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FrameworkLearning
Bregman Clustering
Chapter 5
Local Learning via
Chapter 6Local LearningBregman
via
Related Work &
Chapter 2
Introduction
Chapter 1
Weak Dependency
Strong Dependency
Chapter 9
Conclusion
Chapter 3
Chapter 8
Chapter 7
Homogeneous Data Sources
Model Integration for
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Background
Model Integration for
Heterogeneous Data SourcesCoclustering
Chapter 4Informationtheoretic
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Matrix M2
Basis C1 Basis C2 Basis C3
Basis C4 Basis C5 Basis C6
6 HJR M'
~
0 5 10 15 20 25 30 35 40 45 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Word Clusters
Nor
mal
ized
Mut
ual I
nfor
mat
ion
(Mea
n)Coclustering results on Classic3 (number of doc
clusters=3)
Basis C1, Euc
Basis C2, Euc
Basis C3, Euc
Basis C4, Euc
Basis C5, Euc
Basis C6, Euc
Basis C1, Idiv
Basis C2, Idiv
Basis C3, Idiv
Basis C4, Idiv
Basis C5, Idiv
Basis C6, Idiv
^HJR M
0 5 10 15 20 25 30 35 40 45 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Word Clusters
Nor
mal
ized
Mut
ual I
nfor
mat
ion
(Mea
n)
Coclustering results on Classic3 (number of doc clusters=3)
Basis C2, EucBasis C5, EucBasis C2, IdivBasis C5,
IdivSPKMeans
^HJR MLs'
0 1000 2000 3000 4000 5000 60000.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Number of parameters
Nor
mal
ized
Squ
ared
Err
or
Basis C1Basis C2Basis C3Basis C4Basis C5Basis C6
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0.02
0.03
0.04
0.05
0.06
0.07
0.08
Virtual sample size
KLD
iverg
ence
GlobAvgMinMaxMean
0 2000 6000 10000 140000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Virtual sample size
Squa
red L
2 Dist
ance
GlobAvgMinMaxMean
0 2000 6000 10000 140000
0.1
0.2
0.3
0.4
Virtual sample size
L1 D
istan
ce
GlobAvgMinMaxMean
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0.05
0.1
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0.2
0.25
Virtual sample size
KLD
iverg
ence
GlobAvgMinMaxMean
0 2000 6000 10000 140000
0.5
1
1.5
2
2.5
Virtual sample size
Squa
red L
2 Dist
ance
GlobAvgMinMaxMean
0 2000 6000 10000 140000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Virtual sample size
L1 D
istan
ce
GlobAvgMinMaxMean
%Se~ s W e %`SZ/y~2zS " ~ \ ~2GZ/y~2> `e eZ`~ ~ SySWxS
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0.2
0.3
0.4
0.5
0.6
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Number of clusters
KLD
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1 510 3060 10000
2
4
6
8
10
12
Number of clusters
Squa
red L
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1 510 3060 10000
0.2
0.4
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Number of clusters
L1 D
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1 510 3060 1000100
80
60
40
20
0
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Number of clusters
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1
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1 2 3 4 5 60
0.5
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0.5
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1 2 3 4 5 60
2000
4000
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ared
L2
Dis
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1 2 3 4 5 60
0.5
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1: GLOBAL, 2: AVERAGE, 3: MINIMUM, 4: MAXIMUM, 5: MEAN, 6:
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2 3
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1 2
2P 3P(B,C), (A,C),1
KLDIVERGENCE MINIMIZATION
M
*P
ENTROPY MAXIMIZATIONM
m
LOCAL MODEL 1 LOCAL MODEL 2 LOCAL MODEL 3
GLOBAL MODEL
P (A,B),
argmax { H( P (A,B,C) )}
Pc
P1
P cP3
mP
(A,B,C)
cP P 2 cPargmin { KL( (A,B) || (A,B)) + KL( (B,C) || (B,C))
1
+ KL( (A,C) || (A,C)) }
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