Riemannian Metric

Riemannian metrics define distance and curvature on manifolds, extending Euclidean geometry to non-flat spaces crucial for modeling complex data like images, covariance matrices, and robot configurations. Current research focuses on developing computationally efficient metrics for various manifolds (e.g., Stiefel, Cholesky, SPD), often incorporating neural networks for adaptive metric learning and improved optimization in applications like deep learning and motion planning. This work is significant because it enables the development of more accurate and efficient algorithms for diverse applications, ranging from image processing and brain connectome analysis to robotics and machine learning.

Papers

March 6, 2022

Modeling the Shape of the Brain Connectome via Deep Neural Networks
Haocheng Dai, Martin Bauer, P. Thomas Fletcher, Sarang Joshi
Deep Neural Network Object Shape Riemannian Metric Diffusion Weighted Tractography Method

February 1, 2022

Lagrangian Manifold Monte Carlo on Monge Patches
Marcelo Hartmann, Mark Girolami, Arto Klami
Markov Chain Monte Carlo Hamiltonian Monte Carlo Class Relevant Patch Riemannian Metric

December 17, 2021

A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations
Alessandro Benfenati, Alessio Marta
Riemannian Geometry Riemannian Metric Riemannian Geometry Approach Theoretical Foundation Geometric Framework

December 3, 2021

Deep Efficient Continuous Manifold Learning for Time Series Modeling
Seungwoo Jeong, Wonjun Ko, Ahmad Wisnu Mulyadi, Heung-Il Suk
Time Series Manifold Learning Riemannian Manifold Riemannian Metric

Riemannian Metric

Papers

Modeling the Shape of the Brain Connectome via Deep Neural Networks

Lagrangian Manifold Monte Carlo on Monge Patches

A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations

Deep Efficient Continuous Manifold Learning for Time Series Modeling