Pre-processing HCS
data using
Non-negative Matrix Factorization
S. Stanley Young
National Institute of Statistical Sciences
MBSW, Muncie
19May2009
1
Contention: PCA fails for mixtures.
WH
NMF separates mixtures.
2
Key Idea
Y1
+
Y2
=
Y
NMF
WH
3
Outline
1.
2.
3.
4.
5.
6.
Basics of HCS
Non-negative matrix factorization
The experiment/simulation
NMF versus PCA
Analysis of experiment
Literature
4
Basic Experimental Setup
1. Multiple cells within a well.
2. Treat the wells.
3. Image each well.
4. Image analysis yields a vector for each cell.
5. Summarize the well.
6. Analyze the well summaries.
5
Typical Images
Image analysis will produce a vector of numbers, 5-50,
for each cell within each well. The cells are likely a
mixture of responsive, non-responsive, cells along
with artifacts of various sorts.
6
Equipment
7
Images to Numbers
8
Typical Data
5 vars/cell, 2000 wells/day, 2500 cells/well
36 vars/well, 7,000 wells, 80-400 cells/well
40 vars/well, 6,547 wells, 500 cells/well
Data sets can be enormous, 7GB=>3MB.
9
Major Problem
Cells within wells are sub-samples.
We need a good well summary.
Idea:
1. Cluster the cells (within or across wells)
2. Summary: Proportions of each cell type
Average vectors for each type.
3. Analysis of proportions and vectors.
10
Matrix Factorization Methods
1. Principle component analysis.
2. Singular value decomposition.
3. Non-negative matrix factorization.
4. Independent component analysis.
NMF is an area of active research.
11
NMF Algorithm
Green are the “spectra”.
Red are the “weights”.
Cells
Vars
Y
WH
=
Start with
random
elements in red
and green.
+E
Optimize so
that
(aij – whij)2 is
minimized.
12
Optimization Criteria
Minimize
 (xij – whij)2
 [xij log (xij / whij) + (Xij– whij)]
13
NMF Clustering
1. NMF Clusters the rows and columns.
2. Row clustering is fuzzy.
3. The variables in the column clusters define
nature of each cluster.
4. The column factors are often sparse.
14
Analysis Strategy (1)
X
Samples
Vars
Y
WH
=
W
X
+E
Treatments
15
Junk
Analysis Strategy (2)
Trt 1
vs.
Trt 2
X
Samples
Vars
Y
=
WH
+E
16
Contention: NMF finds “parts”
SVD RH EV elements come from a composite.
(They come from regression.)
NMF commits one vector to each mechanism.
(True??)
“For such databases there is a generative model
in terms of ‘parts’ and
NMF correctly identifies the ‘parts’.”
17
Simulated Data Set
1. Create Y a n x p, 1000 x 10 matrix.
2. Multiply random W (n x k )and H (k x p) matrices.
3. H is 40% sparse.
4. Y = WH where small, 5% of yij, Gausian noise is added.
We sample rows from Y to test NMF and PCA.
18
How many components?
Large Drop
5 components
19
Linearity Test
Exceeds U CL
20
Variables are clustered
Cross correlation
21
These “cells” are Type 1
22
NMF Summary
1. NMF honors the non-negative nature of
the data.
2. Variables are grouped.
3. Samples are clustered.
4. The clustering is “fuzzy”.
5. Sparseness makes interpretation easier.
23
PCA scree plot
24
PCA Eigenvectors
Comments
EV1 All positive
elements
EV2 is a
“contrast”
EV3 is X01 vs
X02.
Junk!
25
PCA Summary
1. 2 or 3 components.
2. 1st component is general sum.
3. 2nd component is a contrast.
4. Variables do not group cleanly.
26
General Comments
SVD is the basis for most linear statistical methods.
PCA is terrible for mixtures.
Where NMF can replace SVD,
it will become increasingly important.
NMF can be extended to complex, multi-block data sets.
We need good software to make NMF accessible.
27
Matrix Factorization References
1. Good (1969) Technometrics – SVD.
2. Liu et al. (2003) PNAS – rSVD.
3. Lee and Seung (1999) Nature – NMF.
4. Brunet et al. (2004) PNAS – Micro array.
5. Fogel et al. (2007) Bioinformatics – Micro array.
28
HCS References
Kümmel A, Gabriel D, Parker CN, Bender A. (2008) Computational methods
to support high-content screening: from compound selection and data analysis
to postulating target hypotheses. Expert Opin. Drug Discovery 4,1-9.
Low J, Huang S, et al. (2008) High-content imaging characterization of cell
cycle therapeutics through in vitro and in vivo subpopulation analysis. Mol
Cancer Ther 7, 2455-2463.
Young DW, Bender A, et al. (2008) Integrating high-content screening and
ligand-target prediction to identify mechanism of action. Nature Chemical
Biology 4, 59-68.
Dürr O, Duval D, et al. (2007) Robust hit identification by quality assurance
and multivariate data analysis of a high-content, cell-based assay. Journal
of Biomolecular Screening 12, 1042-1049.
29
NMF Software
1. irMF: inferential, robust Matrix Factorization
(JMP script) http://www.niss.org/irMF/
2. Array Studio: Software package which provides
state of the art statistics and visualization for
the analysis of high dimensional quantification
data (e.g. Microarray or Taqman data).
OmicSoft Corporation www.omicsoft.com
3. BioNMF – free
30
Future Work : Multi-block
Y
X1
X2
X3
Find sets of co-varying variables.
Relate sets of variables to outcomes.
Find mutual support.
31
Co-Workers
Stan Young, [email protected]
[email protected]
Paul Fogel, [email protected]
George Luta, [email protected]
Joe Maisog, [email protected]
32
Useful Information
Array Studio, www.omicsoft.com
irMF, www.niss.org/irMF
Google (BioNMF)
33
Array Studio
“L” Data Structure
X
Design
Software
Architecture
User
GUI
Script
Y
Intensity
A
Annotation
Vis/Stat
Modules
(~600k lines of code,
~200 users at GSK)
34
Array Studio User Interface
Search box
Views
View
Controller
Project
Explorer
Details
window
Web
details
Memory
indicator
35