Computational Models for Social Network Analysis —mining big social networks (Part IV: Representation)
Jie Tang
Computer Science, Tsinghua University
@WWW’2017

2. Fundamental question
How to represent users, relationships, and groups in a big network?
Fast representation
Embedding representation

3. Example: Who are Similar to Barabási?
[1] Jing Zhang, Jie Tang, Cong Ma, Hanghang Tong, Yu Jing, and Juanzi Li. Panther: Fast Top-k Similarity Search on Large Networks. KDD'15. pp

4. Similar Authors in AMiner.org

5. Let us recall Similarity Search…

6. Does not really consider the topology
Common Neighbors
Two users in a social network are similar if they share many of the same friends (Jaccard, 1901).
Does not really consider the topology
social

7. SimRank
SimRank is a general similarity measure, based on a simple and intuitive graph-theoretic model (Jeh and Widom, KDD’02).

8. Cannot support real-time search!
Path Similarity
Intuition: two vertices are similar if they frequently appear on the same paths. v2 v1 v3 v5 v4
(T=2)
A path is a T-length sequence of vertices p = (v1,··· ,vT+1).
Π is all the T-paths in G.
Path weight:
Sps(v1,v2)=0.37, Sps(v1,v3)=0.42,
Sps(v1,v4)=0.39,
Sps(v1,v5)=0.09.
Low efficiency!
Cannot support real-time search!

9. Related Work and Challenges
Method
Time Complexity
Space Complexity
SimRank [kdd’02]
O(IN2d2)
O(N2)
TopSim [ICDE’12]
O(NTdT)
O(N+M)
RWR [KDD’04]
O(IN2d)
RoleSim [KDD’11]
ReFex [KDD’11]
O(N+I(fM+Nf2))
O(N+Mf) 1
Share many direct/indirect common neighbors. 2
Disconnected, but share similar structure.
Find top-K similar vertices for any vertex in a network
d: average degree, f: feature number, T: path length
Challenges
C1 : How to design a similarity method that applies to both similarities?
C2: Computational efficiency challenge.

10. Panther: Fast Top-k Similarity Search on Big Networks
[1] Jing Zhang, Jie Tang, Cong Ma, Hanghang Tong, Yu Jing, and Juanzi Li. Panther: Fast Top-k Similarity Search on Large Networks. KDD'15. pp

11. Path Similarity 1
Intuition: two vertices are similar if they frequently appear on the same paths. v2 v1 v3 v5 v4
(T=2)
A path is a T-length sequence of vertices p = (v1,··· ,vT+1).
Π is all the T-paths in G.
Path weight:
Sps(v1,v2)=0.37, Sps(v1,v3)=0.42,
Sps(v1,v4)=0.39,
Sps(v1,v5)=0.09.

12. Pantherps Basic idea: random path sampling Simplified path similarity:
O(RT)
O(dT)

13. Upper bound of range set’s VC dimension
Theoretical Analysis
How many random paths shall we sample?
Domain and range set
Upper bound of range set’s VC dimension
Distribution 1 2 3
Required sample size

14. Theoretical Analysis Domain: Π Range set: VC bound: Distribution:
Details
Domain: Π
Range set:
VC bound:
Distribution:
Path similarity is
Conclusion
R random paths can guarantee ε and 1−δ.

15. Proof of Details A set Q of size l can be shattered by RG
Assume
and
A set Q of size l can be shattered by RG
A 1-1 corresponding between each subset in Q and each range Pi in RG
A path belongs only to the ranges w.r.t a pair of vertices in the path
Contradiction

16. Vector Similarity and Panthervs2
Limitation of path similarity: bias to close neighbors.
Vector Similarity: the probability distributions of a vertex linking to all other vertices are similar if their topology structures are similar.
Panthervs : Use top-D path similarities calculated by Pantherps to construct a vector: v
0.13
0.04 u
0.12
0.39
(T=2)
0.13
0.04 w
0.11
0.02
0.12
0.25
0.39
0.12
Svs(u,w)=0.27 > Svs (u,v)=0.16
0.25
0.12
0.11
0.02

17. Time Complexity Random path Vertex-to-path index Kd-tree
Method
Time Complexity
Space Complexity
SimRank
O(IN2d2)
O(N2)
TopSim
O(NTdT)
O(N+M)
RWR
O(IN2d)
RoleSim
ReFex
O(N+I(fM+Nf2))
O(N+Mf)
Pantherps
O(RTc+NdT)
O(RT+Nd)
Panthervs
O(RTc+NdT+Nc)
O(RT+Nd+ND)
Random path
Vertex-to-path index
Kd-tree
Random path sampling
Top-k similarity search for any vertex
Build and query kd-tree

18. Experiments

19. Efficiency Performance
Tencent network
Preprocessing time + top-k similarity search time
|V|
|E|
RWR
[(KDD’04]
TopSim
[ICDE’12]
RoleSim
[KDD’11]
ReFex
Pantherps
Panthervs
6,523
10,000
+7.79hr
+38.58m
+37.26s
3.85s+0.07s
0.07s+0.26s
0.99s+0.21s
25,844
50,000
+>150hr
+11.20hr
+12.98m
26.09s+0.40s
0.28s+1.53s
2.45s+4.21s
48,837
100,000
+30.94hr
+1.06hr
2.02m+0.57s
0.58s+3.48s
5.30s+5.96s
169,209
500,000
+>120hr
+>72hr
17.18m+2.51s
8.19s+16.08s
27.94s+24.17s
230,103
1,000,000
31.50m+3.29s
15.31s+30.63s
49.83s+22.86s
443,070
5,000,000
24.15hr+8.55s
50.91s+2.82m
4.01m+1.29m
702,049
10,000,000
>48hr
2.21m+6.24m
8.60m+6.58m
2,767,344
50,000,000
15.787m+1.36hr
1.60hr+2.17hr
5,355,507
100,000,000
44.09m+4.50hr
5.61hr+6.47hr
26,033,969
500,000,000
4.82hr+25.01hr
32.90hr+47.34hr
51,640,620
1,000,000,000
13.32hr+80.38hr
98.15hr hr
390X speed up
270X speed up
Can scale up to handle 1 billion edges
T=5, c=0.5, ε=√1/|E| and δ=0.1, R=16,609,640

20. Accuracy Performance of Pantherps
Evaluate how Pantherps can approximate common neighbors.
The score represents the improvement over a random method.
KDD
Twitter
Mobile
Co-author networks: |V|=3K, |E| = 7K.
Twitter network: |V| = 100K, |E| = 500K.
Mobile network: |V| = 200K, |E| = 200K.

21. Accuracy Performance of Panthervs
Identity Resolution
Assume the same authors in different networks of the same domain are similar to each other.
Settings
Given any two co-author networks, e.g., KDD and ICDM, if the top-k similar vertices from ICDM consists of the query author from KDD, we say that the method hits a correct instance.
KDD-ICDM
SIGIR-CIKM
SIGMOD-ICDE

22. Parameter Analysis: Path Length T
The performance gets better when T increases.
The performance almost becomes stable When T ≥ 5.
Effect of path length T on the accuracy performance of Panthervs.

23. Parameter Analysis: Error Bound ε
Tencent networks
When |E|/(1/ε)2 ranges from 5 to 20, Pantherps are almost convergent;
The value (1/ε)2 is almost linearly positively correlated with the number of edges in a network;
Therefore, we empirically set ε=√1/|E| in our experiments

24. Deploy in AMiner.org

25. Big Network Analysis BIG Networks User Tie Topology Heterogeneous
data
User
Tie
Topology
Heterogeneous
Micro
Macro
tie
Influence
Dynamic
- User Modeling
- Demographics
- Social Role
- Social Tie/Link
- Homophily
- Social Influence
- Triad Formation
- Community
- Group Behavior
Big&Big
social
Social Theories
Graph Theories
BIG Networks

26. Future Work BIG Networks User Tie Topology Heterogeneous
data
User
Tie
Topology
Heterogeneous
Micro
Macro
Question 1: How to incorporate the huge-volume & streaming individual behavior data into network analysis?
Question 2: What is the Interplay between (Micro) Individual Behavior and (Macro) Network Distribution?
tie
Influence
Dynamic
- User modeling
- Demographics
- Social Role
- Social Tie/Link
- Homophily
- Social Influence
- Triad Formation
- Community
- Group Behavior
Big&Big
social
Social Theories
Graph Theories
BIG Networks

27. Related Publications
Jie Tang, Jimeng Sun, Chi Wang, and Zi Yang. Social Influence Analysis in Large-scale Networks. In KDD’09, pages , 2009.
Chenhao Tan, Jie Tang, Jimeng Sun, Quan Lin, and Fengjiao Wang. Social action tracking via noise tolerant time-varying factor graphs. In KDD’10, pages 807–816, 2010.
Chi Wang, Jiawei Han, Yuntao Jia, Jie Tang, Duo Zhang, Yintao Yu, and Jingyi Guo. Mining Advisor-Advisee Relationships from Research Publication Networks. In KDD'10, pages
Jie Tang, Sen Wu, and Jimeng Sun. Confluence: Conformity Influence in Large Social Networks. In KDD’13, pages , 2013.
Yuxiao Dong, Yang Yang, Jie Tang, Yang Yang, Nitesh V. Chawla. Inferring User Demographics and Social Strategies in Mobile Social Networks. In KDD’14, 2014.
Yutao Zhang, Jie Tang, Zhilin Yang, Jian Pei, and Philip Yu. COSNET: Connecting Heterogeneous Social Networks with Local and Global Consistency. In KDD'15, pages
Jing Zhang, Biao Liu, Jie Tang, Ting Chen, and Juanzi Li. Social Influence Locality for Modeling Retweeting Behaviors. In IJCAI'13, pages , 2013.
Jing Zhang, Jie Tang, Honglei Zhuang, Cane Wing-Ki Leung, and Juanzi Li. Role-aware Conformity Influence Modeling and Analysis in Social Networks. In AAAI'14, 2014.
Jing Zhang, Jie Tang, Yuanyi Zhong, Yuchen Mo, Juanzi Li, Guojie Song, Wendy Hall, and Jimeng Sun. StructInf: Mining Structural Influence from Social Streams. In AAAI'17.
Jie Tang, Jing Zhang, Limin Yao, Juanzi Li, Li Zhang, and Zhong Su. ArnetMiner: Extraction and Mining of Academic Social Networks. In KDD’08, pages , 2008.
Tiancheng Lou and Jie Tang. Mining Structural Hole Spanners Through Information Diffusion in Social Networks. In WWW'13, pages , 2013.
Jiezhong Qiu, Yixuan Li, Jie Tang, Zheng Lu, Hao Ye, Bo Chen, Qiang Yang, and John Hopcroft. The Lifecycle and Cascade of WeChat Social Messaging Groups. In WWW'16, pages
Jie Tang, Tiancheng Lou, Jon Kleinberg, and Sen Wu. Transfer Learning to Infer Social Ties across Heterogeneous Networks. In TOIS, Vol 34 (2), No. 7, 2016
Jimeng Sun and Jie Tang. A Survey of Models and Algorithms for Social Influence Analysis. Social Network Data Analytics, Aggarwal, C. C. (Ed.), Kluwer Academic Publishers, pages 177–214, 2011.

28. References
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29. References(cont.)
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30. References(cont.)
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31. Thank you！
Collaborators: John Hopcroft, Jon Kleinberg, Chenhao Tan (Cornell)
Jiawei Han (UIUC), Philip Yu (UIC)
Jian Pei (SFU), Hanghang Tong (ASU)
Tiancheng Lou (Google&Baidu), Jimeng Sun (GIT)
Wei Chen, Ming Zhou, Long Jiang, Chi Wang, Yuxiao Dong (Microsoft)
Yutao Zhang, Jing Zhang, Zhanpeng Fang, Zi Yang, Sen Wu, etc. (THU)
Jie Tang, KEG, Tsinghua U,
Download all data & Codes,