Manifold Graph

Manifold graphs represent data structures where nodes and their relationships are modeled as points and connections on a curved surface (manifold), capturing complex, non-linear relationships better than traditional graph representations. Current research focuses on developing efficient algorithms, such as graph neural networks (GNNs) and spectral methods, for tasks like graph embedding, homeomorphism detection, and stability analysis on these manifolds. These advancements are improving data analysis across diverse fields, including natural language processing (semantic neighborhood discovery), biomedical image analysis (Alzheimer's disease classification), and robotics (motion planning and obstacle avoidance), by enabling more accurate and computationally efficient processing of complex data.

Papers

September 1, 2024

Detecting Homeomorphic 3-manifolds via Graph Neural Networks
Craig Lawrie, Lorenzo Mansi
Graph Neural Network Field Theory Manifold Graph

May 13, 2024

LGDE: Local Graph-based Dictionary Expansion
Dominik J. Schindler, Sneha Jha, Xixuan Zhang, Kilian Buehling, Annett Heft, Mauricio Barahona
Word Embeddings Community Detection Word Usage Graph Manifold Graph Graph Dictionary

February 13, 2024

SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds
Wuxinlin Cheng, Chenhui Deng, Ali Aghdaei, Zhiru Zhang, Zhuo Feng
Graph Neural Network Class Manifold Stability Analysis Spectral Graph Manifold Graph Graph Dimensionality Reduction

January 25, 2024

Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs
Martin Hanik, Gabriele Steidl, Christoph von Tycowicz
Convolutional Neural Network Multi Layer Riemannian Geometry Graph Diffusion Latent Manifold Neural Network Layer Manifold Graph

November 29, 2023

Improving embedding of graphs with missing data by soft manifolds
Andrea Marinoni, Pietro Lio', Alessandro Barp, Christian Jutten, Mark Girolami
Graph Drawing Raw Data Class Manifold Graph Embeddings Soft Set Manifold Graph

November 2, 2022

Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds
Guillaume Huguet, Alexander Tong, María Ramos Zapatero, Christopher J. Tape, Guy Wolf, Smita Krishnaswamy
Optimal Transport Class Manifold Sinkhorn Algorithm Barycentric Coordinate Manifold Graph

June 17, 2022

Sheaf Neural Networks with Connection Laplacians
Federico Barbero, Cristian Bodnar, Haitz Sáez de Ocáriz Borde, Michael Bronstein, Petar Veličković, Pietro Liò
Graph Neural Network Sheaf Diffusion Manifold Graph

March 24, 2022

DAMON: Dynamic Amorphous Obstacle Navigation using Topological Manifold Learning and Variational Autoencoding
Apan Dastider, Mingjie Lin
Variational Autoencoder Obstacle Avoidance Human Robot Collaboration Topological Learning Efficient Motion Planning Manifold Graph

December 15, 2021

Fast Computation of Generalized Eigenvectors for Manifold Graph Embedding
Fei Chen, Gene Cheung, Xue Zhang
Latent Space Graph Laplacian Matrix Diagonalization Manifold Graph