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![Page 1: Blind Information Processing: Microarray Data Hyejin Kim, Dukhee KimSeungjin Choi Department of Computer Science and Engineering, Department of Chemical.](https://reader036.fdocuments.in/reader036/viewer/2022070418/56649f425503460f94c62567/html5/thumbnails/1.jpg)
Blind Information Processing: Blind Information Processing: Microarray Data Microarray Data
Hyejin Kim , Dukhee KimSeungjin ChoiHyejin Kim , Dukhee KimSeungjin Choi
Department of Computer Science and Engineering,
Department of Chemical Engineering
POSTECH, Korea
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Outline
Blind Information Processing? Independent Component Analysis (ICA)
Application of ICA to Microarray Data Time courses
Yeast cell cycle data
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Information Processing
Blind InformationProcessing
Little Prior Knowledge
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Latent Variable Models
Data Space(observation)
Latent Variable Space
Generative Model(FA, PPCA, ICA, GTM)
Recognition Model(PCA, ICA, SOM)
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What is ICA?
ICA is a statistical method, the goal of which is to decompose given
multivariate data into a linear sum of statistically independent
components.
For example, given two-dimensional vector , x = [ x1 x2 ] T , ICA aims
at finding the following decomposition
saasa
axx
222
121
21
11
2
1
2211 ss aax
where a1, a2 are basis vectors and s1, s2 are basis coefficients
Constraint: Basis coefficients s1 and s2 are statistically independent.
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Information Geometry of ICA
s
y
yp
Mutual information
Marginal mismatch Product manifold
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PCA vs ICA
Linear Transform Compression Classification
PCA Orthogonal transform Second-order statistics Optimal coding in MS sense
ICA Non-orthogonal transform Higher-order statistics Related to the projection pursuit Better than PCA in classification task?
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Example of PCA
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PCA vs ICA
PCA(orthogonal coordinate)
ICA(non-orthogonal coordinate)
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PCA vs ICA
x1 x2ICA
PCA
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Microarray Data (1)
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Microarray Data Analysis(1)
gene influence profile
Expression mode of a sample
x=
gen
e
ge
ne
sample
sample
influence
influ
en
ce
0 100 200-0.05
0
0.05
cdc28
mode 2
0 50 100 150 200-0.2
0
0.2
cdc28
mode 1
gene expression profile
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ICA: Time Courses (1)
Time courses Yeast cell cycle data
77 by 6178 ORF expression ( Spellman et al. 1998 )
Each mode shows specific cell-cycle behavior
ICA modes remain inactive within some of the experi
ments
Dimension reduction improve a prediction of cell-cycl
e regulated genes
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ICA: Time Courses (2)
by Liebermeister
Mode176 components
Mode276 components
Mode112 components
Mode112 components
alpha elucidationcdc15 cdc28
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PCA Results
0 10 20 30 40 50 60 70 800
0.05
0.1
0.15
0.2
0.25
0.3
0.35
PC ratio
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ICA Results(I)
0 20 40 60 80 100 120 140 160-0.5
0
0.5
1fastICA 6 comp4
0 20 40 60 80 100 120 140 160-0.5
0
0.5fastICA 6comp6
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ICA Results (II)
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Conclusion
Linear models of gene expression Model assumptions
Matrix decomposition is simultaneously To interpret expression pattern and
To cluster co-activated genes
ICA advantage More biological meaningful analysis
No order, No orthogonality
More sensitive to detect expression pattern