1 cs/cbb 545 - data mining spectral methods (pca,svd) #2 - application mark gerstein, yale...
TRANSCRIPT
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1
CS/CBB 545 - Data MiningSpectral Methods (PCA,SVD)
#2 - Application
Mark Gerstein, Yale Universitygersteinlab.org/courses/545
(class 2007,03.08 14:30-15:45)
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2
Intuition on interpretation of SVD in terms of genes
and conditions
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SVD for microarray data(Alter et al, PNAS 2000)
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Notation• m=1000 genes
– row-vectors
– 10 eigengene (vi) of dimension 10 conditions
• n=10 conditions (assays)– column vectors
– 10 eigenconditions (ui) of dimension 1000 genes
![Page 6: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/6.jpg)
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Understanding Eigengenes (vi) in terms PCA on (large) gene-gene correlation matrix
![Page 7: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/7.jpg)
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Understanding Eigenconditions (ui) in terms of PCA on (small) condition-condition correlation matrix
Bra - ket notation
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Plotting Experiments in Low Dimension Subspace
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Close up on Eigengenes
![Page 10: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/10.jpg)
10Copyright ©2000 by the National Academy of Sciences
Alter, Orly et al. (2000) Proc. Natl. Acad. Sci. USA 97, 10101-10106
Genes sorted by correlation with top 2 eigengenes
![Page 11: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/11.jpg)
11Copyright ©2000 by the National Academy of Sciences
Alter, Orly et al. (2000) Proc. Natl. Acad. Sci. USA 97, 10101-10106
Same thing different experiment: Genes sorted by relative correlation with first two eigengenes for alpha-factor experiment
![Page 12: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/12.jpg)
12Copyright ©2000 by the National Academy of Sciences
Alter, Orly et al. (2000) Proc. Natl. Acad. Sci. USA 97, 10101-10106
Normalized elutriation
expression in the subspace
associated with the cell cycle
![Page 13: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/13.jpg)
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Biplot Applied to Genes and Conditions
See grouping of arrays and genes on same plot
![Page 14: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/14.jpg)
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Spectral Biclustering
![Page 15: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/15.jpg)
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Biclustering to associate particular genes with certain phenotypes
Conditions
Reo
rder
ed G
enes
(Sor
ted
acco
rdin
g to
a cl
assi
ficat
ion
vect
or)
?
Matrix of raw data
Gen
es
Reordered Conditions(Sorted according to
a classification vector)
Shuffled Matrix(containing checkerboard
“biclusters” of conditions with marker genes)
![Page 16: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/16.jpg)
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Pomeroy et. al. , Nature 415 (2002) 436Prediction of central nervous system embryonal tumor outcome based on gene expression
5 types of brain tumors
![Page 17: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/17.jpg)
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Intuition on Identification of Blocky Matrices
2
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![Page 19: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/19.jpg)
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![Page 20: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/20.jpg)
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Biclustering by SVD
![Page 21: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/21.jpg)
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Identify checkerboard matrices by their action
on classification vectors: Formulation as “eigenproblem”
Checkerboard Matrix A
Condition Classification Vect. x
Conditions
Gen
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Gene Classification Vector y
A A x = x’T
A A y = y’T
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![Page 22: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/22.jpg)
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SVD to Solve Eigenproblem
[Botstein]
![Page 23: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/23.jpg)
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Yuval Kluger et al. Genome Res. 2003; 13: 703-716
Figure 1. Overview of important parts of the biclustering process
![Page 24: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/24.jpg)
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![Page 25: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/25.jpg)
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![Page 26: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/26.jpg)
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1 'TC A y x Rescale columns
![Page 27: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/27.jpg)
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Representative Cancer Data set
• Lymphoma Data from Dalla-Favera et al. at Columbia
• Informatics from Stolovitzky & Califano at IBM
• Supervised learning some identified characteristic genes associated with different types of lymphoma
![Page 28: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/28.jpg)
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Patients (samples) sorted according to projection onto blocky classification eigenvector
(u2)
Gen
es s
orte
d ac
cord
ing
to
proj
ectio
n on
to b
lock
y cl
assi
ficat
ion
eige
nvec
tor
(v2)
Matrix values represent outer products of two blocky
classification eigenvectors
Results on Representative Cancer Data set
![Page 29: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/29.jpg)
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Actual Data with Normalization and Sorting
![Page 30: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/30.jpg)
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Actual Data just with Sorting
(no normalization)
![Page 31: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/31.jpg)
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Actual Data (no normalization
or sorting)
![Page 32: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/32.jpg)
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Actual Data just with Sorting
(no normalization)
![Page 33: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/33.jpg)
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Actual Data with Normalization and Sorting
![Page 34: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/34.jpg)
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Patients (samples) sorted according to projection onto blocky classification eigenvector
(u2)
Gen
es s
orte
d ac
cord
ing
to
proj
ectio
n on
to b
lock
y cl
assi
ficat
ion
eige
nvec
tor
(v2)
Matrix values represent outer products of two blocky
classification eigenvectors
Just signal from top classification
eigenvectors
![Page 35: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/35.jpg)
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Low Dimension Representation
![Page 36: 1 CS/CBB 545 - Data Mining Spectral Methods (PCA,SVD) #2 - Application Mark Gerstein, Yale University gersteinlab.org/courses/545 (class 2007,03.08 14:30-15:45)](https://reader030.vdocuments.us/reader030/viewer/2022032804/56649e425503460f94b352cf/html5/thumbnails/36.jpg)
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Patients (samples) sorted according to projection onto blocky classification eigenvector
(u2)
Gen
es s
orte
d ac
cord
ing
to
proj
ectio
n on
to b
lock
y cl
assi
ficat
ion
eige
nvec
tor
(v2)
Actual Values of Projections onto
Classification Eigenvectors
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Classification of Cancers Based on Projection onto two top classification
eigenvectors: Better with Normalization
Normalized (“bistochastization”)
CLL DLCLFL DLCL
Straight SVD
Four types of Cancer in Della Favera dataset
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Golub, TR et. al., Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science, 1999 286
biclustering bistochastization
SVD bi-normalization Normalized cuts
ALL (B) ALL (T)AML