Manifold Approximation

Manifold approximation aims to represent high-dimensional data using lower-dimensional structures, revealing underlying patterns and simplifying analysis. Current research focuses on improving algorithms like UMAP and t-SNE, incorporating geometric information (e.g., using spherical representations or elastic metrics), and developing methods for interpretability and handling singularities in the data. These advancements are crucial for various applications, including outlier detection in large datasets, improved machine learning model performance, and enhanced understanding of complex systems like biological sequences and physical processes.

Papers

July 31, 2024

Outlier Detection in Large Radiological Datasets using UMAP
Mohammad Tariqul Islam, Jason W. Fleischer
MAESTRO Dataset High Quality Outlier Detection Manifold Approximation Uniform Manifold Approximation and Projection

November 17, 2022

Interpretable Dimensionality Reduction by Feature Preserving Manifold Approximation and Projection
Yang Yang, Hongjian Sun, Jialei Gong, Di Yu
Dimensionality Reduction Singular Value Decomposition Projection Bias Dimensional Space Manifold Approximation

October 26, 2022

Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation
Anna Ivagnes, Nicola Demo, Gianluigi Rozza
Neural Network Inverse Problem Dimensionality Reduction Boundary Prediction Model Order Reduction Manifold Approximation Parametric Solution

October 1, 2022

Identifying Selections Operating on HIV-1 Reverse Transcriptase via Uniform Manifold Approximation and Projection
Shefali Qamar, Manel Camps, Jay Kim
View Selection Projection Bias Isocitrate Dehydrogenase Mutation Mutational Effect Manifold Approximation

September 7, 2022

Dimensionality Reduction using Elastic Measures
J. Derek Tucker, Matthew T. Martinez, Jose M. Laborde
Dimensionality Reduction High Dimensional Data Stochastic Neighbor Embedding Manifold Approximation Elastic Metric

May 19, 2022

Manifold-aligned Neighbor Embedding
Mohammad Tariqul Islam, Jason W. Fleischer
Thy Neighbor Dimensional Manifold Non Linear Manifold Projection Algorithm Manifold Approximation Manifold Alignment

May 1, 2022

Uniform Manifold Approximation with Two-phase Optimization
Hyeon Jeon, Hyung-Kwon Ko, Soohyun Lee, Jaemin Jo, Jinwook Seo
Jina Embeddings Dimensionality Reduction High Dimensional Data Dual Stage Global Structure Manifold Approximation

April 23, 2022

Spherical Rotation Dimension Reduction with Geometric Loss Functions
Hengrui Luo, Jeremy E. Purvis, Didong Li
Dimensionality Reduction Low Dimensional Manifold Spherical Representation Manifold Approximation Geometric Loss

December 7, 2021

Towards Modeling and Resolving Singular Parameter Spaces using Stratifolds
Pascal Mattia Esser, Frank Nielsen
Parametric Model Parameter Space Different Attractor Manifold Approximation Singular Learning