1. Understanding and Managing Cascades on Large Graphs
B. Aditya Prakash
Carnegie Mellon University Virginia Tech.
Christos Faloutsos
Carnegie Mellon University
Aug 29, Tutorial, VLDB 2012, Istanbul

2. Networks are everywhere!
Facebook Network [2010]
Gene Regulatory Network [Decourty 2008]
Human Disease Network [Barabasi 2007]
The Internet [2005]
Prakash and Faloutsos 2012

3. Dynamical Processes over networks are also everywhere!
Prakash and Faloutsos 2012

4. Why do we care? Social collaboration Information Diffusion
Viral Marketing
Epidemiology and Public Health
Cyber Security
Human mobility
Games and Virtual Worlds
Ecology
Prakash and Faloutsos 2012

5. Why do we care? (1: Epidemiology)
Dynamical Processes over networks
[AJPH 2007]
CDC data: Visualization of the first 35 tuberculosis (TB) patients and their 1039 contacts
Diseases over contact networks
Prakash and Faloutsos 2012

6. Why do we care? (1: Epidemiology)
Dynamical Processes over networks
Each circle is a hospital
~3000 hospitals
More than 30,000 patients transferred
Mention number of hospitals
Patients transferred
[US-MEDICARE NETWORK 2005]
Problem: Given k units of disinfectant, whom to immunize?
Prakash and Faloutsos 2012

7. Why do we care? (1: Epidemiology)
~6x fewer!
[US-MEDICARE NETWORK 2005]
CURRENT PRACTICE
OUR METHOD
Hospital-acquired inf. took 99K+ lives, cost $5B+ (all per year)
Prakash and Faloutsos 2012

8. Why do we care? (2: Online Diffusion)
> 800m users, ~$1B revenue [WSJ 2010]
~100m active users
> 50m users
Prakash and Faloutsos 2012

9. Why do we care? (2: Online Diffusion)
Dynamical Processes over networks
Buy Versace™!
Celebrity
Followers
Social Media Marketing
Prakash and Faloutsos 2012

10. Why do we care? (3: To change the world?)
Dynamical Processes over networks
Social networks and Collaborative Action
Prakash and Faloutsos 2012

11. High Impact – Multiple Settings
epidemic out-breaks
Q. How to squash rumors faster?
Q. How do opinions spread?
Q. How to market better?
products/viruses
transmit s/w patches
Prakash and Faloutsos 2012

12. Large real-world networks & processes
Research Theme
ANALYSIS
Understanding
POLICY/ ACTION
Managing
DATA
Large real-world networks & processes
Prakash and Faloutsos 2012

13. Research Theme – Public Health
ANALYSIS
Will an epidemic happen?
POLICY/ ACTION
How to control out-breaks?
DATA
Modeling # patient transfers
Prakash and Faloutsos 2012

14. Research Theme – Social Media
ANALYSIS
# cascades in future?
POLICY/ ACTION
How to market better?
DATA
Modeling Tweets spreading
Prakash and Faloutsos 2012

15. In this tutorial Given propagation models: Q1: What is the epidemic
ANALYSIS
Understanding
Given propagation models:
Q1: What is the epidemic
threshold?
Q2: How do viruses
compete?
Prakash and Faloutsos 2012

16. In this tutorial Q3: How to immunize and control out-breaks better?
POLICY/ ACTION
Managing
Q3: How to immunize and
control out-breaks
better?
Q4: How to detect
outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

17. Large real-world networks & processes
In this tutorial
DATA
Large real-world networks & processes
Q6: How do cascades look
like?
Q7: How does activity
evolve over time?
Q8: How does external
influence act?
Prakash and Faloutsos 2012

18. Outline Motivation Part 1: Understanding Epidemics (Theory)
Part 2: Policy and Action (Algorithms)
Part 3: Learning Models (Empirical Studies)
Conclusion
single virus VS multiple viruses
Prakash and Faloutsos 2012

19. Part 1: Theory Q1: What is the epidemic threshold?
Q2: How do viruses compete?
Prakash and Faloutsos 2012

20. A fundamental question
Strong Virus
Epidemic?
Prakash and Faloutsos 2012

21. example (static graph)
Weak Virus
Epidemic?
Prakash and Faloutsos 2012

22. Problem Statement Find, a condition under which # Infected
above (epidemic)
below (extinction)
# Infected
time
Find, a condition under which
virus will die out exponentially quickly
regardless of initial infection condition
Separate the regimes?
Prakash and Faloutsos 2012

23. Threshold (static version)
Problem Statement
Given:
Graph G, and
Virus specs (attack prob. etc.)
Find:
A condition for virus extinction/invasion
Prakash and Faloutsos 2012

24. Threshold: Why important?
Accelerating simulations
Forecasting (‘What-if’ scenarios)
Design of contagion and/or topology
A great handle to manipulate the spreading
Immunization
Maximize collaboration
…..
Bring the snapshot of previous slide
Prakash and Faloutsos 2012

25. Part 1: Theory Q1: What is the epidemic threshold?
Background
Result and Intuition (Static Graphs)
Proof Ideas (Static Graphs)
Bonus: Dynamic Graphs
Q2: How do viruses compete?
Prakash and Faloutsos 2012

26. “SIR” model: life immunity (mumps)
Background
“SIR” model: life immunity (mumps)
Each node in the graph is in one of three states
Susceptible (i.e. healthy)
Infected
Removed (i.e. can’t get infected again)
Prob. δ
Prob. β
spend less time explaining the stuff….
t = 1
t = 2
t = 3
Prakash and Faloutsos 2012

27. Terminology: continued
Background
Terminology: continued
Other virus propagation models (“VPM”)
SIS : susceptible-infected-susceptible, flu-like
SIRS : temporary immunity, like pertussis
SEIR : mumps-like, with virus incubation
(E = Exposed)
….………….
Underlying contact-network – ‘who-can-infect-whom’
Prakash and Faloutsos 2012

28. Background
Related Work
All are about either:
Structured topologies (cliques, block-diagonals, hierarchies, random)
Specific virus propagation models
Static graphs
R. M. Anderson and R. M. May. Infectious Diseases of Humans. Oxford University Press, 1991.
A. Barrat, M. Barthélemy, and A. Vespignani. Dynamical Processes on Complex Networks. Cambridge University Press, 2010.
F. M. Bass. A new product growth for model consumer durables. Management Science, 15(5):215–227, 1969.
D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos. Epidemic thresholds in real networks. ACM TISSEC, 10(4), 2008.
D. Easley and J. Kleinberg. Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.
A. Ganesh, L. Massoulie, and D. Towsley. The effect of network topology in spread of epidemics. IEEE INFOCOM, 2005.
Y. Hayashi, M. Minoura, and J. Matsukubo. Recoverable prevalence in growing scale-free networks and the effective immunization. arXiv:cond-at/ v2, Aug
H. W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42, 2000.
H. W. Hethcote and J. A. Yorke. Gonorrhea transmission dynamics and control. Springer Lecture Notes in Biomathematics, 46, 1984.
J. O. Kephart and S. R. White. Directed-graph epidemiological models of computer viruses. IEEE Computer Society Symposium on Research in Security and Privacy, 1991.
J. O. Kephart and S. R. White. Measuring and modeling computer virus prevalence. IEEE Computer Society Symposium on Research in Security and Privacy, 1993.
R. Pastor-Santorras and A. Vespignani. Epidemic spreading in scale-free networks. Physical Review Letters 86, 14, 2001.
………
Point out may anderson is a book, survey
Prakash and Faloutsos 2012

29. Part 1: Theory Q1: What is the epidemic threshold?
Background
Result and Intuition (Static Graphs)
Proof Ideas (Static Graphs)
Bonus: Dynamic Graphs
Q2: How do viruses compete?
Prakash and Faloutsos 2012

30. How should the answer look like?
Answer should depend on:
Graph
Virus Propagation Model (VPM)
But how??
Graph – average degree? max. degree? diameter?
VPM – which parameters?
How to combine – linear? quadratic? exponential?
Put example equations (\beta d + \delta/diameter) \beta\sqrt(s)
…..
Prakash and Faloutsos 2012

31. Static Graphs: Our Main Result
Informally,
For,
any arbitrary topology (adjacency
matrix A)
any virus propagation model (VPM) in
standard literature
the epidemic threshold depends only
on the λ, first eigenvalue of A, and
some constant , determined by the virus propagation model λ
No epidemic if λ * < 1
In Prakash+ ICDM 2011
Prakash and Faloutsos 2012

32. Our thresholds for some models
s = effective strength
s < 1 : below threshold
Models
Effective Strength (s)
Threshold (tipping point)
SIS, SIR, SIRS, SEIR
s = λ .
s = 1
SIV, SEIV
(H.I.V.)
Prakash and Faloutsos 2012

33. Our result: Intuition for λ
“Official” definition:
“Un-official” Intuition 
Let A be the adjacency matrix. Then λ is the root with the largest magnitude of the characteristic polynomial of A [det(A – xI)].
Doesn’t give much intuition!
λ ~ # paths in the graph u u
≈ .
Have a better intuition slide ‘unofficial intuition’
(i, j) = # of paths i  j of length k
Prakash and Faloutsos 2012

34. Largest Eigenvalue (λ)
better connectivity higher λ
λ ≈ 2
λ = N
λ = N-1
Square root
λ ≈ 2
λ= 31.67
λ= 999
N = 1000
N nodes
Prakash and Faloutsos 2012

35. Examples: Simulations – SIR (mumps)
Fraction of Infections
Footprint
Cite Barrett and Marathe
(a) Infection profile (b) “Take-off” plot
PORTLAND graph
31 million links, 6 million nodes
Effective Strength
Time ticks
Prakash and Faloutsos 2012

36. Examples: Simulations – SIRS (pertusis)
Fraction of Infections
Footprint
(a) Infection profile (b) “Take-off” plot
PORTLAND graph
31 million links, 6 million nodes
Time ticks
Effective Strength
Prakash and Faloutsos 2012

37. Part 1: Theory Q1: What is the epidemic threshold?
Background
Result and Intuition (Static Graphs)
Proof Ideas (Static Graphs)
Bonus: Dynamic Graphs
Q2: How do viruses compete?
Prakash and Faloutsos 2012

38. Proof Sketch λ * < 1 General VPM structure Model-based Graph-based
λ * < 1
Dimensional arguments…
Full proof 30 pages on arxiv
Graph-based
Topology and stability
Prakash and Faloutsos 2012

39. Models and more models H.I.V. Model Used for SIR Mumps SIS Flu SIRS
Pertussis
SEIR
Chicken-pox
……..
SICR
Tuberculosis
MSIR
Measles
SIV
Sensor Stability
H.I.V.
……….
Prakash and Faloutsos 2012

40. Ingredient 1: Our generalized model
Exogenous Transitions
Endogenous Transitions
Susceptible
Infected
Vigilant
Endogenous Transitions
Susceptible
Infected
Vigilant
(S*I*V*?)
Prakash and Faloutsos 2012

41. Special case: SIR Susceptible Infected Vigilant (S*I*V*?)
Prakash and Faloutsos 2012

42. Special case: H.I.V. Multiple Infectious, Vigilant states
“Non-terminal”
“Terminal”
Multiple Infectious, Vigilant states
Prakash and Faloutsos 2012

43. Ingredient 2: NLDS+Stability
Details
Ingredient 2: NLDS+Stability
View as a NLDS
discrete time
non-linear dynamical system (NLDS)
size
mN x 1 .
size N (number of nodes in the graph) S
Probability vector Specifies the state of the system at time t
Curly braces…say what the blue yellow are… I V
Prakash and Faloutsos 2012

44. Ingredient 2: NLDS + Stability
Details
Ingredient 2: NLDS + Stability
View as a NLDS
discrete time
non-linear dynamical system (NLDS)
size
mN x 1 .
Non-linear function
Explicitly gives the evolution of system
Prakash and Faloutsos 2012

45. Ingredient 2: NLDS + Stability
View as a NLDS
discrete time
non-linear dynamical system (NLDS)
Threshold  Stability of NLDS
Prakash and Faloutsos 2012

46. Special case: SIR Details NLDS size 3N x 1 = probability that node
Apply g on p_T, you get p_t+1
= probability that node
i is not attacked by
any of its infectious
neighbors
NLDS
Prakash and Faloutsos 2012

47. Fixed Point Details State when no node is infected Q: Is it stable? 1.
State when no node is infected
Q: Is it stable?
Prakash and Faloutsos 2012

48. Stability for SIR Stable under threshold Unstable above threshold
Prakash and Faloutsos 2012

49. λ * < 1 See paper for full proof General VPM structure Model-based
λ * < 1
Dimensional arguments…
Graph-based
Topology and stability
Prakash and Faloutsos 2012

50. Part 1: Theory Q1: What is the epidemic threshold?
Background
Result and Intuition (Static Graphs)
Proof Ideas (Static Graphs)
Bonus: Dynamic Graphs
Q2: How do viruses compete?
Prakash and Faloutsos 2012

51. Dynamic Graphs: Epidemic?
Alternating behaviors
DAY
(e.g., work)
adjacency matrix 8
Prakash and Faloutsos 2012

52. Dynamic Graphs: Epidemic?
Alternating behaviors
NIGHT
(e.g., home)
adjacency matrix 8
Prakash and Faloutsos 2012

53. Model Description SIS model Set of T arbitrary graphs recovery rate δ
Infected
Healthy X N1 N3 N2
Prob. β
Prob. δ
SIS model
recovery rate δ
infection rate β
Set of T arbitrary graphs
weekend
day N
night N
, weekend…..
Prakash and Faloutsos 2012

54. Our result: Dynamic Graphs Threshold
Informally, NO epidemic if
eig (S) = < 1
Single number!
Largest eigenvalue of
The system matrix S
Details
S =
In Prakash+, ECML-PKDD 2010
Prakash and Faloutsos 2012

55. Infection-profile Synthetic MIT Reality Mining log(fraction infected)
ABOVE
ABOVE AT AT
write ‘below threshold’ for eig < 1
AT threshold
above threshold
BELOW
BELOW
Time
Prakash and Faloutsos 2012

56. “Take-off” plots Synthetic MIT Reality Our threshold Our threshold
Footprint (# “steady state”)
Synthetic
MIT Reality
EPIDEMIC
Our threshold
Our threshold
EPIDEMIC
Plot variance instead? Size and
NO EPIDEMIC
NO EPIDEMIC
(log scale)
Prakash and Faloutsos 2012

57. Part 1: Theory Q1: What is the epidemic threshold?
Q2: What happens when viruses compete?
Mutually-exclusive viruses
Interacting viruses
Prakash and Faloutsos 2012

58. Competing Contagions iPhone v Android Blu-ray v HD-DVD v Attack
Retreat
Biological common flu/avian flu, pneumococcal inf etc
Prakash and Faloutsos 2012

59. A simple model Virus 2 Virus 1 Details Modified flu-like
Mutual Immunity (“pick one of the two”)
Susceptible-Infected1-Infected2-Susceptible
Android apple sign for the viruses
Virus 1
Virus 2
Prakash and Faloutsos 2012

60. Question: What happens in the end?
green: virus 1
red: virus 2
Number of Infections
Steady State
= ?
Steady-state number of greens/num of reds = ?
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

61. Question: What happens in the end?
Steady State
green: virus 1
red: virus 2
Number of Infections
Strength ?? = 2
Strength
Steady-state number of greens/num of reds = ?
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

62. Answer: Winner-Takes-All
green: virus 1
red: virus 2
Number of Infections
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

63. Our Result: Winner-Takes-All
Given our model, and any graph, the weaker virus always dies-out completely
Details
The stronger survives only if it is above threshold
Virus 1 is stronger than Virus 2, if:
strength(Virus 1) > strength(Virus 2)
Strength(Virus) = λ β / δ  same as before!
In Prakash+ WWW 2012
Prakash and Faloutsos 2012

64. Real Examples [Google Search Trends data] Reddit v Digg
logos
Reddit v Digg
Blu-Ray v HD-DVD
Prakash and Faloutsos 2012

65. Part 1: Theory Q1: What is the epidemic threshold?
Q2: What happens when viruses compete?
Mutually-exclusive viruses
Interacting viruses
Prakash and Faloutsos 2012

66. A simple model: SI1|2S & Virus 1 Virus 2 Modified flu-like (SIS)
Susceptible-Infected1 or 2-Susceptible
Interaction Factor ε
Full Mutual Immunity: ε = 0
Partial Mutual Immunity (competition): ε < 0
Cooperation: ε > 0
&
Virus 1
Virus 2
Prakash and Faloutsos 2012

67. Question: What happens in the end?
ε = 0
Winner takes all
ε = 1
Co-exist independently
ε = 2
Viruses cooperate
Strengths: 6 and 4
What about for 0 < ε <1?
Is there a point at which both viruses can co-exist?
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

68. Answer: Yes! There is a phase transition
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

69. Answer: Yes! There is a phase transition
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

70. Answer: Yes! There is a phase transition
ASSUME:
Virus 1 is stronger than Virus 2
Prakash and Faloutsos 2012

71. Our Result: Viruses can Co-exist
Given our model and a fully connected graph, there exists an εcritical such that for ε ≥ εcritical, there is a fixed point where both viruses survive.
Details
The stronger survives only if it is above threshold
Virus 1 is stronger than Virus 2, if:
strength(Virus 1) > strength(Virus 2)
Strength(Virus) σ = N β / δ
In Beutel+ KDD 2012
Prakash and Faloutsos 2012

72. Real Examples [Google Search Trends data] Hulu v Blockbuster
Prakash and Faloutsos 2012

73. Real Examples [Google Search Trends data] Chrome v Firefox
Prakash and Faloutsos 2012

74. Outline Motivation Part 1: Understanding Epidemics (Theory)
Part 2: Policy and Action (Algorithms)
Part 3: Learning Models (Empirical Studies)
Conclusion
single virus VS multiple viruses
Prakash and Faloutsos 2012

75. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

76. Full Static Immunization
Given: a graph A, virus prop. model and budget k;
Find: k ‘best’ nodes for immunization (removal). ? ?
k = 2 ?
Knight or armor or shield ?
Prakash and Faloutsos 2012

77. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Full Immunization (Static Graphs)
Full Immunization (Dynamic Graphs)
Fractional Immunization
Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

78. Challenges Given a graph A, budget k,
Q1 (Metric) How to measure the ‘shield-value’ for a set of nodes (S)?
Q2 (Algorithm) How to find a set of k nodes with highest ‘shield-value’?
Prakash and Faloutsos 2012

79. Proposed vulnerability measure λ
λ is the epidemic threshold
“Safe”
“Vulnerable”
“Deadly”
Increasing λ
Increasing vulnerability
Prakash and Faloutsos 2012

80. A1: “Eigen-Drop”: an ideal shield value
Eigen-Drop(S)
Δ λ = λ - λs 9 9 Δ 9 11 10 10 1 1 6 2 4 4 8 8 2 3 7 3 7 5 5 6
Original Graph
Without {2, 6}
Prakash and Faloutsos 2012

81. (Q2) - Direct Algorithm too expensive!
Immunize k nodes which maximize Δ λ
S = argmax Δ λ
Combinatorial!
Complexity:
Example:
1,000 nodes, with 10,000 edges
It takes 0.01 seconds to compute λ
It takes 2,615 years to find 5-best nodes!
Prakash and Faloutsos 2012

82. A2: Our Solution Part 1: Shield Value Part 2: Algorithm
Carefully approximate Eigen-drop (Δ λ)
Matrix perturbation theory
Part 2: Algorithm
Greedily pick best node at each step
Near-optimal due to submodularity
NetShield (linear complexity)
O(nk2+m) n = # nodes; m = # edges
N == nodes M = edges
In Tong+ ICDM 2010
Prakash and Faloutsos 2012

83. Our Solution: Part 1 Details Approximate Eigen-drop (Δ λ) A u u = λ .
Δ λ ≈ SV(S) =
Result using Matrix perturbation theory
u(i) == ‘eigenscore’
~~ pagerank(i)
u(i) A u u
= λ .
Prakash and Faloutsos 2012

84. Details P1: node importance P2: set diversity Select by P1
Select by P1+P2
Original Graph
Prakash and Faloutsos 2012

85. Our Solution: Part 2: NetShield
We prove that:
SV(S) is sub-modular (& monotone non-decreasing)
NetShield: Greedily add best node at each step
Corollary: Greedy algorithm works
1. NetShield is near-optimal (w.r.t. max SV(S))
2. NetShield is O(nk2+m)
tell jon’s paper (influence propagation..)
Footnote: near-optimal means SV(S NetShield) >= (1-1/e) SV(S Opt)
Prakash and Faloutsos 2012

86. Experiment: Immunization quality
Log(fraction of
infected
nodes)
PageRank
Betweeness (shortest path)
Degree
Lower is better
Acquaintance
Eigs (=HITS)
NetShield
Time
Prakash and Faloutsos 2012

87. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Full Immunization (Static Graphs)
Full Immunization (Dynamic Graphs)
Fractional Immunization
Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

88. Full Dynamic Immunization
Given:
Set of T arbitrary graphs
Find:
k ‘best’ nodes to immunize (remove)
day N
night N
, weekend…..
In Prakash+ ECML-PKDD 2010
Prakash and Faloutsos 2012

89. Full Dynamic Immunization
day
night
Our solution
Recall theorem
Simple: reduce (= )
Goal: max eigendrop Δ
No competing policy for comparison
We propose and evaluate many policies
Matrix Product
Δ =
Prakash and Faloutsos 2012

90. Performance of Policies
Lower is better
MIT Reality Mining
Prakash and Faloutsos 2012

91. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Full Immunization (Static Graphs)
Full Immunization (Dynamic Graphs)
Fractional Immunization
Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

92. Fractional Immunization of Networks
B. Aditya Prakash, Lada Adamic, Theodore
Iwashyna (M.D.), Hanghang Tong, Christos
Faloutsos
Under Submission
Prakash and Faloutsos 2012

93. Previously: Full Static Immunization
Given: a graph A, virus prop. model and budget k;
Find: k ‘best’ nodes for immunization (removal).
k = 2 ?
Knight or armor or shield ?
Prakash and Faloutsos 2012

94. Fractional Asymmetric Immunization
Fractional Effect [ f(x) = ]
Asymmetric Effect
# antidotes = 3
Prakash and Faloutsos 2012

95. Now: Fractional Asymmetric Immunization
Fractional Effect [ f(x) = ]
Asymmetric Effect
# antidotes = 3
Prakash and Faloutsos 2012

96. Fractional Asymmetric Immunization
Fractional Effect [ f(x) = ]
Asymmetric Effect
Boxes as pills, f(1) = 0.5, f(2) =0.25…
# antidotes = 3
Prakash and Faloutsos 2012

97. Fractional Asymmetric Immunization
Drug-resistant Bacteria (like XDR-TB)
Title and authors (we were happy to have medical doctors as collaborators)
Hospital
Another Hospital
Prakash and Faloutsos 2012

98. Fractional Asymmetric Immunization
Drug-resistant Bacteria (like XDR-TB)
Title and authors (we were happy to have medical doctors as collaborators)
Hospital
Another Hospital
Prakash and Faloutsos 2012

99. Fractional Asymmetric Immunization
Problem: Given k units of disinfectant, how to distribute them to maximize hospitals saved?
Title and authors (we were happy to have medical doctors as collaborators)
Hospital
Another Hospital
Prakash and Faloutsos 2012

100. Our Algorithm “SMART-ALLOC”
~6x fewer!
[US-MEDICARE NETWORK 2005]
Each circle is a hospital, ~3000 hospitals
More than 30,000 patients transferred
Faster
CURRENT PRACTICE
SMART-ALLOC
Prakash and Faloutsos 2012

101. ≈ Running Time Wall-Clock Time > 30,000x speed-up! Lower is better
> 1 week ≈
> 30,000x speed-up!
Lower is better
14 secs
Simulations
SMART-ALLOC
Prakash and Faloutsos 2012

102. Experiments Lower is better SECOND-LIFE PENN-NETWORK K = 200 K = 2000
Prakash and Faloutsos 2012

103. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

104. Break! Terraces of hot springs and carbonate minerals
Pamukkale, Turkey
Prakash and Faloutsos 2012

105. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

106. Outbreak detection Spot contamination points
Minimize time to detection, population affected
Maximize probability of detection.
Minimize sensor placement cost.
Compare each goal to blogs
Blogs
Posts
Links
Information cascade
Prakash and Faloutsos 2012

107. Outbreak detection Spot `hot blogs’
Minimize time to detection, population affected
Maximize probability of detection.
Minimize sensor placement cost.
Compare each goal to blogs
Blogs
Posts
Links
Information cascade
Prakash and Faloutsos 2012

108. J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, N
J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, N. Glance. "Cost-effective Outbreak Detection in Networks” KDD 2007
Prakash and Faloutsos 2012

109. CELF: Main idea Given: a graph G(V,E) Place the sensors
a budget of B sensors
data on how contaminations spread over the network:
Place the sensors
To minimize time to detect outbreak
CELF algorithm uses submodularity
and lazy evaluation
They call the algorihtm CELF
(contaminations data-- adjacency)
Minimzie time to detect outbreak
Similar to sensor placement-- compare water to blogs
Prakash and Faloutsos 2012

110. Blogs: Comparison to heuristics
Benefit
(higher=better)
Prakash and Faloutsos 2012

111. “Best 10 blogs to read”
NP - number of posts, IL- in-links, OLO- blog out links, OLA- all out links
k PA score Blog NP IL OLO OLA
Finds ones with small “cost”
Prakash and Faloutsos 2012

112. Part 2: Algorithms Q3: Whom to immunize? Q4: How to detect outbreaks?
Q5: Who are the culprits?
Prakash and Faloutsos 2012

113. B. Aditya Prakash, Jilles Vreeken, Christos Faloutsos ‘Detecting Culprits in Epidemics: Who and How many?’
Under Submission
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114. Problem definition 2-d grid ‘+’ -> infected Who started it?
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115. Problem definition 2-d grid ‘+’ -> infected Who started it?
Prior work: [Lappas et al. 2010, Shah et al. 2011]
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116. Culprits: Exoneration
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117. Culprits: Exoneration
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118. Who are the culprits Two-part solution Running time =
use MDL for number of seeds
for a given number:
exoneration = centrality + penalty
our method uses smallest eigenvector of Laplacian submatrix
Running time =
linear! (in edges and nodes)
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119. Outline Motivation Part 1: Understanding Epidemics (Theory)
Part 2: Policy and Action (Algorithms)
Part 3: Learning Models (Empirical Studies)
Conclusion
single virus VS multiple viruses
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120. Part 3: Empirical Studies
Q6: How do cascades look like?
Q7: How does activity evolve over time?
Q8: How does external influence act?
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121. Cascading Behavior in Large Blog Graphs
Blogs
Posts
Information cascade
Links
How does information propagate
over the blogosphere?
A topic I’m fond of…
J. Leskovec, M.McGlohon, C. Faloutsos, N. Glance, M. Hurst. Cascading Behavior in Large Blog Graphs. SDM 2007.
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122. Cascades on the Blogosphere1 a B2 B1 1 B2 b c 1 2 d 1 B3 3 B3 B4 B4 e
Blogosphere
blogs + posts
Blog network
links among blogs
Post network
links among posts
Some graphs we will use a b c d
Cascade is graph induced by a time ordered propagation of information (edges) e e
Cascades
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123. Blog data 45,000 blogs participating in cascades
All their posts for 3 months (Aug-Sept ‘05)
2.4 million posts
~5 million links (245,404 inside the dataset)
Number of posts
Number of posts
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Time [1 day]

124. Popularity over time Post popularity drops-off – exponentially?
Faloutsos
Popularity over time
# in links
lag: days after post 1 2 3
Post popularity drops-off – exponentially? @t
@t + lag
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125. Popularity over time Post popularity drops-off – exponentially?
Faloutsos
Popularity over time
# in links
(log)
days after post
(log)
Post popularity drops-off – exponentially?
POWER LAW!
Exponent?
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126. Popularity over time Post popularity drops-off – exponentially?
Faloutsos
Popularity over time
# in links
(log)
-1.6
days after post
(log)
Post popularity drops-off – exponentially?
POWER LAW!
Exponent? -1.6
close to -1.5: Barabasi’s stack model
and like the zero-crossings of a random walk
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127. -1.5 slope
J. G. Oliveira & A.-L. Barabási Human Dynamics: The Correspondence Patterns of Darwin and Einstein. Nature 437, 1251 (2005) . [PDF]
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128. Topological Observations
How do we measure how information flows through the network?
Common cascade shapes extracted using algorithms in [Leskovec, Singh, Kleinberg; PAKDD 2006].
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129. Topological Observations
What graph properties do cascades exhibit?
Cascade size distributions also follow power law.
Observation 2: The probability of observing a cascade on n nodes follows a Zipf distribution:
p(n) n-2
the first two points --- singletons (don’t care), pairs (2 node chains)
a=-2
Count
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Cascade size (# of nodes)

130. Topological Observations
What graph properties do cascades exhibit?
Stars and chains also follow a power law, with different exponents (star -3.1, chain -8.5).
a=-3.1
Count
a=-8.5
Chains drop off much more steeply
This could be due to the time delay
Count
Size of star (# nodes)
Size of chain (# nodes)
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131. to identify communities?
Blogs and structure
Cascades take on different shapes (sorted by frequency):
How can we use cascades
to identify communities?
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132. PCA on cascade types Perform PCA on sparse matrix. Use log(count+1)
Project onto 2 PC…
~9,000 cascade types
% ->
…………
.01 …
.07
.67
1.1
2.1
5.1
4.2
3.4
3.2
boingboing
.09
4.6
slashdot
~44,000 blogs
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133. PCA on cascade types
Observation: Content of blogs and cascade behavior are often related.
Distinct clusters for “conservative” and “humorous” blogs (hand-labeling).
M. McGlohon, J. Leskovec, C. Faloutsos, M. Hurst, N. Glance. Finding Patterns in Blog Shapes and Blog Evolution. ICWSM 2007. 28
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134. PCA on cascade types
Observation: Content of blogs and cascade behavior are often related.
Distinct clusters for “conservative” and “humorous” blogs (hand-labeling).
We think the PCs correspond o stars and chains-- humorous blogs tend to go all at once, no deep discussions.
M. McGlohon, J. Leskovec, C. Faloutsos, M. Hurst, N. Glance. Finding Patterns in Blog Shapes and Blog Evolution. ICWSM 2007. 29
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135. Part 3: Empirical Studies
Q6: How do cascades look like?
Q7: How does activity evolve over time?
Q8: How does external influence act?
Prakash and Faloutsos 2012

136. Rise and fall patterns in social media
Meme (# of mentions in blogs)
short phrases Sourced from U.S. politics in 2008
“you can put lipstick on a pig”
“yes we can”
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137. Rise and fall patterns in social media
Can we find a unifying model, which includes these patterns?
four classes on YouTube [Crane et al. ’08]
six classes on Meme [Yang et al. ’11]
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138. Rise and fall patterns in social media
Answer: YES!
We can represent all patterns by single model
In Matsubara+ SIGKDD 2012
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139. Main idea - SpikeM β 1. Un-informed bloggers (uninformed about rumor)
2. External shock at time nb (e.g, breaking news)
3. Infection (word-of-mouth) β
Time n=0
Time n=nb
Time n=nb+1
Infectiveness of a blog-post at age n:
Strength of infection (quality of news)
Decay function (how infective a blog posting is)
Power Law
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140. SpikeM - with periodicity
Details
SpikeM - with periodicity
Full equation of SpikeM
Periodicity
12pm
Peak activity
3am
Low activity
Time n
Bloggers change their activity over time
(e.g., daily, weekly, yearly)
activity
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141. SpikeM -> exponential
Details
Analysis – exponential rise and power-raw fall
Rise-part
SI -> exponential
SpikeM -> exponential
Liner-log
Log-log
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142. Details SI -> exponential SpikeM -> power law
Analysis – exponential rise and power-raw fall
Fall-part
SI > exponential
SpikeM -> power law
Liner-log
Log-log
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143. Tail-part forecasts SpikeM can capture tail part
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144. “What-if” forecasting
e.g., given (1) first spike,
(2) release date of two sequel movies
(3) access volume before the release date
(1) First spike
(2) Release date
(3) Two weeks before release ? ?
Prakash and Faloutsos 2012

145. “What-if” forecasting
SpikeM can forecast not only tail-part, but also rise-part!
SpikeM can forecast upcoming spikes
(1) First spike
(2) Release date
(3) Two weeks before release
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146. Part 3: Empirical Studies
Q6: How do cascades look like?
Q7: How does activity evolve over time?
Q8: How does external influence act?
Prakash and Faloutsos 2012

147. Tweets Diffusion: Problem Definition
Given:
Action log of people tweeting a #hashtag ( )
A network of users ( )
Find:
How external influence varies with #hashtags? ?? ?? ? ?
Prakash and Faloutsos 2012 ? ?

148. Results: External Influence vs Time
“External Effects”
Long-running tags
#nowwatching, #nowplaying, #epictweets
“Word-of-mouth”
#purpleglasses, #brits, #famouslies
Bursty, external events
#oscar, #25jan
#openfollow, #ihatequotes, #tweetmyjobs
“Word-of-mouth” Not trending
time
Can also use for Forecasting, Anomaly Detection!
Prakash and Faloutsos 2012

149. Outline Motivation Part 1: Understanding Epidemics (Theory)
Part 2: Policy and Action (Algorithms)
Part 3: Learning Models (Empirical Studies)
Conclusion
single virus VS multiple viruses
Prakash and Faloutsos 2012

150. Conclusions Epidemic Threshold Fast Immunization Bursts: SpikeM model
It’s the Eigenvalue
Fast Immunization
Max. drop in eigenvalue,
linear-time near-optimal algorithm
Bursts: SpikeM model
Exponential growth,
Power-law decay
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151. Propagation on Networks
Biology
Theory & Algo.
Physics
Comp. Systems
Propagation on Networks
Social Science
ML & Stats.
Econ.
Prakash and Faloutsos 2012

152. References Prakash and Faloutsos 2012
Winner-takes-all: Competing Viruses or Ideas on fair-play networks (B. Aditya Prakash, Alex Beutel, Roni Rosenfeld, Christos Faloutsos) – In WWW 2012, Lyon
Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks (B. Aditya Prakash, Deepayan Chakrabarti, Michalis Faloutsos, Nicholas Valler, Christos Faloutsos) - In IEEE ICDM 2011, Vancouver (Invited to KAIS Journal Best Papers of ICDM.)
Times Series Clustering: Complex is Simpler! (Lei Li, B. Aditya Prakash) - In ICML 2011, Bellevue
Epidemic Spreading on Mobile Ad Hoc Networks: Determining the Tipping Point (Nicholas Valler, B. Aditya Prakash, Hanghang Tong, Michalis Faloutsos and Christos Faloutsos) – In IEEE NETWORKING 2011, Valencia, Spain
Formalizing the BGP stability problem: patterns and a chaotic model (B. Aditya Prakash, Michalis Faloutsos and Christos Faloutsos) – In IEEE INFOCOM NetSciCom Workshop, 2011.
On the Vulnerability of Large Graphs (Hanghang Tong, B. Aditya Prakash, Tina Eliassi-Rad and Christos Faloutsos) – In IEEE ICDM 2010, Sydney, Australia
Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms (B. Aditya Prakash, Hanghang Tong, Nicholas Valler, Michalis Faloutsos and Christos Faloutsos) – In ECML-PKDD 2010, Barcelona, Spain
MetricForensics: A Multi-Level Approach for Mining Volatile Graphs (Keith Henderson, Tina Eliassi-Rad, Christos Faloutsos, Leman Akoglu, Lei Li, Koji Maruhashi, B. Aditya Prakash and Hanghang Tong) - In SIGKDD 2010, Washington D.C.
Parsimonious Linear Fingerprinting for Time Series (Lei Li, B. Aditya Prakash and Christos Faloutsos) - In VLDB 2010, Singapore
EigenSpokes: Surprising Patterns and Scalable Community Chipping in Large Graphs (B. Aditya Prakash, Ashwin Sridharan, Mukund Seshadri, Sridhar Machiraju and Christos Faloutsos) – In PAKDD 2010, Hyderabad, India
BGP-lens: Patterns and Anomalies in Internet-Routing Updates (B. Aditya Prakash, Nicholas Valler, David Andersen, Michalis Faloutsos and Christos Faloutsos) – In ACM SIGKDD 2009, Paris, France.
Surprising Patterns and Scalable Community Detection in Large Graphs (B. Aditya Prakash, Ashwin Sridharan, Mukund Seshadri, Sridhar Machiraju and Christos Faloutsos) – In IEEE ICDM Large Data Workshop 2009, Miami
FRAPP: A Framework for high-Accuracy Privacy-Preserving Mining (Shipra Agarwal, Jayant R. Haritsa and B. Aditya Prakash) – In Intl. Journal on Data Mining and Knowledge Discovery (DKMD), Springer, vol. 18, no. 1, February 2009, Ed: Johannes Gehrke.
Complex Group-By Queries For XML (C. Gokhale, N. Gupta, P. Kumar, L. V. S. Lakshmanan, R. Ng and B. Aditya Prakash) – In IEEE ICDE 2007, Istanbul, Turkey.
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153. Acknowledgements Collaborators Christos Faloutsos
Roni Rosenfeld,
Michalis Faloutsos,
Lada Adamic,
Theodore Iwashyna (M.D.),
Dave Andersen,
Tina Eliassi-Rad,
Iulian Neamtiu,
Varun Gupta,
Jilles Vreeken,
Deepayan Chakrabarti, Hanghang Tong, Kunal Punera, Ashwin Sridharan, Sridhar Machiraju, Mukund Seshadri, Alice Zheng, Lei Li, Polo Chau, Nicholas Valler, Alex Beutel, Xuetao Wei
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154. Acknowledgements
Funding
Prakash and Faloutsos 2012

155. Dynamical Processes on Large Networks
B. Aditya Prakash
Christos Faloutsos
Analysis
Policy/Action
Data
Prakash and Faloutsos 2012