Riemannian Manifold

Riemannian manifolds, curved spaces extending Euclidean geometry, are increasingly central to machine learning and related fields, offering a natural framework for modeling data with inherent non-Euclidean structure, such as rotations or covariance matrices. Current research focuses on developing and analyzing algorithms for optimization and statistical inference on these manifolds, including extensions of established methods like logistic regression, Kalman filtering, and gradient descent, as well as novel approaches leveraging geometric properties like curvature. This work has significant implications for diverse applications, improving accuracy and efficiency in areas ranging from robotics and computer vision to quantum computing and structural health monitoring.

Papers

November 16, 2024

SPDFusion: An Infrared and Visible Image Fusion Network Based on a Non-Euclidean Representation of Riemannian Manifolds
Huan Kang, Hui Li, Tianyang Xu, Rui Wang, Xiao-Jun Wu, Josef Kittler
Image Fusion Riemannian Manifold Richer RGB Infrared Feature Visible Image Fusion Cross Modal Fusion Non Euclidean Euclidean Embeddings

October 31, 2024

Residual Deep Gaussian Processes on Manifolds
Kacper Wyrwal, Andreas Krause, Viacheslav Borovitskiy
Class Manifold Riemannian Manifold Residual Neural Network Deep Gaussian Process

October 28, 2024

On Probabilistic Pullback Metrics on Latent Hyperbolic Manifolds
Luis Augenstein, Noémie Jaquier, Tamim Asfour, Leonel Rozo
Latent Space High Dimensional Data Riemannian Manifold Latent Manifold Probabilistic Metric Gaussian Process Latent Variable Model Hyperbolic Scaling

October 23, 2024

Spiking Graph Neural Network on Riemannian Manifolds
Li Sun, Zhenhao Huang, Qiqi Wan, Hao Peng, Philip S. Yu
Graph Neural Network Riemannian Manifold Artificial Neuron Backpropagation Through Time

September 28, 2024

RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang, Xiaojun Wu, Nicu Sebe
Riemannian Manifold Multinomial Logistic Complex Geometry Riemannian Classifier Riemannian Graph

September 2, 2024

Kalman Filtering for Precise Indoor Position and Orientation Estimation Using IMU and Acoustics on Riemannian Manifolds
Mohammed H. AlSharif, Mohanad Ahmed, Mohamed Siala, Tareq Y. Al-Naffouri
Kalman Filter Riemannian Manifold Inertial Navigation System Unscented Kalman Filter Orientation Estimation Indoor Positioning Acoustic Analysis Orientation Detection

August 25, 2024

Neural Spacetimes for DAG Representation Learning
Haitz Sáez de Ocáriz Borde, Anastasis Kratsios, Marc T. Law, Xiaowen Dong, Michael Bronstein
Riemannian Manifold DAG Learning

August 21, 2024

Chernoff Bounds for Tensor Expanders on Riemannian Manifolds Using Graph Laplacian Approximation
Shih-Yu Chang
Random Walk Riemannian Manifold Graph Laplacian Large Deviation Tail Bound Dimensional Random Vector

July 14, 2024

Parameter Estimation for Generalized Low-Rank Matrix Sensing by Learning on Riemannian Manifolds
Osbert Bastani
Convergence Guarantee Parameter Estimation Riemannian Manifold Optimal Estimation Local Convergence Matrix Sensing Link Function

June 6, 2024

Leveraging SPD Matrices on Riemannian Manifolds in Quantum Classical Hybrid Models for Structural Health Monitoring
Azadeh Alavi, Sanduni Jayasinghe
Structural Health Monitoring Riemannian Manifold Multiple Physical Qubits Deep Quantum Finite Element Model Hybrid Quantum Symmetric Positive Definite

June 4, 2024

May 29, 2024

Matrix Manifold Neural Networks++
Xuan Son Nguyen, Shuo Yang, Aymeric Histace
Hyperbolic Space Riemannian Manifold Grassmann Manifold

May 22, 2024

Riemannian Bilevel Optimization
Sanchayan Dutta, Xiang Cheng, Suvrit Sra
Bilevel Optimization Stochastic Optimization Riemannian Manifold Riemannian Gradient

April 23, 2024

Score matching for sub-Riemannian bridge sampling
Erlend Grong, Karen Habermann, Stefan Sommer
Performance Score Riemannian Manifold Diffusion Process Diffusion Bridge Sub Riemannian

April 15, 2024

Federated Learning on Riemannian Manifolds with Differential Privacy
Zhenwei Huang, Wen Huang, Pratik Jawanpuria, Bamdev Mishra
Differential Privacy Private Federated Learning Riemannian Manifold Riemannian Geometry Convergence Property

March 11, 2024

Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
Clément Bonet, Lucas Drumetz, Nicolas Courty
Wasserstein Distance Riemannian Manifold Wasserstein Gradient General Flow Sliced Wasserstein Distance

February 29, 2024

StiefelGen: A Simple, Model Agnostic Approach for Time Series Data Augmentation over Riemannian Manifolds
Prasad Cheema, Mahito Sugiyama
Data Augmentation Time Series Model Agnostic Riemannian Manifold Noise Injection Stiefel Manifold

February 15, 2024

Efficient Sampling on Riemannian Manifolds via Langevin MCMC
Xiang Cheng, Jingzhao Zhang, Suvrit Sra
Langevin Dynamic Wasserstein Distance Riemannian Manifold Langevin Monte Carlo Efficient Sampling Metropolis Adjusted Langevin Algorithm

February 6, 2024

A Framework for Bilevel Optimization on Riemannian Manifolds
Andi Han, Bamdev Mishra, Pratik Jawanpuria, Akiko Takeda
New Framework Bilevel Optimization Riemannian Manifold Stochastic Bilevel Optimization Hypergradient Descent Hypergradient Estimation