SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.
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Transcript of SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.
![Page 1: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/1.jpg)
SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL
Zi Yang
![Page 2: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/2.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 3: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/3.jpg)
BACKGROUND
Social network
Example: Digg.com A popular social news website for people to discover
and share content Various types of behaviors of the users
submit, digg, comment and reply a comment Edges
if one diggs or comments a story of another
![Page 4: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/4.jpg)
BACKGROUND
Community discovery Modularity property
Affinity propagation Clustering via factor graph model Update rules:
,,
exp [ ]2i j
i j i ji j
k ky y
m
Pair-wise constrain
' . . '
' . . ' { , }
' . . ' { }
( , ) ( , ) max { ( , ') ( , ')}
( , ) min{0, ( , ) max{0, ( ', )}}
( , ) max{0, ( ', )}
k s t k k
i s t i i k
i s t i k
r i k s i k a a k s i k
a i k r k k r i k
a k k r i k
![Page 5: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/5.jpg)
BACKGROUND
Affinity propagation
Local factor
1: 1:1 1
, if but :( ) ( , ) ( ) where ( )
0, otherwise
N Nk i
i k N k Ni k
c k i c kS c s i c c c
Regional constrain
![Page 6: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/6.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 7: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/7.jpg)
CHALLENGES
How to capture the local properties for social network analysis?
Community discovery as a graph clustering, and how to consider the edge information directly?
Homophily
What constraint can be applied to describe the formation/evolution of community?
![Page 8: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/8.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 9: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/9.jpg)
REPRESENTATIVE USER FINDING
Problem definition given a social network and (optional) a
confidence for each user , the objective is to find a pair-wise representativeness on each edge in the network, and estimate the representative degree of each user in the network, which is denoted by a set of variables satisfying . . In other words, represents the user that mostly trusts (or relies on).
( , )G V Ei iv
iv{ }iy
{1, , }iy N iy
iv
![Page 10: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/10.jpg)
REPRESENTATIVE USER FINDING
Modeling Input
Variables
v3
v4v1
v2
y3
y4y1
y2
v3
v4v1
v2
Represent the representative
![Page 11: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/11.jpg)
REPRESENTATIVE USER FINDING
Modeling Node feature function
y3
y4y1
y2
v3
v4v1
v2
g1(y1) g3(y3) g4(y4)g2(y2)
,
,( )
if ( )
( ) ( ) if
0 otherwise
ii y i
i i i j i ij NB i
w y O i
g g y w y i
iy
Normalization factor
Observation: similarity between the node and variable
Self-representative
Neighbor Representative
![Page 12: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/12.jpg)
REPRESENTATIVE USER FINDING
Modeling Edge feature function
y3
y4y1
y2
v3
v4v1
v2
g1(y1) g3(y3) g4(y4)g2(y2)
f2,4(y2,y4)
f2,3(y2,y3)
f3,2(y3,y2)f3,2(y3,y2)
f2,1(y2,y1)
, ,
if ( , ) ( , )
1 if i j
i j i j i ji j
y yf f y y
y y
i jy y
Undirected edge: bidirected influence
If vertexes of the edge have the same representativeIf vertexes of the edge have different representative
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REPRESENTATIVE USER FINDING
Modeling Regional feature function
a feature function defined
on the set of neighboring
nodes of and itself.y3
y4y1
y2
v3
v4v1
v2
g1(y1) g3(y3) g4(y4)g2(y2)
f2,4(y2,y4)
f2,3(y2,y3)
f3,2(y3,y2)f3,2(y3,y2)
f2,1(y2,y1)
h4(y4,y2)h3(y3,y1)h2(y2,y3,y4)
h1(y1,y2)
( ) { } ( ) { }
0 if and ( ),( ) ( )
1 otherwise k i
k k I k k
y k i I k y kh h y
I k ky
To avoid “leader without followers”
iv
![Page 14: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/14.jpg)
REPRESENTATIVE USER FINDING
Modeling Objective function
Solving Max-sum algorithm
:
,
,
:
: , ( ) { }1 1
, ( ) { }1 1
max log ( )
1( ) ( ) ( , ) ( )
1( ) ( , ) ( )
i j
i j
N N
i i j ki e E k
N N
i i i j i j k I k ki e E k
P
P g f hZ
g y f y y h yZ
1N1 N
y
1 N i i j I k k
y
y y y y y
![Page 15: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/15.jpg)
REPRESENTATIVE USER FINDING
Model learning
( )
( ) { }
( ) { } { }( ) ( ) ( ) ( )
( )( ) ( ) { }
max min ,0
min min ,0 max min ,0 ,max ,0
max
max
ii kjk I j
ij jj kj jjk I j i
ij ij ikj ij ij ikjj O i i j
k I i O i k I i O i
ijk ik ik ikl ij ij ij O i
l I i O i j
a r
a r r r
r g c g a c
p g a c g a c
‚
‚
‚ ( ) ( ) { }
max log ,01
ljl I i O i j
ijk jikc p
‚
![Page 16: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/16.jpg)
REPRESENTATIVE USER FINDING
A bit explanation : how likely user persuades to take as his
representative : how likely user compliances the suggestion
from that he considers as his representative The direction of such process
Along the directed edges
ijkp iv jv kv
ijkc iv
jv kv
v1 v2
v3
v1 v2
v3
v1 v2
v3
![Page 17: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/17.jpg)
REPRESENTATIVE USER FINDING
Algorithm
![Page 18: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/18.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 19: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/19.jpg)
COMMUNITY DISCOVERY
Problem definition given a social network and an expected number
of communities , correspondingly a virtual node . is introduced for each community, and the objective is to find a community for each person satisfying , which represents the community that belongs to, such that maximize the preservation of structure (or maximize the modularity of the community).
G
C
cu Uiy
iv {1, , }iy C iv
Q
![Page 20: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/20.jpg)
COMMUNITY DISCOVERY
Feature definition – What’s different? Node feature function
Edge feature function
y3
y4
y1
y2
v3
v4v1
v2
u1 u2
g4(y4)f2,4(y2,y4)
f3,2(y3,y2)f1,3(y1,y3)
f2,1(y2,y1)
g3(y3)g2(y2)g1(y1)
f2,3(y2,y3)
, ,
,
( , ) exp
exp[ ]2
i j i j i j
i ji j i j
f y y q
k ky y
m
,
( ) ( )
( ) exp [ ] 1| |
j
i ji i j i
j I i O i y
g y y yX
![Page 21: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/21.jpg)
COMMUNITY DISCOVERY
Algorithm
Result output and Variable updates
![Page 22: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/22.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 23: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/23.jpg)
Experiments
Dataset: Digg.com a popular social news website for people to
discover and share content 9,583 users, 56,440 contacts various types of behaviors of the users
submit, digg, comment and reply a comment Edges (In total: 308,362)
if one diggs or comments a story of another Weight of the edge: the total number of diggs and
comments
![Page 24: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/24.jpg)
Experiments
Dataset: Digg.com 9,583 users, 56,440 contacts 308,362 edges
weight of the edge: the total number of diggs and comments
Settings: Parameter 0.6
![Page 25: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/25.jpg)
Experiments
Result: 3 most self-representative users on 3 different topics for Digg user network
![Page 26: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/26.jpg)
Experiments
Result: 3 most representative users of 5 communities on 3 different subset
![Page 27: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/27.jpg)
Experiments
Result: Representative network on a sub graph in Digg-2 Network
pyrates
0.00
00
0.00
0 3
mikek814
0.0005
rocr69
1nfiniteL oop
0.0003
pavelmah
0.0000
0.0010
G ordonF ree
maxthreepwood0.0007
0.0007 0.0000
0.0000
upick
0.0000
ritubpant
wonderwal
0.0000
0.0000
mklopez
Omek
0.0000
SirP opper
irfanmp
0.0024
0.0024numberneal
0.0020mpind176
louiebaur
0.0015
0.00100.0009
zohaibusman
0.0007
optimusprime01
0.0006 0.0007
0.0006
0.00
20
0.00
06
0.0006
0.0006
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
![Page 28: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/28.jpg)
OUTLINE
Background Challenge Unsupervised case 1
Representative user finding Unsupervised case 2
Community discovery Experiments Supervised case
Modeling information diffusion in social network
![Page 29: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/29.jpg)
Modeling information diffusion in social network
Supervised model Bridging the actual value (label) with the
variable. More variables to come?
Learning the weights
![Page 30: SOCIAL NETWORK ANALYSIS VIA FACTOR GRAPH MODEL Zi Yang.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649dff5503460f94ae7970/html5/thumbnails/30.jpg)
Thanks