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Nonnegative Matrix Factorization via Rank-one DowndatePowerPoint Presentation

Nonnegative Matrix Factorization via Rank-one Downdate

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Department of Statistics and Actuarial Science

David R. Cheriton School of Computer Science

University of Waterloo

Joint work with

Stephen Vavasis and Michael Biggs

University of Waterloo

Nonnegative Matrix Factorization via Rank-one DowndatePower method

- Computes the leading singular vectors/value (or eigenvector/value) of a matrix

1

2 while not converged

3

4

5

6 end

Naive approach to NMF using this observation

1

2

3

4

5 for all set

6 end for

Without step 5, this will simply compute the SVD (Jordan's algorithm, Camille Jordan 1874. )

Modified power iteration: Demo

v:

0.0 0.00.64 0.410.55

0.16

0.21

0.22

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Modified power iteration: Demo

v:

0.0 0.0 0.64 0.41 0.55

0.0

0.0

0.0

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Modified power iteration: Demo

v:

0.0 0.0 0.64 0.41 0.55

0.0

0.0

0.0

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Modified power iteration: Demo

v:

0.0 0.0 0.60 0.28 0.59

0.0

0.0

0.0

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Modified power iteration: Demo

v:

0.0 0.0 0.60 0.28 0.59

0.0

0.0

0.0

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Modified power iteration: Demo

v:

0.0 0.0 0.60 0.28 0.59

0.0

0.0

0.0

0.44

0.74

0.20

Rank-1

submatrix

Rank-1

submatrix

Zero-out!

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