Linear Regression under Fixed-Rank Constraints: A Riemannian Approach

@inproceedings{Meyer2011LinearRU,
  title={Linear Regression under Fixed-Rank Constraints: A Riemannian Approach},
  author={Gilles Meyer and Silvere Bonnabel and Rodolphe Sepulchre},
  booktitle={ICML},
  year={2011}
}
In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to highdimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixedrank matrices. Numerical experiments on benchmarks suggest that the… CONTINUE READING
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References

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Efficient Kernel Discriminant Analysis via Spectral Regression

Seventh IEEE International Conference on Data Mining (ICDM 2007) • 2007
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ADMiRA: Atomic Decomposition for Minimum Rank Approximation

IEEE Transactions on Information Theory • 2010
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Grassmann algorithms for low rank approximation of matrices with missing values

L. Simonsson, L. Eldén
BIT Numerical Math., • 2010
View 1 Excerpt

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