1. Presented by: Mingyuan Zhou Duke University, ECE February 18, 2011
Weighted Low-Rank Approximation Nathan Srebro and Tommi Jaakkola ICML 2003
Presented by: Mingyuan Zhou
Duke University, ECE
February 18, 2011

2. Outline Introduction Low rank matrix factorization
Missing values and an EM procedure
Low rank logistic regression
Experimental results
Conclusions

3. Introduction Factor model Weighted norms
Efficient optimization methods

4. Low rank matrix factorization
Objective function
Solutions ( = 1)

5. Low rank matrix factorization
Solutions

6. Low rank matrix factorization
Since are unlikely to be diagonalizable for all rows, The critical points of the weighted low-rank approximation problem lack the eigenvector structure of the unweighted case.
Another implication of this is that the incremental structure of unweighted low-rank approximations is lost: an optimal rank-k factorization cannot necessarily be extended to an optimal rank-(k + 1) factorization.

7. Low rank matrix factorization

8. Missing values and an EM procedure
Initializing X with A or 0
Initializing X with 0 and let

9. Missing values and an EM procedure

10. Low rank logistic regression

12. Experimental results

13. Experimental results

14. Conclusions