Nonnegative matrix factorization via rank one downdate
Download
1 / 43

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


  • 139 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Nonnegative Matrix Factorization via Rank-one Downdate' - munin


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Nonnegative matrix factorization via rank one downdate

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



-2.19

-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










Power method
Power 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
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
Modified power iteration: Demo

Rank-1

submatrix

A =

Rank-1

submatrix


Modified power iteration demo1
Modified power iteration: Demo

v:

0.14 0.07 0.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix


Modified power iteration demo2
Modified power iteration: Demo

v:

0.0 0.00.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix


Modified power iteration demo3
Modified power iteration: Demo

v:

0.0 0.00.64 0.41 0.55

Rank-1

submatrix

Rank-1

submatrix


u:

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


u:

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


u:

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


u:

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


u:

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


u:

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!


Modified power iteration demo4
Modified power iteration: Demo

Rank-1

submatrix

Anew =

















ad