Weighted Low-Rank Approximation Nathan Srebro and Tommi Jaakkola

ICML 2003

Presented by: Mingyuan ZhouDuke University, ECE

February 18, 2011

Outline

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

Introduction

• Factor model• Weighted norms• Efficient optimization methods

Low rank matrix factorization

• Objective function

• Solutions ( = 1)

Low rank matrix factorization• Solutions

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.

Low rank matrix factorization

Missing values and an EM procedure

• Initializing X with A or 0• Initializing X with 0 and let

Missing values and an EM procedure

Low rank logistic regression

Experimental results

Experimental results

Conclusions