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Discovering Leaders from Community Actions. Amit Goyal 1 Francesco Bonchi 2 Laks V.S. Lakshmanan 1 Oct 27, 2008. 2. 1. Context & Motivations: Viral Marketing. We are more influenced by our friends than strangers

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discovering leaders from community actions

Discovering Leaders from Community Actions

Amit Goyal1

Francesco Bonchi2

Laks V.S. Lakshmanan1

Oct 27, 2008

2

1

word of mouth and viral marketing
We are more influenced by our friends than strangers

68% of consumers consult friends and family before purchasing home electronics (Burke 2003)

Word of Mouth and Viral Marketing

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

viral marketing
Also known as Target Advertising

Initiate chain reaction by Word of mouth effect

Low investments, maximum gain

Viral Marketing

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

viral marketing as an optimization problem
Given: Network with influence probabilities

Problem: Select top-k leaders such that by targeting them, the spread of influence is maximized

Hao Ma et al 2008, Domingos et al 2001, Richardson et al 2002, Kempe et al 2003

How to calculate true influence probabilities?

Viral Marketing as an Optimization Problem

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

a pattern mining approach
A pattern mining approach
  • We propose a completely different approach based on frequentpattern mining.
  • We focus on the actions performed by users:
      • Joining a community (as in flickr/facebook community)
      • Rating a song, a movie (as in Y! Music, Y! Movie)
  • Importance of time in which actions are performed
  • Assumption: Users can see their friends’ actions

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

our contributions
Our Contributions
  • Formally define the notion of leaders and its various flavors
  • Efficient algorithms for extracting these leaders
  • Demonstrate the utility and scalability of our algorithms, via an extensive set of experiments on a real world dataset
    • Yahoo! Messenger (social graph)
    • Yahoo! Movies rating (actions log)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

rest of the talk
Rest of the talk
  • Framework definition:
    • Influence propagation on the social network
    • Various notions of leaders
  • Algorithms
  • Experiments
  • Related Work
  • Conclusion

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

input data 1
Input Data (1)
  • A social network, i.e., an undirected graph G=(V,E) where nodes are users and edges represent social ties.
  • Users declare their friends. e.g. Facebook, Yahoo! Messenger etc

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

input data 2
An actions log sorted in chronological order, i.e., a relation

Actions(User, Action, Time)

Example: Jack joined Yoga community at time 5

Assumption:

Users can see their friends actions (feeds)

Input Data (2)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

action propagation
Action Propagation

Jack

Jill

3 time units

  • Jack and Jill are friends
  • Jack and Mary are friends
  • Action is “Joining the Yoga community”

Joined Yoga

Community at time 8

Joined Yoga

Community at time 5

995 time units

Mary

Joined Yoga

Community at time 1000

  • Action Propagated from Jack to Jill
  • Action propagated from Jack to Mary

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

propagation graph
Propagation Graph

Jack

Jill

Joined Yoga

Community at time 8

Joined Yoga

Community at time 5

Ben

Joined Yoga

Community at time 15

Joey

Mary

Joined Yoga

Community at time 12

Joined Yoga

Community at time 1000

Can we say Mary got influenced by Jack?? NO

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

user influence graph
When an action propagates from user uto user v,we may think of vbeing influenced by u

Influence should decay in time

Size of influence graph << Size of PG

User Influence Graph

Propagation Graph

User Influence Graph for Jack

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

leaders first definition

Jack

Jack

Jack

Jack

Jill

Jill

Jill

Jill

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Community at time 8

Community at time 8

Community at time 8

Community at time 8

Community at time 5

Community at time 5

Community at time 5

Community at time 5

Ben

Ben

Ben

Ben

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Community at time 15

Community at time 15

Community at time 15

Community at time 15

Joey

Joey

Joey

Joey

Mary

Mary

Mary

Mary

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Joined Yoga

Community at time 12

Community at time 12

Community at time 12

Community at time 12

Community at time 1000

Community at time 1000

Community at time 1000

Community at time 1000

Leaders – first definition
  • Who should be a leader?
    • For an action, should influence sufficiently large number of users ( >ψ )
    • For an action, should influence these users in a reasonable amount of time ( <π )
    • Should act as a leader in sufficiently large number of actions ( >σ )

3

3

If ψ= 2, π = 15, σ = 1

then, both Jack and Jill are leaders

7

7

7

7

4

3

995

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

tribe leader
A leader may influence different users for different actions

What if a leader lead a fixed set of users for different actions?

We call these leaders as Tribe Leaders

Can be considered as small communities

Tribe Leader

jack

A2

A3

A1

A1, A2 and A3 are 3 different actions

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

additional constraint genuineness
It may happen that one user acts as a leader but in concrete he is always a follower of the other leaders

We want to avoid this kind of fake leaders.

gen(Jill) = 1/3

Another constraint: confidence

Additional Constraint: Genuineness

Jack

Tom

A1

A2

Jill

A1

A3

A2

A1, A2 and A3 are 3 different actions

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

algorithms overview
Algorithms: Overview
  • Assumptions:
    • Social graph is huge – millions of nodes
    • Actions log is huge – millions of tuples
    • For an action, size of user Influence Graph << size of Propagation Graph for all users
  • Our algorithms are able to extract the patterns (leaders and tribe leaders) in no more than one scan of the action log table.

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

algorithms overview1
Algorithms: Overview
  • Scan the action log table by means of a window of sizeπbackward in time, i.e., starting from the most recent timestamp (bottom of the table if we assume tuples to be ordered by time).
  • Efficiently compute the influence matrix, i.e., a matrix Users x Actions
    • IMπ(u, a) represents number of users, influenced by u w.r.t. action a within timeπ
  • Compute leaders from IM

IM10(Jack, “joining yoga community”) = 3

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

computing influence matrix 1
Computing Influence Matrix (1)
  • We use a bit vector to track which users are influenced by a given user. Updated incrementally
  • Locking mechanism using another bit vector
    • 0 => free bit; 1 => occupied bit
  • Node to bit index mapping stored in a queue
  • Bits must be dynamically allocated.

Queue

Head

R

Time window on propagation graph

S

T

W

V

01010111

Lock bit Vector

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

computing influence matrix 2
Computing Influence Matrix (2)
  • Slide up the current window – delete node V
  • Delete the entry from queue
  • Update the lock
  • Update influence vectors

Queue

Head

R

Time window on propagation graph

S

T

W

V

01010011

Lock bit Vector

01010111

Lock bit Vector

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

computing influence matrix 3
Computing Influence Matrix (3)
  • New node P added
  • Issue a lock, add entry to the queue
  • Compute its Influence Vector by propagation
  • Number of followers of P = 4
  • IM(P,a) = 4

Queue

Head

P

Time window on propagation graph

R

S

T

W

01010011

Lock bit Vector

01010111

Lock bit Vector

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

mining tribe leaders
Mining Tribe Leaders
  • Influence Matrix not enough
  • We use influence cube: Users x Actions x Users
    • ICπ(u,a,v) = 1, when user v is influenced by user u for action a within time π
  • We do not explicitly compute the whole cube due to sparsity.
  • Problem same as discovering existence of frequent itemsets of size larger than a given threshold

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

algorithms final comments
Algorithms - Final Comments
  • The only truly mandatory threshold is π(time threshold)
  • Influence Matrix: O(TAn2) in bit level operations
    • T = total number of tuples in action log
    • A = total number of distinct actions
    • n = maximum number of nodes visible in any position of the time window
    • n << N, where N is the total number of users
  • Tribe Leaders:
    • Influence Cube: O(TAn2)
    • Finding existence of frequent itemsets: exponential in number of followers
      • But very fast due to optimizations (Bonchi 2003)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

data preparation
Data Preparation
  • Data
    • Social graph: Yahoo! Instant Messenger
    • Actions log: Yahoo! Movies
      • Action = user u rated movie m at time t
    • joined through common users identifiers
  • Started from Yahoo! Instant Messenger subgraph of “most active” users (110M nodes) and 21M ratings from Yahoo! Movies.
  • Ended with 217.5K nodes, 221.4K edges and 1.8M ratings.

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

data characteristics connected components
Data characteristics: connected components

Total 46,650 connected components

Giant component

94K Users (43.2% of connected users)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

leaders vs tribe leaders
Leaders Vs. Tribe leaders

π – threshold on time

σ – threshold on number of actions

ψ – threshold on number of influenced users

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

number of leaders found
Number of leaders found

π – threshold on time

σ – threshold on number of actions

ψ – threshold on number of influenced users

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

run time
Run-time

π – threshold on time

σ – threshold on number of actions

ψ – threshold on number of influenced users

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

genuineness an almost binary concept
Genuineness: an almost binary concept!

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

top 10 tribe leaders w r t tribe size
Top-10 tribe leaders w.r.t. tribe size
  • Tribe leaders exhibit high confidence.
  • Tribe leaders with low genuineness were found dominated by other tribe leaders present in the tables.
  • We found many users acting as leader in many actions but not being a tribe leader.

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

related work 1
Related Work (1)
  • Identifying influential users
    • Domingos et al 2001, Richardson et al 2002, Kempe et al 2005
  • Identifying influential bloggers
    • Agarwal et al 2008
  • Identifying communities in Social Networks
    • Hoproft et al 2003, Kumar et al 2006, Backstrom et al 2006, Tantipathananadh et al 2007, Huang et al 2008, Friedland at el 2007

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

related work 2
Related Work (2)
  • Influence and Correlation in Social Networks
    • Aris Anagnostopoulos et al 2008
  • Revenue maximization
    • Hartline et al 2008
  • Near optimal sensor placement for outbreak detection
    • Leskovec et al 2007
  • Heat Diffusion Model
    • Hao Ma et al 2008 (CIKM)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

conclusions
Conclusions
  • Proposed framework based on frequent pattern mining for discovering leaders in social networks
  • Formally define the problem of extracting leaders from social graph and actions log.
    • Various notions of leader, tribe leader
    • Their confidence and genuine variants
  • Efficient algorithms for extracting leaders of various flavors
    • Just one pass over the actions log table
  • Demonstrate the utility and scalability of our algorithms, via an extensive set of experiments on a real world dataset
    • Yahoo! Messenger (social graph)
    • Yahoo! Movies rating (actions log)

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

ongoing future work
Ongoing/Future Work
  • Gurumine: Pattern Mining System for Discovering Leaders and Tribes (Demo paper to appear in ICDE 2009)
  • Leadership Cube: What kind of leaders attract what kind of followers for what kind of actions?
  • Viral Marketing
  • Stronger notions of influence?

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

thanks

Thanks!

3

1

4

1

3

13

4

2

3

3

2

7

5

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

number of leaders found1
Number of leaders found

π – threshold on time

σ – threshold on number of actions

ψ – threshold on number of influenced users

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

additional constraint confidence
Additional constraint: confidence
  • Similarly to association rules, we can have a confidence measure for leaders.
  • Leadership confidence =

# actions in which is a leader / # actions performed

  • Example: Lets say Jack performed 10 actions out of which in 7 actions, he acted as a leader (i.e. more than ψ users followed in short time), then conf(Jack) = 7/10

http://cs.ubc.ca/~goyal/

Amit Goyal (University of British Columbia)

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