Group Formation in Large Social Networks: Membership, Growth, and Evolution

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Group Formation in Large Social Networks
Membership, Growth, and Evolution

• Lars Backstrom, Dan Huttenlocher, Joh Kleinberg,
  Xiangyang Lan
• Presented by Natalia Dragan
• Data Mining Techniques(CS6/73015-001) Fall06
• Kent State University

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Outline

• Introduction
• Motivation
• Present work contributions
• Related work
• Membership, Growth, Evolution
• Conclusions

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Introduction

• Structure of society people tend to come
  together and form groups
• Why it is important to study
• To understand better decision-making behavior
• Tracking early stages of an epidemic
• Following popularity of new ideas and
  technologies
• Significant growth in the scale and richness of
  on-line communities and social media (MySpace,
  Face book, LiveJournal, Flickr)

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Problems with the studying social processes

• Easy to build theoretical models (subgraph
  branching out rapidly over links in the network
  or collection of small disconnected components
  growing in a speckled fashion)
• Hard to make concrete empirical statements about
  these types of processes
• Lack of reasonable vocabulary for studying group
  evolution

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Present work

• Principles by which groups develop and evolve in
  large-scale social networks
• Crucial point focusing on networks where the
  members have explicitly identified themselves as
  a group or community
• (vs. an unsupervised graph clustering problem of
  inferring community structures in a network)
• 3 main types of questions Membership, Growth,
  Change

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Membership, Growth, Change

• Membership
• Structural features that influence whether a
  given individual will join a particular group
• Growth
• Structural features that influence whether a
  given group will grow significantly over time
• Change
• How focus of interest changes over time
• How these changes are correlated with changes in
  the set of group members

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Related work

• Identifying tightly-connected clusters within a
  given graph
• Dill et al. consider implicitly identified
  communities
• For a set of features (ZIP code, particular
  keyword, etc.) they consider a subgraph of the
  Web consisting of all pages containing this
  feature
• Use of online social networks for data mining
• The structure of the communities is not exploited
• Diffusion on innovation study
• Property which is diffusing in the present work
  membership in a given group

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Diffusion of Innovations

• Diffusion of Innovations is a theory that
  analyzes, as well as helps explain, the
  adaptation of a new innovation. In other words it
  helps to explain the process of social change.
• An innovation is an idea, practice, or object
  that is perceived as new by an individual or
  other unit of adoption. The perceived newness of
  the idea for the individual determines his/her
  reaction to it (Rogers, 1995).
• In addition, diffusion is the process by which an
  innovation is communicated through certain
  channels over time among the members of a social
  system. Thus, the four main elements of the
  theory are the innovation, communication
  channels, time, and the social system.
• http//hsc.usf.edu/kmbrown/Diffusion_of_Innovatio
  ns_Overview.htm

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Related work on Diffusion of Innovation

• How a social network evolves as its members
  attributes change (Sarkar and Moore, Holme and
  Newman)
• Social network evolution in a university setting
  (Kossinets and Watts)
• Evolution of topics over time (Wang and McCallum)
• Property which is diffusing in the present work
  is a membership in a given group

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Road map

• Introduction
• Motivation
• Present work contributions
• Related work
• Membership, Growth, Evolution
• Conclusions

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Sources of data

• LiveJournal
• Free on-line community with 10 mln members
• 300,000 update the content in 24-hour period
• Maintaining journals, individual and group blogs
• Declaring who are their friends and to which
  communities they belong
• DBLP
• On-line database of computer science publications
  (about 400,000 papers)
• Friendship network co-authors in the paper
• Conference - community

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Community Membership

• Study of processes by which individuals join
  communities in a social network
• Fundamental question about the evolution of
  communities who will join in the future?
• Membership in a community behavior that
  spreads through the network
• Diffusion of innovation study perspective for
  this question

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Dependence on number of friends start towards
membership prediction

• Underlying premise in diffusion studies an
  individual probability of adopting a new behavior
  increases with the number of friends (K) already
  engaging in the behavior
• Theoretical models concentrate on the effect of
  K, while the structural properties are more
  influential in determining membership

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Approach hypothesis

• For moderate values of K an individual with K
  friends in a group is significantly more likely
  to join if these K fiends are themselves mutual
  friends than if there are not

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Dependence on number of friends

• 1st snapshot 2nd
  snapshot

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- user (u) , C - community, - friend
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K 3
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P(k) 2/3
Probability P(k) of joining community fraction
of triples (u,C,k)
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Law of Diminishing returns

• In economics, diminishing returns is the short
  form of diminishing marginal returns. In a
  production system, having fixed and variable
  inputs, keeping the fixed inputs constant, as
  more of a variable input is applied, each
  additional unit of input yields less and less
  additional output. This concept is also known as
  the law of increasing opportunity cost or the law
  of diminishing returns.
• http//en.wikipedia.org/wiki/Diminishing_returns

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Dependence on number of friends LiveJournal
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Dependence of number of friends DBLP
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Discussion of results

• The plots for LJ and DBLP have similar shapes,
  dominated by diminishing returns property
  (curve continues increasing, but more and more
  slowly even for large K)
• P(2)gt2P(1) benefit of having a second friend is
  particularly strong (S-shaped behavior)
• Curve for LJ is quite smooth (1/2 billion triples
  vs. 7.8 million for DBLP)

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A broader range of features

• Features related to the community C (11)
• Number of members (C)
• Number of individuals with a friend in C (fringe
  of C)
• Number of edges with both ends in the community
  (Ec)
• etc.
• Features related to an individual u and her set S
  of friends in community C (8)
• Number of friend in community (S)
• Number of adjacent pairs in S
• Number of pairs in S connected via a path in Ec
• etc.

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Estimating probability on a broader range of
features

• Decision-tree techniques were applied to these
  features to make advances in estimating the
  probability of an individual joining a community
• The technique incorporates
• Individuals position in the network (structural
  features)
• Level of activities among members (group
  features)

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Predictions for LJ and DBLP

• 1st snapshot
  2nd snapshot

Data point (u,C)
Probability U?C
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Fringe
Fringe
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C
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C
LJ 14,448 joined community DBLP 71,618
joined community
LJ 17,076,344 data points, 875 communities
DBLP 7,651,013 data points
20 decisions tree were built for estimation about
joining
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Splitting process for LJ

• Each of 875 communities have half of their fringe
  members included in the training set (with the
  independent probability 0.5)
• At each node in the decision tree
• Every possible feature
• Every binary split treshold for that feature
• were examined
• Of all such pairs the split which produces the
  largest decrease in entropy was chosen

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Splitting process for LJ

• New splits were installed until there are fewer
  than 100 positive cases at the node
• Leaf nodes predict the ratio of positive to total
  cases for that node
• Averaging technique
• For every case the set of decision trees, for
  which this case is not included in the training
  set, were built
• The average of these predictions is a prediction
  for the case

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Averaging model (Simple description)

• Selecting a model that explains the data from all
  the possible models, the one which better fits
  the data is usually selected.
• But sometimes there is some model that explains
  really well the data, creating a model selection
  uncertainty, which is usually ignored.
• BMA (Bayesian Model Averaging) provides a
  coherent mechanism for accounting for this model
  uncertainty, combining predictions from the
  different models according to their probability.
  
• J. A.and Madigan D. Hoeting and A.E.and Volinsky
  C.T. Raftery. Bayesian model averaging A
  tutorial (With Discussion). Statistical Science,
  44(4)382--417, 1999

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Averaging model (Simple description)

• Example we have an evidence D and 3 possible
  hypothesis h1, h2 and h3. The posterior
  probabilities for those hypothesis are P( h1 D
  ) 0.4, P( h2 D ) 0.3 and P( h3 D ) 0.3
• Giving a new observation, h1 classifies it as
  true and h2 and h3 classify it as false, then the
  result of the global classifier (BMA) would be
  calculated as follows

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Top two level splits for predicting single
individuals joining communities in LJ
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Performance achieved with the decision trees
Prediction performance for single individuals
joining communities in LJ
Prediction performance for single individuals
joining communities in DBLP
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Internal connectedness of friends
Individuals whose friends in community are linked
to one another are significantly more likely to
join the community
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Road map

• Introduction
• Motivation
• Present work contributions
• Related work
• Membership, Growth, Evolution
• Conclusions

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Community Growth

• Prediction task identifying which communities
  will grow significantly over a given period of
  time
• Binary classification problem
• Training set

Community growth
gt9
lt 18
Class 1 (49.4)
Class 0 (50.6)
Data set 13 570 communities To make predictions
100 decision trees on 100 independent samples
using the community features were built Binary
split is installed until a node has less than 50
data points
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Top two levels of decision tree splits for
predicting community growth in LJ

• The features and splits varied depending on the
  sample, but the top 2 splits were stable

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Solution to the problem

• Averaging tree techniques was used
• Three baselines with a single feature were
  considered
• Size of the community
• Number of people in the fringe of the community
• Ratio of these two features and combination of
  all three features

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Results
Predicting community growth baselines based on
three different features, and performance using
all features By including the full set of
features predictions with reasonably good
performance were received
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Road map

• Introduction
• Motivation
• Present work contributions
• Related work
• Membership, Growth, Evolution
• Conclusions

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Movement between communities

• How people and topics move between communities
• Fundamental question given a set of overlapping
  communities
• do topics tend to follow people
• or do people tend to follow topics
• Experiment set up 87 conferences for which there
  is DBLP data over at least 15-year period
• Cumulative set of words in titles is a proxy for
  top-level topics

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Time Series and Detected Bursts Term Bursts
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OOPSLA03

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Tw,C(y) 2/6
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Micro-Pattern Evolution
Micro-Pattern in Java
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Tw,C
Micro-Pattern is hot at OOPSLA in 2003
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y
2000
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Term bursts
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Time Series and Detected Bursts Term Bursts

• Tw,C(y) fraction of paper titles at conference
  C in year y that contain the word w
• Bursts in the usage of w
• For each time series Tw,C is an interval in
  which Tw,C(y) is twice the average rate (burst
  rate)
• Burst detection technique exploiting stochastic
  model for term generation is used
• Burst intervals serve to identify the hot
  topics (focus of interest at a conference)
• Word w is hot at conference C in year y if the
  year y is contained in a burst interval of the
  time series Tw,C

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Time Series and Detected Bursts Movement Bursts

• Author movement
• Authors do not publish every year
• Movement is asymmetric
• Member of a conference C in year y
• Has published there in the 5 years leading up to
  y
• Author a moves into C from B in year y (B -gt C)
• a has a paper in conference C in year y and
• a is a member of B in year y-1
• Property of two conferences and a year

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C
B
Micro-Pattern Evolution
Smith
2002
2003
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Time Series and Detected Bursts Movement Bursts
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MB,C(y) 2/5
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Dill
2002
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MB,C
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y
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Movement bursts
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Time Series and Detected Bursts Movement Bursts

• MB,C(y) fraction of authors at conference C in
  year y with the property that they are moving
  into C from B (B -gt C)
• MB,C time series representing author movement
• B -gt C movement bursts
• an interval of y in which the value MB,C(y)
  exceeds the overall average by an absolute
  difference of .10
• Burst detection is used to find burst intervals

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Goal of the Experiment 1

• Identify how word burst and movement burst
  intervals are aligned in time?
• Word burst intervals identify hot terms
• Movement burst intervals identify conference
  pairs B,C during which there was significant
  movement

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Experiment 1 Papers contributing to Movement
Bursts

• Characteristics of papers associated with some
  movement burst into a conference C
• They exhibit different properties from arbitrary
  papers at C
• Using of terms currently hot at C
• Using of terms that will be hot at C in the
  future
• Paper at C in y contributes to some movement
  burst at C
• If one of the authors is moving B -gt C in y
• y is a part of B -gt C movement bursts

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Micro-pattern Evolution
Smith
OOPSLA03
ICPC02
2002
2004
2003
Movement burst
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Papers contributing to Movement Bursts

• Paper uses hot term
• If one of the words in its title is hot for the
  conference and year in which it appears
• Question do papers contributing to movement
  bursts differ from arbitrary papers in the way
  they use hot terms?

Papers contributing to a movement burst contain
elevated frequencies of currently and expired
hot terms, but lower frequencies of future hot
terms A burst of authors moving into C from B
are drawn to topics currently hot at C
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Experiment 2 Alignment between different
conferences

• Conferences B and C are topically aligned in a
  year y
• If some word is hot at both B and C in year y
• Property of two conference and a specific year
• Hypothesis two conferences are more likely to be
  topically aligned in a given year if there is
  also a movement burst going between them

Micro-pattern
OOPSLA03
Micro-pattern
ICSM03
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Results

• 56.34 of all triples (B,C,y) such that there is
  B-gtC movement burst containing year y have the
  property that B and C are topically aligned in
  year y
• 16.2 of all triples (B,C,y) have the property
  that B and C are topically aligned in year y
• The presence of a movement burst between 2
  conferences enormously increases the chance they
  share a hot term

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Movement bursts or term bursts come first?

• There is a B -gt C movement burst, and hot terms w
  such that B and C are topically aligned via w in
  some year y inside the movement burst
• 3 events of interest
• The start of the burst for w at conference B
• The start of the burst for w at conference C
• The start of the B -gt C movement burst

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Four patterns of author movement and topical
alignment
Term burst intervals
B -gt C movement burst
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194
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Shared interest is 50
more frequent than others Much more frequent for
B and C to have a shared burst term that is
already underway before the increase in author
movement takes place
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Conclusions

• The ways in which communities in social network
  grow over time were considered
• At the level of individuals and their decision to
  join communities
• At a more global level, in which a community can
  evolve in membership and content

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Thank you!