# Maximum Margin Matrix Factorization using Smooth Semidefinite Optimization

@inproceedings{Srebro2005MaximumMM, title={Maximum Margin Matrix Factorization using Smooth Semidefinite Optimization}, author={Nathan Srebro}, year={2005} }

Introduction • Semidefinite programming (SDP): efficient solutions to highly nonlinear problems. • Interior Point solvers: memory constraints limit the max. problem size. • First-order method (Bundle, subgradient, etc): limited memory requirements but very slow convergence. • Today: optimal first-order methods for structured semidefinite programs.

## References

SHOWING 1-10 OF 16 REFERENCES

A Direct Formulation for Sparse Pca Using Semidefinite Programming

- MathematicsNIPS 2004
- 2004

We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The…

A Matlab toolbox for optimization over symmetric cones

- Mathematics, Computer Science
- 1999

This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.

A rank minimization heuristic with application to minimum order system approximation

- Computer Science, MathematicsProceedings of the 2001 American Control Conference. (Cat. No.01CH37148)
- 2001

It is shown that the heuristic to replace the (nonconvex) rank objective with the sum of the singular values of the matrix, which is the dual of the spectral norm, can be reduced to a semidefinite program, hence efficiently solved.

A Direct Formulation for Sparse PCA Using Semidefinite Programming

- Computer Science, MathematicsSIAM Rev.
- 2007

A modification of the classical variational representation of the largest eigenvalue of a symmetric matrix is used, where cardinality is constrained, and a semidefinite programming-based relaxation is derived for the sparse PCA problem.

Non-euclidean restricted memory level method for large-scale convex optimization

- Mathematics, Computer ScienceMath. Program.
- 2005

A new subgradient-type method for minimizing extremely large-scale nonsmooth convex functions over “simple” domains, allowing for flexible handling of accumulated information and tradeoff between the level of utilizing this information and iteration’s complexity.

Smooth minimization of non-smooth functions

- Mathematics, Computer ScienceMath. Program.
- 2005

A new approach for constructing efficient schemes for non-smooth convex optimization is proposed, based on a special smoothing technique, which can be applied to functions with explicit max-structure, and can be considered as an alternative to black-box minimization.

Practical Aspects of the Moreau-Yosida Regularization: Theoretical Preliminaries

- Mathematics, Computer ScienceSIAM J. Optim.
- 1997

The most important part of this study concerns second-order differentiability: existence of a second- order development of f implies that its regularization has a Hessian.

Learning with matrix factorizations

- Computer Science
- 2004

This thesis addresses several issues related to learning with matrix factorizations, study the asymptotic behavior and generalization ability of existing methods, suggest new optimization methods, and present a novel maximum-margin high-dimensional matrix factorization formulation.

SDPT3 -- A Matlab Software Package for Semidefinite Programming

- Computer Science
- 1996

This invention relates to stabilizing compositions that comprises a vinyl chloride or vinylidene chloride homopolymer or copolymer and a stabilizing amount of an organotin halide exhibiting the formula RSnX3.

Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

- Mathematics, Computer ScienceSIAM Rev.
- 2003

Methods involv- ing approximation theory, dierential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed, indicating that some of the methods are preferable to others, but that none are completely satisfactory.