Robust Geodesic Regression

  title={Robust Geodesic Regression},
  author={Ha-Young Shin and Hee‐Seok Oh},
  journal={Int. J. Comput. Vis.},
This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables. The existing work on geodesic regression uses the sum-of-squared errors to find the solution, but as in the classical Euclidean case, the least-squares method is highly sensitive to outliers. In this paper, we use M-type estimators, including the $L_1$, Huber… 
Geo-FARM: Geodesic Factor Regression Model for Misaligned Pre-shape Responses in Statistical Shape Analysis
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Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
  • P. Fletcher
  • Mathematics
    International Journal of Computer Vision
  • 2012
Specific examples are given for a set of synthetically generated rotation data and an application to analyzing shape changes in the corpus callosum due to age, which can be generally applied to data on any manifold.
Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
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
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Multivariate Regression with Gross Errors on Manifold-Valued Data
A new regression model to deal with the presence of grossly corrupted manifold-valued responses, a bottleneck issue commonly encountered in practical scenarios is proposed, and its convergence property is investigated, where it is shown to converge to a critical point under mild conditions.
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The results show that Riemannian polynomials provide a practical model for parametric curve regression, while offering increased flexibility over geodesics.
Robust Nonparametric Regression with Metric-Space Valued Output
This paper shows pointwise and Bayes consistency for all estimators in the family for the case of manifold-valued output and illustrates the robustness properties of the estimators with experiments.
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Nonparametric Regression between General Riemannian Manifolds
Characterizing interesting and sometimes counterintuitive implications and new open problems that are specific to learning between Riemannian manifolds and are not encountered in multivariate regression in Euclidean space are characterized.