# Geodesic regression

@article{Hansen2020GeodesicR, title={Geodesic regression}, author={Frank Hansen}, journal={ArXiv}, year={2020}, volume={abs/2005.01326} }

The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of finite dimension. There is a unique geodesic curve connecting two positive definite operators, and it is given by the weighted geometric mean. The function that measures the squared Riemannian metric distance between an operator and a geodesic curve is not…

## 2 Citations

### Longitudinal Prediction of Infant MR Images With Multi-Contrast Perceptual Adversarial Learning

- Computer ScienceFrontiers in Neuroscience
- 2021

This paper adapts generative adversarial networks (GAN) to a new application: longitudinal image prediction of structural MRI in the first year of life and shows that the MPGAN is an effective solution for longitudinal MR image data imputation in the infant brain.

### Statistical Inference on the Hilbert Sphere with Application to Random Densities

- Mathematics
- 2021

: The inﬁnite-dimensional Hilbert sphere S ∞ has been widely employed to model density functions and shapes, extending the ﬁnite-dimensional counterpart. We consider the Fr´echet mean as an intrinsic…

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