1. Non-Negative Matrix Factorization NCSU ECCR Workshop Stan Young NCSU ECCR, NISS NISS 23, 24 Feb 2007

2. Outline Introduction NMF Chemistry Problem
Non-negative matrix factorization
Logistics

3. NMF Algorithm Green are the “spectra”. Red are the “weights”. = + E WH
Com-
pounds A
Features
Optimize so that
(aij – whij)2 is minimized.
Start with random elements in red and green.

4. NCSU ECCR – Chemical Informatics

5. PowerMV

6. Data File

7. NMF for Clustering Profile Likelihood

8. RH Vector

9. Cluster 1 Compounds

10. Cluster 1 Compounds

11. 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’.”

12. Key Papers Good (1969) Technometrics – SVD.
Liu et al. (2003) PNAS – rSVD.
Lee and Seung (1999) Nature – NMF.
Kim and Tidor (2003) Genome Research.
Brunet et al. (2004) PNAS – Micro array.
Fogel et al. (2007) Bioinformatics

13. Summary NMF is an attractive alternative to SVD.
Mechanisms appear to be captured in separate vectors.
SVD is central to many linear statistical methods.
Substitute NMF for SVD!
4. Many statistical problems are open for research.

14. Logistics Two Rooms and web. Locals with cars identify yourselves.
See
CS, Applications, Statistics.

15. Friday Program Speaker Topic 1:00-1:15 Stan Young Introduction
1:15-3: Team Teaching* Review of NMF
and Comparison of popular NMF algorithms
*Atina Brooks
Barbara Ball
Amy Langville
3:00-3: Paul Fogel Linking genetic profiles to biological outcome
3:45-4: Break
4:00-4: Michael Berry Using Non-negative Matrix and Tensor
Factorizations for Surveillance
4:45-5: Kevin Heinrich Automated Gene Classification
Using NMF within SGO

16. Saturday Program 8:00 – 8:45 Continental Breakfast Speaker Topic
8:45 – 9: Inderjit S. Dhillon Fast Newton-type Methods for
Nonnegative Matrix Approximation
9:30 – 10:00 Haesun Park Sparse NMF via Alternating Non-negativity Constrained Least Squares
10:00-10:30 Break
10:30-11:15 Doug Hawkins Two-Block Analysis
11:15-12:00 Moody Chu Low Dimensional Polytope Approximation
and Its Applications to NMF
12:00-1: Lunch
1:00-1: Bob Plemmons Nonnegative Tensor Factorization for Object
Identification using Hyperspectral Data
1:30-2: Gary Howell Computational Efficiency and
2:00-2: (Break) Low Rank Factorization
2:15-3: Panel Discussion James Cox, SAS; Jackie Hughes-Oliver, NCSU;
Mike Marshall, Fortune Interactive;
Bob Plemmons, WFU