Rise and Fall Patterns of Information Diffusion: Model and Implications �Yasuko Matsubara (Kyoto University), Yasushi Sakurai (NTT), B. Aditya Prakash (CMU), Lei Li (UCB), Christos Faloutsos (CMU) �

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Motivation �

Social media facilitate faster diffusion of news and rumors

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Q: How do news and rumors spread in social media? �

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News spread in social media �

MemeTracker [Leskovec et al. KDD’09] short phrases sourced from U.S. politics in 2008

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“you can put lipstick on a pig” (# of mentions in blogs)

“yes we can”

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News spread in social media �

MemeTracker [Leskovec et al. KDD’09] short phrases sourced from U.S. politics in 2008

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“you can put lipstick on a pig” (# of mentions in blogs)

“yes we can”

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Breaking news�

Decay �News

spread

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Rise and fall patterns in social media�

Twitter (# of hashtags per hour)

Google trend (# of queries per week)

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“#assange” “#stevejobs”

“harry potter” (2010 - 2011) “tsunami” (in 2005)

(per hour, 1week) (per hour, 1 week)

(per week, 1 year) (per week, 2 years)

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Rise and fall patterns in social media�

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How many patterns are there? -Earlier work claims there’re several classes •  four classes on YouTube [Crane et al. PNAS’08] •  six classes on Media [Yang et al. WSDM’11]

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Rise and fall patterns in social media�

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Q. How many classes are there after all?

A. Our answer is “ONE”!

We can represent all patterns by single model

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Outline �

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-  Motivation -  Problem definition -  Proposed method -  Experiments -  Discussion – SpikeM at work -  Conclusions �

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Problem definition �

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Goal: predict/model social activity �

Given:

-  Network of bloggers/users -  External shock/event -  Quality of the event β Find:

-  How blogging activity will evolve over time

Problem 1 (What-if?)�β

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Problem definition �

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Goal: predict/model social activity �

Given:

-  Behavior of spikes Find:

-  Equation/model that can explain them, e.g., -  # of potential bloggers -  Strength of external shock -  Quality of the event β

Epidemic process by word-of-mouth

Problem 2 (Model design) �

β

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Outline �

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-  Motivation -  Problem definition -  Proposed method -  Experiments -  Discussion – SpikeM at work -  Conclusions �

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Proposed method�

SpikeM capture 3 properties of real spike

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1. periodicities

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Proposed method�

SpikeM capture 3 properties of real spike

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2. avoid infinity

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1. periodicities

Proposed method�

SpikeM capture 3 properties of real spike

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3. power-law fall

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1. periodicities 2. avoid infinity

Proposed method�

SpikeM capture 3 properties of real spike

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3. power-law fall

SpikeM capture behavior of real spikes using few parameters

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1. periodicities 2. avoid infinity

Main idea (details) �-  1. Un-informed bloggers (clique of N bloggers/nodes)

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Time n=0

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Nodes (bloggers) consist of two states

- Un-informed of rumor

-  informed, and Blogged about rumor

U

B

Main idea (details) �-  1. Un-informed bloggers (clique of N bloggers/nodes)

-  2. External shock at time nb (e.g, breaking news)

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Time n=0 Time n=nb

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External shock

-  Event happened at time -  bloggers are informed, blog about news

nb

Sb

Sb

Main idea (details) �-  1. Un-informed bloggers (clique of N bloggers/nodes)

-  2. External shock at time nb (e.g, breaking news)

-  3. Infection (word-of-mouth effects)

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

β

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Infectiveness of a blog-post

-  Strength of infection (quality of news) -  Decay function (how infective a blog posting is)

!f (n)

Main idea (details) �-  1. Un-informed bloggers (clique of N bloggers/nodes)

-  2. External shock at time nb (e.g, breaking news)

-  3. Infection (word-of-mouth effects)

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

β

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Infectiveness of a blog-post

-  Strength of infection (quality of news) -  Decay function (how infective a blog posting is)

!f (n)

Decay function: �

f (n) = ! *n!1.5

f (n)

n

Linear scale f (n)

n

Log scale

-1.5

SpikeM-base (details) �Equations of SpikeM (base)

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-  Total population of available bloggers -  Strength of infection/news -  External shock at birth (time ) -  Background noise

nbSb

N

nb,Sb

!

!

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!B(n+1) =U(n) " (!B(t)+ S(t)) " f (n+1# t)+!t=nb

n

$

U(n+1) =U(n)!"B(n+1)Un-informed

Blogged

SpikeM - with periodicity (details) �Full equation of SpikeM

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U(n+1) =U(n)!"B(n+1)

Un-informed

Blogged

!B(n+1) = p(n+1) " U(n) " (!B(t)+ S(t)) " f (n+1# t)+!t=nb

n

$%

&''

(

)**Periodicity

12pm Peak activity 3am

Low activity

Time n

activity

p(n)Bloggers change their

activity over time (e.g., daily, weekly, yearly)�

Learning parameters -  Given a real time sequence -  Minimize the error (Levenberg-Marquardt (LM) fitting)

Model fitting (Details) �

SpikeM consists of 7 parameters

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! = {N,",nb,Sb,#,Pa,Ps}

X = {X(1),...X(n),...,X(nd )}

D(X,! ) = (X(n)!"B(n))2n=1

nd

#

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Analysis �

SpikeM matches reality exponential rise and power-raw fall

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rise fall

SpikeM vs. SI model (susceptible infected model)

Analysis �

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Linear-log

Log-log

Rise-part SpikeM: exponential SI model: exponential

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rise fall

Reverse x-axis�

Analysis �

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Linear-log

Log-log

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rise fall

Fall-part SpikeM: power law SI model: exponential

SpikeM matches reality

Outline �

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-  Motivation -  Problem definition -  Proposed method -  Experiments -  Discussion – SpikeM at work -  Conclusions �

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Experiments�

We answer the following questions…

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Q1. Match real spikes - Q1-1: K-SC clusters - Q1-2: MemeTracker - Q1-3: Twitter - Q1-4: Google trend

Q2. Forecast future patterns

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Q1-1 Explaining K-SC clusters�

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Six patterns of K-SC [Yang et al. WSDM’11]

SpikeM can generate all patterns in K-SC

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Q1-2 Matching MemeTracker patterns �

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MemeTracker (memes in blogs) [Leskovec et al. KDD’09]

SpikeM can fit various patterns in blog

Linear scale

Log scale

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Noise-robust

fitting�Outliers

Q1-3 Matching Twitter data�

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Twitter data (hashtags)

SpikeM can generate various patterns in social media

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Linear scale

Log scale

Q1-4 Matching Google trend data�

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Volume of searches for queries on Google

SpikeM can capture various patterns

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Q2 Tail-part forecasts�

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- Given a first part of the spike - forecast the tail part

SpikeM can capture tail part (AR: fail)

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Outline �

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-  Motivation -  Problem definition -  Proposed method -  Experiments -  Discussion – SpikeM at work -  Conclusions �

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SpikeM at work �

SpikeM is capable of various applications

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-  A1. What-if forecasting

-  A2. Outlier detection

-  A3. Reverse engineering

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A1. “What-if” forecasting �

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Forecast not only tail-part, but also rise-part!

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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A1. “What-if” forecasting �

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Forecast not only tail-part, but also rise-part!

SpikeM can forecast upcoming spikes

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(1) First spike (2) Release date (3) Two weeks before release

A2. Outlier detection �

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Fitting result of “tsunami (Google trend)” in log-log scale

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Another earthquake �

One year after Indian Ocean earthquake �Indian Ocean

earthquake �

A3. Reverse engineering �

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SpikeM provide an intuitive explanation PDF of parameters over 1,000 memes/hashtags

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Meme�

Twitter�

A3. Reverse engineering �

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SpikeM provide an intuitive explanation PDF of parameters over 1,000 memes/hashtags

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Observation 1 Total population N is

almost same

N =1,000 ~ 2,000

Meme�

Twitter�

A3. Reverse engineering �

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SpikeM provide an intuitive explanation PDF of parameters over 1,000 memes/hashtags

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Observation 2 Strength of first burst (news) is

! *N =1.0

Meme�

Twitter�

A3. Reverse engineering �

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SpikeM provide an intuitive explanation PDF of parameters over 1,000 memes/hashtags

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Observation 3 Daily periodicity with phase shift

Every meme has the same periodicity without lag

Ps = 0

(Twitter) Daily periodicity with

more spread in (i.e., Multiple time zone)

Ps

Meme�

Twitter�

Outline �

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-  Motivation -  Background -  Proposed method -  Experiments -  Discussion – SpikeM at work -  Conclusions �

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Conclusions�

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SpikeM has following advantages:

•  Unification power It includes earlier patterns/models

•  Practicality: It Matches real datasets

•  Parsimony It requires only 7 parameters

•  Usefulness: What-if scenarios, outliers, etc.

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Acknowledgements

Thanks Jaewon Yang & Jure Leskovec for the six clusters [WSDM’11]

Funding

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Thank you�

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Code: http://www.kecl.ntt.co.jp/csl/sirg/people/yasuko/software.html

Email: matsubara.yasuko lab.ntt.co.jp

Yasushi Sakurai

Yasuko Matsubara

B. Aditya Prakash

Lei Li Christos Faloutsos