Large-Scale Social Network Data Mining withMulti-View Information
Hao Wang
Dept. of Computer Science and EngineeringShanghai Jiao Tong University
Supervisor: Wu-Jun Li
2013.6.19
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Our work
1 Hao Wang£�§¤, Binyi Chen, Wu-Jun Li. Collaborative Topic Regressionwith Social Regularization for Tag Recommendation. Proceedings of theTwenty-Third International Joint Conference on Artificial Intelligence(IJCAI), 2013.
2 Hao Wang£�§¤, Wu-Jun Li. Relational Collaborative Topic Regressionfor Recommendation Systems. IEEE Transactions on Knowledge and DataEngineering (TKDE), 2013. (submitted)
3 Hao Wang£�§¤, Wu-Jun Li. Online Egocentric Models for CitationNetworks. Proceedings of the Twenty-Third International Joint Conferenceon Artificial Intelligence (IJCAI), 2013.
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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Motivation
Content:1 Lee et al., 20102 Chen et al., 20103 Lipczak et al., 2009
Ratings:1 Salakhutdinov et al., 20072 Herlocker et al., 1999
Hybrid:1 Purushotham et al., 20122 Wang and Blei, 20113 Agarwal and Chen, 20104 A. Said, 2010
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Contribution
1 Integrate ratings, contents and item networks2 Significantly improve the accuracy3 Even less training time4 Extend to dynamic networks
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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Graphical model of RCTR
l jj ', v
sj vj
j
ui
ui
r ji,
w nj,z nj,
sj ' vj '
'j z nj ,' w nj ,'
r ji ',
u
kI
I
J
J
K
N
N
e
r
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Objective function
The log-likelihood:
L = ρ∑(j,j′)
log σ(ηT (sj ◦ sj′) + ν)
−λr2
∑j
(sj − vj)T (sj − vj)−λe2η+
Tη+
− λu2
∑i
uTi ui −λv2
∑j
(vj − θj)T (vj − θj)
+∑j
∑n
log(∑k
θjkβk,wjn)−
∑i,j
cij2(rij − uTi vj)2.
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Updating rules
For U and V :
ui ← (V CiVT + λuIK)−1V CiRi,
vj ← (UCiUT + λvIK + λrIK)−1(UCjRj + λvθj + λrsj),
For η+:
∇η+L = ρ∑lj,j′=1
(1− σ(η+Tπ+j,j′))π+j,j′ − λeη
+,
For φjnk:
φjnk ∝ θjkβk,wjn.
For βkw:
βkw ∝∑j
∑n
φjnk1[wjn = w].
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Datasets
Description of datasets
citeulike-a citeulike-t
#users 5551 7947
#items 16980 25975
#tags 19107 52946
#citations 44709 32565
#user-item pairs 204987 134860
sparsity 99.78% 99.93%
#relations 549447 438722
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Experimental results
50 100 150 200 250 300
0.05
0.1
0.15
0.2
0.25
0.3
M
Rec
all
CFCTRRCTR
The user-oriented recall of RCTR, CTR, and CF when M ranges from 50 to 300on dataset citeulike-t. P is set to 1. Similar phenomenon can be observed forother values of P .
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Case study
Interpretability of the learning latent structures
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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Objective function
The log-likelihood:
L = −λl2tr(SLaS
T )− λr2
∑j
(sj − vj)T (sj − vj)
− λu2
∑i
uTi ui −λv2
∑j
(vj − θj)T (vj − θj)
+∑j
∑n
log(∑k
θjkβk,wjn)−
∑i,j
cij2(rij − uTi vj)2.
where
tr(SLaST ) =
1
2
J∑j=1
J∑j′=1
Ajj′ ||S∗j − S∗j′ ||2
=1
2
J∑j=1
J∑j′=1
[Ajj′K∑k=1
(Skj − Skj′)2]
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Updating rules
For U and V :
ui ← (V CiVT + λuIK)−1V CiRi,
vj ← (UCiUT + λvIK + λrIK)−1(UCjRj + λvθj + λrsj),
For S:
Sk∗(t+ 1)← Sk∗(t) + δ(t)r(t)
r(t)← λrVk∗ − (λlLa + λrIJ)Sk∗(t)
δ(t)← r(t)T r(t)
r(t)T (λlLa + λrIJ)r(t)
For φjnk:
φjnk ∝ θjkβk,wjn.
For βkw:
βkw ∝∑j
∑n
φjnk1[wjn = w].
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Experimental results
1 2 3 4 5 6 7 8 9 10
0.05
0.1
0.15
0.2
0.25
0.3
P
Rec
all
SCFSCF+LDACFTAGCOCTRCTR−SR
Recall@50 for all methods in citeulike-a.
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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From DEM to OEM
Three parts of variables:
1 Model parameters β2 Link features3 Topic features
Dynamic Egocentric Models (DEM, adapting only Model parameters):
L(β) =
m∏e=1
exp(βT sie(te))n∑i=1
Yi(te) exp(βT si(te))
Online Egocentric Models (OEM, adapting all three parts):
minimize − logL(β,ω) + λn∑k=1
‖ωk − θk‖22
subject to : ωk � 0, 1Tωk = 1,
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Updating rules
Using coordinate descent:
1 Online β Step:
Lw(β) =
x+q−1∏e=x+q−Wt
exp(βT sie(te))n∑i=1
Yi(te) exp(βT si(te))
.
2 Online Topic Step:
∂f
∂ωk=−
p∑i=1
ai +
p∑i=1
aiαi exp(aTi ωk)
Ai + αi exp(aTi ωk)
+
q∑u=p+1
buγu exp(bTuωk)
Bu + γu exp(bTuωk)
+ 2λ(ωk − θk)
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Datasets
Information of data sets
Data Set #Papers #Citations #Unique TimesarXiv-TH 14226 100025 10500arXiv-PH 16526 125311 1591
Data set partition for building, training and testing.
Data Sets Building Training TestingarXiv-TH 62239 1465 36328arXiv-PH 82343 1739 41229
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Experimental results
0 5 10 15 20 25
−12
−11
−10
−9
−8
Paper batches
Ave
rage
log−
likel
ihoo
d
DEMOEM−betaOEM−apprOEM−full
(a) arXiv-TH
0 5 10 15 20 25
−11
−10
−9
−8
Paper batches
Ave
rage
log−
likel
ihoo
d
DEMOEM−betaOEM−apprOEM−full
(b) arXiv-PH
0 5 10 15 20 250.25
0.3
0.35
0.4
0.45
Paper batches
Rec
all
DEMOEM−betaOEM−apprOEM−full
(c) arXiv-TH(K=250)
0 5 10 15 20 250.2
0.25
0.3
0.35
0.4
Paper batches
Rec
all
DEMOEM−betaOEM−apprOEM−full
(d) arXiv-PH(K=250)
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Outline
1 Motivation
2 Relational CTR
3 CTR with Social Regularization
4 Online Egocentric Models
5 Conclusion
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Conclusion
Data Mining with Multi-View Information:
1 Relational CTR:Social information as prior
2 CTR with Social regularization:Social information as observation
3 Online Egocentric Models:Dynamic social information
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Publication
1 Hao Wang£�§¤, Binyi Chen, Wu-Jun Li. CollaborativeTopic Regression with Social Regularization for TagRecommendation. Proceedings of the Twenty-Third InternationalJoint Conference on Artificial Intelligence (IJCAI), 2013.
2 Hao Wang£�§¤, Wu-Jun Li. Online Egocentric Models forCitation Networks. Proceedings of the Twenty-ThirdInternational Joint Conference on Artificial Intelligence (IJCAI),2013.
3 Hao Wang£�§¤, Wu-Jun Li. Relational Collaborative TopicRegression for Recommendation Systems. IEEE Transactions onKnowledge and Data Engineering (TKDE), 2013. (submitted)
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