Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds

@article{Fletcher2012GeodesicRA,
  title={Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds},
  author={P. Thomas Fletcher},
  journal={International Journal of Computer Vision},
  year={2012},
  volume={105},
  pages={171-185}
}
This paper develops the theory of geodesic regression and least-squares estimation on Riemannian manifolds. Geodesic regression is a method for finding the relationship between a real-valued independent variable and a manifold-valued dependent random variable, where this relationship is modeled as a geodesic curve on the manifold. Least-squares estimation is formulated intrinsically as a minimization of the sum-of-squared geodesic distances of the data to the estimated model. Geodesic… CONTINUE READING
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