Manifold Similarity

Manifold similarity research focuses on understanding and quantifying the geometric structure of data, particularly when that data resides on a lower-dimensional manifold within a higher-dimensional space. Current research investigates methods to compare and measure the similarity between manifolds, employing techniques like heat diffusion and graph embeddings, often within the context of generative models (e.g., GANs) and dimensionality reduction algorithms (e.g., t-SNE, PHATE). These advancements have significant implications for improving few-shot learning, transfer learning, and reinforcement learning, particularly in scenarios with imbalanced or limited labeled data, as well as for evaluating the performance of generative models for complex data structures like graphs.

Papers

August 12, 2024

A Unified Manifold Similarity Measure Enhancing Few-Shot, Transfer, and Reinforcement Learning in Manifold-Distributed Datasets
Sayed W Qayyumi, Laureance F Park, Oliver Obst
Reinforcement Learning Transfer Learning Shot Learning Formality Transfer Manifold Similarity

March 8, 2024

Quantifying Manifolds: Do the manifolds learned by Generative Adversarial Networks converge to the real data manifold
Anupam Chaudhuri, Anj Simmons, Mohamed Abdelrazek
Generative Adversarial Network Machine Learning Model GAN Model Topological Feature Class Manifold Real Data Manifold Similarity

July 13, 2023

GRAN is superior to GraphRNN: node orderings, kernel- and graph embeddings-based metrics for graph generators
Ousmane Touat, Julian Stier, Pierre-Edouard Portier, Michael Granitzer
Generative Model Kernel Extension Graph Generator Manifold Similarity Embedding Based Metric

May 30, 2023

A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction
Guillaume Huguet, Alexander Tong, Edward De Brouwer, Yanlei Zhang, Guy Wolf, Ian Adelstein, Smita Krishnaswamy
Manifold Learning Generalized Geodesic Heat Diffusion Manifold Similarity

April 27, 2023

Adaptive manifold for imbalanced transductive few-shot learning
Michalis Lazarou, Yannis Avrithis, Tania Stathaki
Shot Learning Adaptive Importance High Quality Benchmark Transductive Few Shot Learning Manifold Similarity

February 23, 2023

Learning Manifold Dimensions with Conditional Variational Autoencoders
Yijia Zheng, Tong He, Yixuan Qiu, David Wipf
Variational Autoencoder Low Dimensional Manifold Conditional Variational Manifold Similarity