Linear Regression under Fixed-Rank Constraints: A Riemannian Approach

  title={Linear Regression under Fixed-Rank Constraints: A Riemannian Approach},
  author={Gilles Meyer and Silvere Bonnabel and Rodolphe Sepulchre},
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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Publications referenced by this paper.
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