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Fast Alternating Projections on Manifolds Based on Tangent Spaces

Guang-Jing Song,M. Ng

Published 2020 in arXiv.org

ABSTRACT

In this paper, we study alternating projections on nontangential manifolds based on the tangent spaces. The main motivation is that the projection of a point onto a manifold can be computational expensive. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by alternating projections on two nontangential manifolds based on tangent spaces, converges linearly to a point in the intersection of the two manifolds where the convergent point is close to the optimal solution. Numerical examples for nonnegative low rank matrix approximation and low rank image quaternion matrix (color image) approximation, are given to demonstrate that the performance of the proposed method is better than that of the classical alternating projection method in terms of computational time.

PUBLICATION RECORD

  • Publication year

    2020

  • Venue

    arXiv.org

  • Publication date

    2020-03-23

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 2003.10324
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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