Robust Geodesic Regression

@article{Shin2022RobustGR,
  title={Robust Geodesic Regression},
  author={Ha-Young Shin and Hee-Seok Oh},
  journal={ArXiv},
  year={2022},
  volume={abs/2007.04518}
}
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… 

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References

SHOWING 1-10 OF 23 REFERENCES
Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
  • P. Fletcher
  • Mathematics, Computer Science
    International Journal of Computer Vision
  • 2012
TLDR
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.
[Regression models].
  • S. Sarna
  • Medicine
    Duodecim; laaketieteellinen aikakauskirja
  • 1988
Multivariate Regression with Gross Errors on Manifold-Valued Data
TLDR
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.
Multivariate General Linear Models (MGLM) on Riemannian Manifolds with Applications to Statistical Analysis of Diffusion Weighted Images
TLDR
The variational algorithm efficiently solves for multiple geodesic bases on the manifold concurrently via gradient updates and allows us to answer questions such as: what is the relationship of the measurement at voxel y to disease when conditioned on age and gender.
Principal geodesic analysis for the study of nonlinear statistics of shape
TLDR
The method of principal geodesic analysis is developed, a generalization of principal component analysis to the manifold setting and demonstrated its use in describing the variability of medially-defined anatomical objects.
Robust geodesic regression
  • M.S. Thesis, Seoul National University. SNU Open Repository.
  • 2020
Regression Models on Riemannian Symmetric Spaces.
TLDR
A general regression framework for the analysis of manifold-valued response in a Riemannian symmetric space and its association with multiple covariates of interest, such as age or gender, in Euclidean space is developed.
A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis
TLDR
A novel nonlinear kernel-based regression method that is applicable to manifold valued data that is tested on a large number of real data sets acquired from Alzhiemers and movement disorder patients.
Parametric Regression on the Grassmannian
TLDR
The utility of the proposed solution to intrinsic parametric regression on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips, can be conveniently solved.
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