1. Discovering Leaders from Community Actions
Amit Goyal1
Francesco Bonchi2
Laks V.S. Lakshmanan1
Oct 27, 2008
Hi! Good afternoon everyone. I am Amit Goyal, a Masters student in UBC. The topic of my talk is “Dis..”. This is a joint work with my supervisor Prof. laks and Francesco, who is working in Yahoo! Research, Barcelona. 1 2

2. Context & Motivations: Viral Marketing
Lets first talk about the context and motivations, which is Viral Marketing.

3. 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)
We are .. than strangers because we trust our friends. According to a study by Burke, ….
This idea has often been exploited in advertising domains and this kind of advertising is known as viral marketing.
Amit Goyal (University of British Columbia)

4. Viral Marketing Also known as Target Advertising
Exponential Growth by Spreading the Word
Low investments, maximum gain
It is also known as Target advertising.
By identifying and targeting influential users in a community, it is possible to spread the desire to perform certain actions through initiating a chain reaction by word of mouth effect
This form of advertising is one of the oldest and most effective form of advertising, Often companies use it to achieve maximum gains through low investments.
Amit Goyal (University of British Columbia)

5. 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
Domingos et al 2001, Richardson et al 2002, Kempe et al 2003
How to calculate true influence probabilities?
One of the attractive ways to study it is as an optimization problem. The problem is defined as follows. Input is a network with influence probabilities, e.g. …. and the problem ask to select top-k leaders such that by targ…
Some of the classical papers which talk about it are ..
But they an open the issue of calculating influence prob? In real world datasets, these probabilities are not available.
Amit Goyal (University of British Columbia)

6. A pattern mining approach
We propose a completely different approach based on frequent pattern 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
We propose a completely different approach based of frequent pattern mining. As most of you know, frequent pattern mining is a method for discovering interesting relations between items of transaction datasets.
We focus on the actions performed by users .. which can be ..
Why we focus on actions .. because this is what is available in real world datasets.
We give importance to time at which actions are performed and influence propagates. It makes sense to consider time as one of the parameter as advertisers often want to estimate the time in which they get returns.
Our assumption is … feeds
Amit Goyal (University of British Columbia)

7. 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)
Amit Goyal (University of British Columbia)

8. Rest of the talk Framework definition: Algorithms Experiments
Influence propagation on the social network
Various notions of leaders
Algorithms
Experiments
Related Work
Conclusion
Amit Goyal (University of British Columbia)

9. Framework Definition

10. 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
We consider two types of input data, first is a social network ..
Amit Goyal (University of British Columbia)

11. 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)
Amit Goyal (University of British Columbia)

12. Action Propagation Jack Jill Jack and Jill are friends
3 time units
Jill
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
Amit Goyal (University of British Columbia)

13. Propagation Graph Jack Jill Ben Joey Mary
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
Amit Goyal (University of British Columbia)

14. User Influence Graph
When an action propagates from user u to user v, we may think of v being influenced by u
Influence should decay in time
Size of influence graph << Size of PG
Propagation Graph
User Influence Graph for Jack
Amit Goyal (University of British Columbia)

15. 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 )
Jack
Jill
Joey
Joined Yoga
Community at time 5
Community at time 8
Community at time 1000
Mary
Ben
Community at time 12
Community at time 15
Jack
Jill
Joey
Joined Yoga
Community at time 5
Community at time 8
Community at time 1000
Mary
Ben
Community at time 12
Community at time 15
Jack
Jill
Joey
Joined Yoga
Community at time 5
Community at time 8
Community at time 1000
Mary
Ben
Community at time 12
Community at time 15
Jack
Jill
Joey
Joined Yoga
Community at time 5
Community at time 8
Community at time 1000
Mary
Ben
Community at time 12
Community at time 15 3 3
If ψ= 2, π = 15, σ = 1
then, both Jack and Jill are leaders 7 7 7 7 4 3
995
Amit Goyal (University of British Columbia)

16. 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
jack A2 A3 A1
A1, A2 and A3 are 3 different actions
Amit Goyal (University of British Columbia)

17. 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
Jack
Tom A1 A2
Jill A1 A3 A2
A1, A2 and A3 are 3 different actions
Amit Goyal (University of British Columbia)

18. Algorithms but how will I discover the leaders??

19. 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.
Amit Goyal (University of British Columbia)

20. Algorithms: Overview Compute leaders from IM
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
Amit Goyal (University of British Columbia)

21. Computing Influence Matrix (1)
We use a bit vector to track which users are influenced by a given user.
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.
(V,2)
(W,1)
(T,4)
(S,6)
(R,0)
Queue
Head R
Node
InfVec R S T W V
Time window on propagation graph S T
To compute IM, we use influence bit vectors which keep track of the info about which nodes influenced what nodes in the current time window.
As the time window moves, some nodes will drop off the window and some nodes will appear. Hence, the influence bit vectors should be computed incrementally. To do that, we make use of two operations called update and propagate which we will look into next slides.
As nodes enter and drop out of time window, we need to manage which nodes are represented by which bits of the influence bit vector. To do that, we make use of locking mechanism through lock bit vector which serves as an index. In a lock bit vector, 0 means free bit and 1 means the lock has been been occupied by some node. W V
Lock bit Vector
Amit Goyal (University of British Columbia)

22. Computing Influence Matrix (2)
Slide up the current window – delete node V
Delete the entry from queue
Update the lock
Update influence vectors
(V,2)
(W,1)
(T,4)
(S,6)
(R,0)
(V,2)
(W,1)
(T,4)
(S,6)
(R,0)
Queue
Head R
Node
InfVec R S T W V
Node
InfVec R S T W V
Time window on propagation graph S T W
Lock bit Vector
Lock bit Vector V
Amit Goyal (University of British Columbia)

23. 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
(W,1)
(T,4)
(S,6)
(R,0)
(W,1)
(T,4)
(S,6)
(R,0)
(P,2)
Queue
Head P
Node
InfVec P R S T W
Time window on propagation graph
Node
InfVec R S T W R S T
Lock bit Vector W
Lock bit Vector
Amit Goyal (University of British Columbia)

24. 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
Amit Goyal (University of British Columbia)

25. 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)
Amit Goyal (University of British Columbia)

26. Experiments enough talking, show me the results dude!!

27. 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.
Amit Goyal (University of British Columbia)

28. Data characteristics: connected components
Total 46,650 connected components
Giant component
94K Users (43.2% of connected users)
Amit Goyal (University of British Columbia)

29. Leaders Vs. Tribe leaders
π – threshold on time
σ – threshold on number of actions
ψ – threshold on number of influenced users
Amit Goyal (University of British Columbia)

30. Number of leaders found
π – threshold on time
σ – threshold on number of actions
ψ – threshold on number of influenced users
Amit Goyal (University of British Columbia)

31. Run-time π – threshold on time σ – threshold on number of actions
ψ – threshold on number of influenced users
Amit Goyal (University of British Columbia)

32. Genuineness: an almost binary concept!
Amit Goyal (University of British Columbia)

33. 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.
Amit Goyal (University of British Columbia)

34. 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
Amit Goyal (University of British Columbia)

35. 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
Amit Goyal (University of British Columbia)

36. Conclusions Various notions of leader, tribe leader
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)
Amit Goyal (University of British Columbia)

37. 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?
Amit Goyal (University of British Columbia)

38. Thanks! 3 1 4 13 2 7 5 Amit Goyal (University of British Columbia)

39. Backup

40. Number of leaders found
π – threshold on time
σ – threshold on number of actions
ψ – threshold on number of influenced users
Amit Goyal (University of British Columbia)

41. 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
Amit Goyal (University of British Columbia)