1. │ University of Texas at Dallas │
Lecture 7-1
Rumor Blocking
Ding-Zhu Du
│ University of Texas at Dallas │
Social network analysis [SNA] is the mapping and measuring of relationships and flows between people, groups, organizations, computers or other information/knowledge processing entities.
The nodes in the network are the people and groups while the links show relationships or flows between the nodes.
The advantage of social network analysis is that, unlike many other methods, it focuses on interaction (rather than on individual behavior).
Network analysis allows us to examine how the configuration of networks influences how individuals and groups, organizations, or systems function.

2. Least Cost Rumor Blocking in
Social networks
Lidan Fan, Zaixin Lu, Weili Wu, Bhavani Thuraisingham, Huan Ma, Yuanjun Bi.
Published in ICDCS2013
11/12/2018

3. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
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4. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
11/12/2018

5. Social networks
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6. Social Network Social network is a social structure
made up of individuals and relations
between these individuals
Social network provides a
platform for influence diffusion
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7. Applications Single cascade …… Multiple cascades Political election
Viral marketing
Recommender systems
Feed ranking ……
Multiple cascades
Political election
Multiple products promotion
Rumor/misinformation controlling
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8. Social network properties
Small-world effect
The average distance between vertices in a network is short.
Power-law or exponential form
There are many nodes with low degree and a small number with
high degree.
Clustering or network transitivity
Two vertices that are both neighbors of the same third vertex have
a high probability of also being neighbors of one another.
Community structure
The connections within the same community are dense and
between communities are sparse.
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9. Influence spreads fast within the same community.
Influence spreads slow across different communities.
Social networks have community structure, with the property that the edges within the same community is dense and among communities is sparse.
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11. When misinformation or rumor spreads in social networks, what will happen?
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12. A misinformation said that the president of Syria is dead, and it hit the twitter greatly and was circulated fast among the population, leading to a sharp, quick increase in the price of oil.
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13. In August, 2012, thousands of people in Ghazni province left their houses in the middle of the night in panic after the rumor of earthquake. In
August, 2012, thousands of people in Ghazni province
left their houses in the middle of the night in panic
after the rumor of earthquake, which said that a major
earthquake would hit the area until 5 am [3]. Believing
in it, many people from the Ghazni city and some other
districts of the province left their house and spent the
whole night outside. The panic spread by the rumor
was so intense that the people, who were in thousands,
did not dare to return to their houses till morning.
Mirwais, a resident of Ghazni city, talked to a news
agency about this announcement. Later, the imams of
the mosques had started believing in it and according
to the statement made by Mirwais, Then, imams of
mosques also started announcing about the earthquake.
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14. Control the spread of rumors
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15. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
11/12/2018

16. Rumors generated in a community will influence the members in the network.
Find protectors to reduce the influence of rumors.
Real-world limitation: the overhead spent on protectors and protected members should be balanced.
Rumors spread very fast within their community---too much cost
Rumors spread slow across different communities---little cost
Find least number of protectors to reduce rumor influence to the members in other communities.
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17. Our Tasks Determine influence diffusion models.
Design efficient algorithms to find protectors.
Obtain real world data to evaluate our algorithms.
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18. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
11/12/2018

19. 11/12/2018

20. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
11/12/2018

21. Opportunistic One Activate One (OPOAO)
Deterministic One Activate Many (DOAM)
Opportunistic One Activate One (OPOAO)
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22. Common properties Two cascades: rumor and protector;
Diffusion starts time: the same;
Tie breaking rule: protector has priority over rumor;
Status of each node: inactive, infected, protected;
Monotonicity assumption: the status of infected or protected never changes.
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23. Deterministic One Activate Many (DOAM)
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24. Additional properties of the DOAM model
When a node becomes active (infected or protected), it has a single chance to activate all of its currently inactive (not infected and not protected) neighbors.
The activation attempts succeed with a probability 1.
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25. Example Two kinds of influence cascades: rumors and protectors.6 2 1 5
Two kinds of influence cascades: rumors and protectors.
Each individual has three status: inactive, rumored, protected.
The active individual activates all of its neighbors successfully.
When rumors and protectors influence an individual at the same time, then the individual is protected.
Each individual only has one chance to influence their neighbors.
A node will never change its status if it has been activated. 3 4
1 is a rumor, 6 is a protector.
Step 1: 1--2,3; 6--2,4. 2 and 4 are protected, 3 is infected.
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26. Example 6 2 1 5 3 4
Step 2: is protected.
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27. Opportunistic One Activate One (OPOAO)
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28. Additional properties of the OPOAO model
At each step, each active (infected or protected) node u can only choose one of its neighbors as its target, and each neighbor is chosen with a probability of 1/deg(u).
Each active (infected or protected) node has unlimited chance to select the same node as its target.
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29. Example 1 is a rumor, 6 is a protector.2 1 5 3 4
1 is a rumor, 6 is a protector.
Step 1:1--2, is protected.
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30. Example Two kinds of influence cascades: rumors and protectors.6 2 1 5 3 4
Two kinds of influence cascades: rumors and protectors.
Each individual has three status: inactive, rumored, protected.
The active individual only activates one of its neighbors successfully.
When rumors and protectors influence an individual at the same time, then the individual is protected.
Each individual has unlimited opportunities to influence their neighbors.
Each node will never change its status if it has been activated.
Step 2:1--3, is infected.
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31. Example Step 3:1--2, 3--4, 6--4. 4 is protected. 6 2 1 5 3 4
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32. Example Step 4:1--3, 3--2, 6--4, 4--5. 5 is protected. 6 2 1 5 3 4
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33. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
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34. Least Cost Rumor Blocking Problem (LCRB)
Bridge ends:
form a vertex set;
belong to neigborhood communities of rumor community;
each can be reached from the rumors before others in its own community. C0
Red node is a rumor;
Yellow nodes are bridge ends. C2 C1
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35. LCRB-D problem for the DOAM model
Given:
community structure
rumors
rumor community
Goal:
Find least number of protectors to protect all of the bridge
ends.
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36. Set Cover Based Greedy (SCBG) Algorithm
Main idea
Convert to set cover problem using Breadth First Search (BFS) method.
Three stages:
construct Rumor Forward Search Trees (RFST)--bridge ends
construct Bridge End Backward Search Trees (BEBST)--protector candidates
construct vertex sets used in set cover problem
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37. Construct Rumor Forward Search Trees (RFST)7 6 9 5 8 10 3 4 11 2 1
Yellow nodes are bridge ends. 12 14 13
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38. Rumor 4 Forward Search Tree
The minimal hops:
1 hop between 4 and 5;
2 hops between 4 and 12;
3 hops between 4 and 8.
5,8,12 are the bridge ends. 1 2 5 3 12 8
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39. Construct Bridge End Backward Search Trees (BEBST)7 6 9 5 8 10 3 4
Blue nodes are protector candidates. 11 2 1 12 14 13
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40. Bridge End Backward Search Trees4 3 4 7 4 11 2 9 10 3 2 5 8 12
Record the protector candidate sets for each bridge end:
5: {5,7}; :{2,3,8,9,10,11}; :{2,3,12}
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41. Apply the Greedy algorithm
Construct vertex sets in set cover problem
Find the bridge ends that each candidate can protect:
2:{8,12}; 3:{8,12} ; 5:{5}; 7:{5}; 8:{8}; 9:{8}; 10:{8};11{8}; 12{12}
Apply the Greedy algorithm
choose 2 or 3 , bridge ends 8 and 12 are protected;
choose 5 or 7, bridge end 5 is protected;
the output is {2,5} or {2,7} or {3,5} or {3,7}.
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42. Theoretical Results
There is a polynomial time O(ln n)−approximation algorithm for the LCRB-D problem, where n is the number of vertices in the set of bridge ends.
If the LCRB-D problem has an approximation algorithm with ratio k(n) if and only if the set cover problem has an approximation algorithm with ratio k(n).
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43. Set-Cover
Given a collection C of subsets of a set E, find a minimum subcollection C’ of C such that every element of E appears in a subset in C’ .

44. Example of Submodular Function

45. Greedy Algorithm

46. Analysis

50. Weighted Set Cover
Given a collection C of subsets of a set E and a weight function w on C, find a minimum total-weight subcollection C’ of C such that every element of E appears in a subset in C’ .

51. A General Problem

52. Greedy Algorithm

53. A General Theorem
Remark:

54. Proof

60. 1 2 3

61. ze1
zek
Ze2

62. Proof can be found in

63. Experiments Two datasets
Collaboration Network (
Covers scientific collaborations between authors with papers submitted to High Energy Physics.
Nodes: Papers
Edge (i,j): Author i co-authored a paper with author j
Network (
Covers all the communications within a dataset of around half million s.
Nodes: addresses
Edge (i, j): Address i sends at least one to address j
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64. # of selected communities 1 2
Datasets
HEP-PH
Enron-
# of nodes
15233
36692
# of edges
58891
367662
Average degree
7.73 10
# of selected communities 1 2
Description of the communities chosen
Size:308
Bridge end size: 387
Size: 80
Bridge end size:135
Size: 2631
Bridge end size: 2250
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65. Experimental Results Our algorithm performs the best.
SCBG
Proximity
MaxDegree
Hep/15233/308 1%
32.9
25.3
140.6 5%
42.1
74.3
147.8
10%
48.9
133.8
152.6
/36692/80
6.2
43.7
72.7
8.2
46.9
79.3
20%
13.8
62.9
91.1
/36692/2631
20.4
289.3
1208.8
50.9
1067.6
1350.2
68.4
1422.6
1683.8
Our algorithm performs the best.
The third community, which is dense and has large number of nodes,
shows that our algorithm is robust and scalable.
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66. Experiments
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67. Experiments Our algorithm performs in all figures except Fig7(a).
the network is sparse, when the number of rumors is small, it is possible that Proximity
performs better than ours
Proximity is better than MaxDegree in Fig7and Fig8.
number of rumors is small and network is sparse
MaxDegree is better than Proximity in Fig9.
number of rumor is large and network is dense
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68. Rumor Blocking problem under the OPOAO model
Given:
the community structure
Rumor sources R
rumor community
number of protectors k
Goal:
Find k protectors such that the expected number of bridge ends protected
is maximized.
Influence function σ(A) of node set A:
Expected number of nodes that would be infected if A is selected
as the protector seeds initially.
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69. 11/12/2018

70. Property of Submodularity
PB(A): the set of nodes that can be
protected by set A.
PB(A+v)-PB(A):
can be protected by A+v
can not be protected by A A B v
PB(A)
PB(B)
PB(v)
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71. Main Results
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72. Proof of Submodularity Timestamp assignment of rumor diffusionx y x y
y.1
y.2
y.3
y.4
x.1
x.2
x.4
x.3
x.1
x.3
y.1
y.3 u v
y.3 u v
x.2
x.3
x.4
y.4
y.2
y.4
x.2
y.4
x.4
x.4
y.2
x.3
x.3 w z w z
x.t: the influence spread of rumor x arrive a node at step t
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73. Proof of Submodularity
Prove the submodularity of cardinality function |PB(A)|
The nodes in PB(A) satisfies:
infected if the set of protectors is empty
not infected if the set of protectors is A
Create rumor(protector) random diffusion graph-Gr(Gp).
Among the incoming edges of bridge end u in Gr and Gp:
find the oldest timestamp in Gr and Gp respectively
compare them
if the oldest one in Gp is older than the one in Gr
then u can be protected
otherwise
then u will be infected
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74. Example
Determine whether u is protected or infected r
r.3 r
r.1
r.2 w u
r.3
p.3 u w
p.1
r.1
p.1
p.2 w u
p.3 p
Random rumor diffusion graph Gr p
Random protector diffusion graph Gp
Graph G
r: rumor
p: protector
Since p.1 is older than r.3, then u is protected.
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75. σ(A) is submodular. Submodularity of function σ(A)
Fact: A non-negative linear combination of monotone and submodular functions is still monotone and submodular.
Probabilities are non-negative;
|PB(A)| is submodular;
σ(A) is submodular.
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76. 11/12/2018

77. 11/12/2018

78. A general result on greedy algorithm
With non-integer potential function
Consider a monotone increasing, submodular function
Consider the following problem:
where
is a nonnegative cost function

79. Greedy Algorithm G

80. Theorem Suppose in Greedy Algorithm G, selected x always satisfies
Then its p.r.
where

81. Proof. Let be obtained by Greedy Algorithm G. Denote Let
be an optimal solution.
Denote

83. Note that
There exists i such that

84. Let
Let
Note that So

85. Note
Hence,

86. 11/12/2018

87. Experiments
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88. Experiments
In Fig4, Fig5 and Fig6, our algorithm performs the best except in several early hops.
number of rumors is small
Proximity is better than MaxDegree in Fig4, Fig5 and Fig6.
stochastic selection mechanism
The difference between Proximity and MaxDegree in Fig4 is larger than that in Fig5
and Fig6.
network in Fig4 is sparse
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89. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
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90. Conclusions The least cost rumor blocking (LCRB) problem in two models
Introduce two influence diffusion models
Deterministic One Activate Many --DOAM
Opportunistic One Activate One--OPOAO
The least cost rumor blocking (LCRB) problem in two models
LCRB-D problem under the DOAM—protect all the bridge ends
Algorithm: Set Cover Based Greedy (SCBG)
Data: collaboration network and network
Our algorithm: robust and scalable.
LCRB-P problem under the OPOAO—protect α fraction of the bridge ends
Influence function σ(A): submodularity
Method: timestamp assignment
Algorithm: Greedy
Data: collaboration network and network.
Our algorithm: robust and scalable
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91. Outline Background Related Works Our Contribution Conclusions
Motivation
Problem formulation
Related Works
Our Contribution
Two influence diffusion models
Least cost rumor blocking problem
Conclusions
Future Works
11/12/2018

92. Future Works Establish continuous time influence propagation model
In real world, under most situations,
influence diffuses in continuous time.
Measure the diffusion time based on
factors such as individual attributes,
information properties, strength of
relations, etc.
Knowing these sources is very important
to the network administrators in the following essences: (1) it
helps to understand the ultimate goals for the misinformation,
who the misleading information targets to as well as the
potential size of the misinformation spread, and (2) it provides
valuable insights into designing effective strategies for the containment campaign.
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93. Future Works
Study rumor blocking and influence diffusion under dynamic social structures
Under most cases, the relations between individuals change along with time, that is, social structures change along with time, what results can we get for rumor blocking and influence diffusion in dynamic situation.
Knowing these sources is very important
to the network administrators in the following essences: (1) it
helps to understand the ultimate goals for the misinformation,
who the misleading information targets to as well as the
potential size of the misinformation spread, and (2) it provides
valuable insights into designing effective strategies for the containment campaign.
2018/11/12

94. Future Works Detect rumor sources
Previous works in controlling rumor diffusion assume that rumor sources are known. However, in reality, it is hard to know the accurate rumor sources.
Estimate rumor sources accurately using existing information.
Knowing these sources is very important
to the network administrators in the following essences: (1) it
helps to understand the ultimate goals for the misinformation,
who the misleading information targets to as well as the
potential size of the misinformation spread, and (2) it provides
valuable insights into designing effective strategies for the containment campaign.
2018/11/12

95. Thank you!
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