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

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Weighted Low-Rank Approximation Nathan Srebro
and Tommi JaakkolaICML 2003

• Presented by Mingyuan Zhou
• Duke University, ECE
• February 18, 2011

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Outline

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

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Introduction

• Factor model
• Weighted norms
• Efficient optimization methods

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Low rank matrix factorization

• Objective function
• Solutions ( 1)

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Low rank matrix factorization

• Solutions

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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.

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Low rank matrix factorization
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Missing values and an EM procedure

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

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Missing values and an EM procedure
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Low rank logistic regression
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(No Transcript)
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Experimental results
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Experimental results
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Conclusions