Opinion Maximization
in Social Networks
Evimaria Terzi (BU)
joint work with
Aristides Gionis
Aalto Univ.
Wednesday, July 24, 13
Panayiotis Tsaparas
Univ. of Ioannina
Which are the most influential nodes
in a social network?
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When influential nodes
- buy products or adopt opinions.....
- others follow them
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Influential nodes create trends
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Product/action marketing [....]
- select k initial adopters in a social
network
- to maximize the spread of adoption of a
product / action / ...
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Products
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Actions in social networks (re-tweets)
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Independent-cascade model [Kempe03....]
- at time t : a node u adopts
- at time t+1: a neighbor v adopts with prob puv
- one-time opportunity
u
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v
puv
independent-cascade model
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independent-cascade model
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independent-cascade model
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independent-cascade model
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independent-cascade model
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independent-cascade model
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independent-cascade model
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Products/actions propagate in a binary
fashion
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independent-cascade model
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But not everything is black and white...
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prevent global warming
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prevent global warming
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prevent global warming
reduce military spending
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prevent global warming
reduce military spending
Wednesday, July 24, 13
prevent global warming
reduce military spending
fight poverty
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prevent global warming
reduce military spending
fight poverty
Wednesday, July 24, 13
It’s Black Friday, the day in the year retail turns
from red to black and starts to make real money.
COMMON THREADS INITIATIVE
But Black Friday, and the culture of consumption it
REDUCE
reflects, puts the economy of natural systems that
support all life firmly in the red. We’re now using the
WE make useful gear that lasts a long time
YOU don’t buy what you don’t need
resources of one-and-a-half planets on our one and
REPAIR
DON’T BUY
THIS JACKET
Because Patagonia wants to be in business for a good
long time – and leave a world inhabitable for our kids –
we want to do the opposite of every other business
today. We ask you to buy less and to reflect before
ruptcy, can happen very slowly, then all of a sudden.
This is what we face unless we slow down, then
reverse the damage. We’re running short on fresh
WE help you repair your Patagonia gear
YOU pledge to fix what’s broken
REUSE
WE help find a home for Patagonia gear
you no longer need
YOU sell or pass it on*
RECYCLE
WE will take back your Patagonia gear
that is worn out
YOU pledge to keep your stuff out of
the landfill and incinerator
water, topsoil, fisheries, wetlands – all our planet’s
natural systems and resources that support
The environmental cost of everything we make is
Jacket shown, one
of our best sellers. To make it required 135 liters of
Wednesday, July 24, 13
REIMAGINE
TOGETHER we reimagine a world where we take
only what nature can replace
- opinions assume a continuous range
of values
- constantly evolving and being refined
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Our problem
- In a setting of constantly changing
opinions
- select k initial nodes to convince 100%
about your idea
- to maximize the overall positive opinion
of the crowd on this idea
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Rest of the talk
- How people form opinions
- How to select k nodes (efficiently)
- Experiments
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Forming opinions
- opinion modeled as a value in [0,1]
- person i has
- predisposition
si
- expressed opinion zi
- personal cost expressing conflict
Wednesday, July 24, 13
Forming opinions
- opinion modeled as a value in [0,1]
- person i has
- predisposition
si
- expressed opinion zi
- personal cost expressing conflict
c(zi ) = (zi
2
si ) +
X
j2N (i)
Wednesday, July 24, 13
wij (zi
zj )
2
your loyalty to
Red Sox ?
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your loyalty to
Red Sox ?
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your loyalty to
Red Sox ?
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your loyalty to
Red Sox ?
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Forming opinions
- egoistic agents minimizing their costs
c(zi ) = (zi
2
si ) +
X
j2N (i)
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wij (zi
zj )
2
Forming opinions
- egoistic agents minimizing their costs
c(zi ) = (zi
2
si ) +
X
wij (zi
j2N (i)
gives
si +
P
w
z
ij
j
j2N (i)
P
zi =
1 + j2N (i) wij
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zj )
2
Nash equilibrium vs. social optimal
- Nash optimum :
c(zi ) = (zi
2
zi that optimizes
si ) +
X
wij (zi
j2N (i)
- social optimum :
Wednesday, July 24, 13
that optimizes
zj )
2
Nash equilibrium vs. social optimal
- Nash optimum :
c(zi ) = (zi
2
zi that optimizes
si ) +
X
wij (zi
j2N (i)
- social optimum :
that optimizes
price of anarchy =
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zj )
2
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Interpretation of opinion
zi
- value in the equilibrium state of the
spring model
- value at absorption in an absorbing
random walk
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zi =
X
j2B
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P (j|i)fj
- find k users to set
zi = 1
- maximize the overall expressed opinion
(or average opinion)
g(z) =
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P
i2V
zi
Characterization of the
- NP-hard
- function g(z) =
P
problem
i2V
zi
is monotone and submodular
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Example : monotonicity
- objective g(z) =
- where
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P
i2V
zi
Example : monotonicity
- objective g(z) =
- where
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P
i2V
zi
Algorithms
- GREEDY (matrix inversion vs power iteration)
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Algorithms
- GREEDY (matrix inversion vs power iteration)
30
internal opinion
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Karate club
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ures of graph nodes plotted in order selected by the Greedy algorithm.
e algorithm is by storing,
yet selected, its marginal
t the last time it was comis commonly
used in opWednesday,
July 24, 13
nodes are nodes with high degree, connected to man
nodes with small values of si .
Armed with intuition from this analysis we no
proceed to describe our heuristics.
Algorithms
- GREEDY (matrix inversion vs power iteration)
30
internal opinion
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degree to free neighbors
Karate club
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k
- DEGREE
ures of graph nodes plotted in order selected by the Greedy algorithm.
- MINS
e algorithm -is by
storing,
RWR
yet selected, its marginal
t the last time it was comis commonly
used in opWednesday,
July 24, 13
nodes are nodes with high degree, connected to man
nodes with small values of si .
Armed with intuition from this analysis we no
proceed to describe our heuristics.
k
k
On a larger dataset Figure 2:
Performance of the algorithms
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k
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60000
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g(z)
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30000
RWR
free.degree
degree
min.s
min.z
6000
g(z)
10000
Bibsonomy −− data mining
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Remarks
-
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with setting
easy
Thank you!
Wednesday, July 24, 13