Making Diffusion Work for You

B. Aditya PrakashComputer Science

Virginia Tech.

GraphEx Symposium, MIT Endicott House, Aug 21, 2014

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Thanks!

• Ali Pinar• Ben Miller

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Networks are everywhere!

Human Disease Network [Barabasi 2007]

Gene Regulatory Network [Decourty 2008]

Facebook Network [2010]

The Internet [2005]

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Dynamical Processes over networks are also everywhere!

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

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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

SI Model

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Why do we care? (1: Epidemiology)

• Dynamical Processes over networks

• Each circle is a hospital• ~3000 hospitals• More than 30,000 patients transferred

[US-MEDICARE NETWORK 2005]

Problem: Given k units of disinfectant, whom to immunize?

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Why do we care? (1: Epidemiology)

CURRENT PRACTICE OUR METHOD

~6x fewer!

[US-MEDICARE NETWORK 2005]

Hospital-acquired inf. took 99K+ lives, cost $5B+ (all per year)

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Why do we care? (2: Online Diffusion)

> 800m users, ~$1B revenue [WSJ 2010]

~100m active users

> 50m users

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Why do we care? (2: Online Diffusion)

• Dynamical Processes over networks

Celebrity

Buy Versace™!

Followers

Social Media Marketing

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Why do we care? (3: To change the world?)

• Dynamical Processes over networks

Social networks and Collaborative Action

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High Impact – Multiple Settings

Q. How to squash rumors faster?

Q. How do opinions spread?

Q. How to market better?

epidemic out-breaks

products/viruses

transmit s/w patches

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Research Theme

DATALarge real-world

networks & processes

ANALYSISUnderstanding

POLICY/ ACTIONManaging/

Utilizing

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Research Theme – Public Health

DATAModeling # patient

transfers

ANALYSISWill an epidemic

happen?

POLICY/ ACTION

How to control out-breaks?

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Research Theme – Social Media

DATAModeling Tweets

spreading

POLICY/ ACTION

How to market better?

ANALYSIS# cascades in

future?

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In this talk

Q1: How to ‘zoom-out’ of graphs?

Q2: How to control out-breaks?

POLICY/ ACTIONUtilizing

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In this talk

DATALarge real-world

networks & processes

Q3: How does ‘activity’ evolve over time?

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Outline

• Motivation• Part 1: Policy and Action (Algorithms)• Part 2: Learning Models (Empirical Studies)• Conclusion

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Part 1: Algorithms

• Q1: How to zoom-out of a network?• Q2: How to control out-breaks?

(Broad theme: Network Topology Manipulation)

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“Zoom-out” of the network• “Zoom-out” of the cascade graph to get a

quick picture (= summarization)

Coarsening

Big graph

Zoom-out

A

FE

D

CB

Smaller representation of the network

A

CB

E

F

D

[Purohit, Prakash, et, al. SIGKDD 2014]

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Challenges

• C1: How do we maintain diffusive characteristics when coarsening networks?

• C2: How do we merge node to get the coarse network?

• C3: how do we find the best node to merge fast?

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C1: Modeling diffusion• Information spreads over networks– e.g.:, rumor/meme spreads over Twitter following

network

• Independent cascade model (IC) [Kempe+, KDD03]

– Weights pij: propagation prob. from i to j– Each node has only one chance to infect its neighbors

Meme spreading

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Diffusive characteristics• First eigenvalue λ1 (of adjacency matrix) is sufficient

for most diffusion models. [Prakash et al. ICDM’12 selected for best papers]

λ1 is the epidemic threshold (will there be an epidemic?)

“Safe” “Vulnerable” “Deadly”

Increasing λ1 , Increasing vulnerability

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C1: maintain diffusive characteristics

• Goal: maintain the diffusive characteristics of the original network in the coarsened network

Original network

coarsen

A

FE

D

CB

Coarsened network

A

CB

E

F

D

Make the coarsened network have the least change in the first eigenvalue

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C2: How to merge nodes• Goal: Merge nodes of graph G to get the

coarsened graph that “approximates” G with respect to diffusion

Merge b and a can get the least change of λ1

Is this correct?

0.375!

Original network

Influence from d to b: 0.5Influence from d to a: 0.25Average: 0.375

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• In general: C2: How to merge nodes

Merging a,b

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Problem DefinitionGraph Coarsening Problem (GCP)• Given: a large graph G, and the reduction factor• Find: the best set of adjacent nodes • To minimize |λG-λH| where H is the coarsened graph

– i.e.: H has the least change in the first eigenvalue– we use to λG represent the first eigenvalue of G

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C3: which nodes to merge

• Goal: – Find the best nodes to merge– Fast, scalable to large network

Original network

coarsen

A

FE

D

CB

Coarsened network

A

CB

E

F

D

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Naive Greedy HeuristicStep:• Score every edge by the change in eigenvalue• Greedily choose the edge (a,b) with the least score, and

merge (a,b)• Re-evaluate the scores of every edge and repeat

• Too slow! O(m2) time to score all edges• Lose time benefits of analyzing the smaller

graph

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CoarseNet: idea• Can we approximate the edge scores faster?

– Yes!

• Use matrix perturbation arguments to estimate (up to first order terms) the score of an edge in constant time (skipping details)

• Score all edges in O(m) time– Naive Heuristic: O(m2) time

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CoarseNet: Complete algorithm

• Step1: compute scores for all edge pairs2: Merge nodes with smallest score3. Goto step 1 until αn nodes left

Original Network (weight=0.5)

Assigning scores

Merging edges

Coarsened Network

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How do we perform?

The first eigenvalue gets preserved well up to large coarsening factors!

Amazon

(See more results in the paper)

DBLP

Higher is better

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Application 1: Influence Maximization

• Methodology:Step 1: Coarsen the large social network using CoarsenNetStep 2: Solve influence maximization on the coarsened networkStep 3: Randomly select one node from each selected “supernode”

Step 1: Coarsen

A

CB

E

F

DStep 2: Solve influence maximization

A

CB

E

F

D

Step 3: Randomly select one node from C

We call it CSPIN

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Quality of CSPIN w.r.t

We can merge up to 95% of the vertices are merged without significantly affecting the influence spread!

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Application 2: Diffusion Characterization

• Goal: use Graph Coarsening to understand information cascades

• Dataset: Flixster– a fridendship network with movie ratings

– Cascade: the same movie rating from friends

• Methodology– coarsen the network using CoarseNet with the reduction

factor α=0.5– study the formed groups (supernodes)– Can get non-network surrogates

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Diffusion observation

Observation 1: a very large fraction of movies propagate in a small number of groupsObservation 2: a multi-modal distribution

Stats: • 1891 groups • mean group size: 16.6 • the largest group: 22061

nodes (roughly 40% of nodes)

(See more results in the paper)

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Future work…

• How is it related to community structure? • More applications, like Visualization…• Parallelization

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Part 1: Algorithms

• Q1: How to zoom-out of a network?• Q2: How to control out-breaks?

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Immunization (= Interventions)

• Different Flavors:– Pre-emptive– Data-aware

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Pre-emptive: Vulnerability (Again!)

• First eigenvalue λ1 (of adjacency matrix) is sufficient for most diffusion models.

[Prakash et al. ICDM’12 selected for best papers]

λ1 is the epidemic threshold

“Safe” “Vulnerable” “Deadly”

Increasing λ1 , Increasing vulnerability

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Goal

• Decrease λ1 as much as possible

• Node based [Tong, P., + ICDM 2010]• Edge-based [Tong, P., Eliassi-Rad+ CIKM 2012,

Best Paper Award]• Edge-Manipulation [P., Adamic+ SDM 2013]

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Latest results

• First (provable) approximation algorithms for edge-based problem (under submission [Saha, Adiga, P., Vullikanti 2014])– O(log^2 n)--factor (can be improved to O(log n)) • Based on the idea of removing closed walks

– Semi-Definite Programming Rounding-based O(1) factor

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Data-aware Immunization

Dominator tree

Graph with infected nodes

Given: Graph and Infected nodesFind: ‘best’ nodes for immunization• Complexity

– NP-hard– Hard to approximate within an absolute error

• DAVA-tree– Optimal solution on the tree

• DAVA and DAVA-fast– Merging infected nodes– Build a “dominator tree”, and run DAVA-tree

• Running time: subquadratic– DAVA: O(k(|E|+ |V|log|V|))– DAVA-fast: O(|E|+|V|log|V|)

[Zhang and Prakash, SDM 2014]

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Extensions

• Can be extended to Uncertain and noisy initial data as well!

[Zhang and Prakash, CIKM 2014]

Twitter Firehose API1% sample

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Outline

• Motivation• Part 1: Policy and Action (Algorithms)• Part 2: Learning Models (Empirical Studies)• Conclusion

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Part 2: Empirical Studies

• Q3: How does activity evolve over time?

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Google Search Volume

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

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Patterns

X

Y

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Patterns

X

Y

More Data

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Patterns

X

YAnomaly

?

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Patterns

X

YAnomaly

?

Extrapolation

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Patterns

X

YAnomalyImputation

Extrapolation

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Patterns

AnomalyImputation

Extrapolation

Compression

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• Meme (# of mentions in blogs)– short phrases Sourced from U.S. politics in 2008

“you can put lipstick on a pig”

“yes we can”

Rise and fall patterns in social media

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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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Rise and fall patterns in social media

• Answer: YES!

• We can represent all patterns by single model

In Matsubara, Sakurai, Prakash+ SIGKDD 2012

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Main idea - SpikeM- 1. Un-informed bloggers (uninformed about rumor)- 2. External shock at time nb (e.g, breaking news)- 3. Infection (word-of-mouth)

Infectiveness of a blog-post at age n:

- Strength of infection (quality of news)

- Decay function (how infective a blog posting is)

Time n=0 Time n=nb Time n=nb+1

β

Power Law

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-1.5 slopeJ. G. Oliveira et. al. Human Dynamics: The

Correspondence Patterns of Darwin and Einstein. Nature 437, 1251 (2005) . [PDF]

(also in Leskovec, McGlohon+, SDM 2007)

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SpikeM - with periodicity

• Full equation of SpikeM

Periodicity

12pmPeak activity 3am

Low activity

Time n

Bloggers change their activity over time

(e.g., daily, weekly, yearly)

activity

Details

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Tail-part forecasts

• SpikeM can capture tail part

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“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

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“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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Modeling Malware Penetration

• Worldwide Intelligence Network– Which machine got which malware (or legitimate files)– 1 Billion nodes– 37 Billion edges

• Q: Temporal patterns?

[Papalexakakis et. al. + 2013]

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Q: Temporal Patterns

Looks familiar?

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SpikeM again (or SharkFin)

7 parameters only!

~ 400 points ~ 400 points

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Latent Propagation Patterns

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Bonus: Protest Predictions

• Can Twitter provide a lead time?• South American twitter dataset– Language: Spanish/Portuguese– Idea

1. Look for trending keywords.2. Predict event type for protest using SpikeMparameters!

A political tweet

Violent Protest (VP)

Non Violent Protest (P)

[Sundereisan et al. ASONAM 2014][Jin et al. SIGKDD 2014]

VP

P

Outline

• Motivation• Part 1: Learning Models (Empirical Studies)• Part 2: Understanding Epidemics (Theory)• Part 3: Policy and Action (Algorithms)• Conclusion and Future Plans

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Future Plans

DATALarge real-world

networks & processes

ANALYSISUnderstanding

POLICY/ ACTIONManaging

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Scalability – Big Data

• Datasets of unprecedented scale– High dimensionality and sample size!

• Need scalable algorithms for – Learning Models– Developing Policy

• Leverage parallel systems– Map-Reduce clusters (like Hadoop) for data-intensive

jobs (more than 6000 machines) – Parallelized compute-intensive simulations (like Condor)

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Uncertain Data in Cascade analysis

Original, Nodes sampled off

Culprits, and missing nodes filled in

Sundereisan, Vreeken, Prakash. 2014

Correcting for missing data Designing More Robust Immunization Policies

Zhang and Prakash. CIKM 2014

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Social Biological Contagion

Automatically learnmodels

Chen, Prakash+. 2014

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References1. Scalable Vaccine Distribution in Large Graphs given Uncertain Data (Yao Zhang and B. Aditya Prakash) -- In

CIKM 2014.2. Fast Influence-based Coarsening for Large Networks (Manish Purohit, B. Aditya Prakash, Chahhyun Kang, Yao

Zhang and V. S. Subrahmanian) – In SIGKDD 20143. DAVA: Distributing Vaccines over Large Networks under Prior Information (Yao Zhang and B. Aditya Prakash) --

In SDM 20144. Fractional Immunization on Networks (B. Aditya Prakash, Lada Adamic, Jack Iwashnya, Hanghang Tong, Christos

Faloutsos) – In SDM 20135. Spotting Culprits in Epidemics: Who and How many? (B. Aditya Prakash, Jilles Vreeken, Christos Faloutsos) – In

ICDM 2012, Brussels Vancouver (Invited to KAIS Journal Best Papers of ICDM.)6. Gelling, and Melting, Large Graphs through Edge Manipulation (Hanghang Tong, B. Aditya Prakash, Tina Eliassi-

Rad, Michalis Faloutsos, Christos Faloutsos) – In ACM CIKM 2012, Hawaii (Best Paper Award)7. Rise and Fall Patterns of Information Diffusion: Model and Implications (Yasuko Matsubara, Yasushi Sakurai, B.

Aditya Prakash, Lei Li, Christos Faloutsos) – In SIGKDD 2012, Beijing8. Interacting Viruses on a Network: Can both survive? (Alex Beutel, B. Aditya Prakash, Roni Rosenfeld, Christos

Faloutsos) – In SIGKDD 2012, Beijing9. Winner-takes-all: Competing Viruses or Ideas on fair-play networks (B. Aditya Prakash, Alex Beutel, Roni

Rosenfeld, Christos Faloutsos) – In WWW 2012, Lyon10. 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.)

11. Times Series Clustering: Complex is Simpler! (Lei Li, B. Aditya Prakash) - In ICML 2011, Bellevue12. 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

13. Formalizing the BGP stability problem: patterns and a chaotic model (B. Aditya Prakash, Michalis Faloutsos and Christos Faloutsos) – In IEEE INFOCOM NetSciCom Workshop, 2011.

14. On the Vulnerability of Large Graphs (Hanghang Tong, B. Aditya Prakash, Tina Eliassi-Rad and Christos Faloutsos) – In IEEE ICDM 2010, Sydney, Australia

15. 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

16. 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.

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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, V. S. Subrahmanian John Brownstein (M.D.)

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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Acknowledgements

• Students Liangzhe Chen Shashidhar Sundereisan Benjamin Wang Yao Zhang

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Acknowledgements

Funding

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Analysis Policy/Action Data

Making Diffusion Work for You

B. Aditya Prakash http://www.cs.vt.edu/~badityap