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# Nonnegative Matrix Factorization via Rank-one Downdate - PowerPoint PPT Presentation

Ali Ghodsi 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 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 Downdate

-3.19

-0.02

1.02

2 by 1965

560 by 1965

560 by 2

20 by 28

2 by 1

2 by 1

20 by 28

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

1

2 while not converged

3

4

5

6 end

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. )

Rank-1

submatrix

A =

Rank-1

submatrix

v:

0.14 0.07 0.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix

v:

0.0 0.00.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix

v:

0.0 0.00.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix

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!

Rank-1

submatrix

Anew =