Weighted Low-Rank Approximation Nathan Srebro and Tommi Jaakkola ICML 2003
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Transcript of Weighted Low-Rank Approximation Nathan Srebro and Tommi Jaakkola ICML 2003
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