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We study the swelling effect along polynomial curves on SPD manifolds with respect to three Riemannian metrics: Log-Cholesky, Log-Euclidean, and affine-invariant. We also derive the normal equations for the polynomial regression problem with respect to the Log-Cholesky metric and analyse the corresponding swelling effect.

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Swelling Effect Along Riemannian Polynomials on SPD Manifolds

  • 会议论文

  • 发表日期：

    2025年

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  • Luís Machado,
  • Margarida Camarinha,
  • Fátima Silva Leite

摘要

We study the swelling effect along polynomial curves on SPD manifolds with respect to three Riemannian metrics: Log-Cholesky, Log-Euclidean, and affine-invariant. We also derive the normal equations for the polynomial regression problem with respect to the Log-Cholesky metric and analyse the corresponding swelling effect.