Manifold Learning

Manifold learning aims to uncover the underlying low-dimensional structure hidden within high-dimensional data, assuming that data points lie on or near a lower-dimensional manifold. Current research focuses on developing robust algorithms, such as those based on Riemannian geometry, Ollivier-Ricci curvature, and spectral graph wavelets, to accurately learn this structure even in the presence of noise and complex geometries, including intersecting manifolds. These advancements improve data visualization, dimensionality reduction, and downstream tasks like classification and imputation, impacting fields ranging from drug discovery and materials science to single-cell analysis and brain imaging. The development of more explainable and scalable manifold learning methods remains a key area of ongoing investigation.

Papers

June 12, 2024

Inductive Global and Local Manifold Approximation and Projection
Jungeum Kim, Xiao Wang
Dimensionality Reduction Manifold Learning Dimension Reduction Dimensional Embeddings Projection Bias

June 4, 2024

MS-IMAP -- A Multi-Scale Graph Embedding Approach for Interpretable Manifold Learning
Shay Deutsch, Lionel Yelibi, Alex Tong Lin, Arjun Ravi Kannan
Contrastive Learning Constructive Approach Jina Embeddings Manifold Learning Multi Scale Graph Spectral Graph Wavelet

June 3, 2024

Hardness of Learning Neural Networks under the Manifold Hypothesis
Bobak T. Kiani, Jason Wang, Melanie Weber
Neural Network Manifold Learning Low Dimensional Manifold Hardness Result Non Linear Manifold Manifold Hypothesis

May 30, 2024

A novel fault localization with data refinement for hydroelectric units
Jialong Huang, Junlin Song, Penglong Lian, Mengjie Gan, Zhiheng Su, Benhao Wang, Wenji Zhu, Xiaomin Pu, Jianxiao Zou, Shicai Fan
Manifold Learning Sparse Autoencoders Fault Localization Hydropower Plant Data Refinement

May 20, 2024

A Metric-based Principal Curve Approach for Learning One-dimensional Manifold
Elvis Han Cui, Sisi Shao
LeArning Abstract Manifold Learning Dimensional Manifold Differential Geometry Principal Curve

May 17, 2024

Manifold Learning via Memory and Context
Xin Li
Context Information Learning Based Memory Trace Manifold Learning Associative Memory Semantic Memory Human Hippocampus

April 29, 2024

Post-hoc and manifold explanations analysis of facial expression data based on deep learning
Yang Xiao
Deep Learning Deep Learning Model Facial Expression Manifold Learning Human Cognition Deep Learning Technology Post Hoc Facial Data

March 21, 2024

Genetic Programming for Explainable Manifold Learning
Ben Cravens, Andrew Lensen, Paula Maddigan, Bing Xue
Manifold Learning Genetic Programming Interpretable Tree

March 13, 2024

Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy
Eleni D. Koronaki, Luise F. Kaven, Johannes M. M. Faust, Ioannis G. Kevrekidis, Alexander Mitsos
Manifold Learning Raman System Raman Spectroscopy

March 12, 2024

A Multimodal Intermediate Fusion Network with Manifold Learning for Stress Detection
Morteza Bodaghi, Majid Hosseini, Raju Gottumukkala
Manifold Learning Dimension Reduction Stress Detection Multimodal Deep Learning Multimodal Network Multimodal Fusion Network

March 11, 2024

Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's disease
Fatemeh Ahmadi, Mohamad Ebrahim Shiri, Behroz Bidabad, Maral Sedaghat, Pooran Memari
Alzheimer'S Disease Common Disease Manifold Learning 3D Brain Covariance Alignment Ricci Flow

February 20, 2024

Learning on manifolds without manifold learning
H. N. Mhaskar, Ryan O'Dowd
LeArning Abstract Average Approximation Manifold Learning Class Manifold Function Approximation Manifold Hypothesis ONE Shot Unknown Manifold

February 14, 2024

February 6, 2024

Multilinear Kernel Regression and Imputation via Manifold Learning
Duc Thien Nguyen, Konstantinos Slavakis
Low Rank Manifold Learning Imputation Method Knowledge Enhanced Conditional Imputation Multilinear Discriminant Analysis

January 24, 2024

EMP: Effective Multidimensional Persistence for Graph Representation Learning
Ignacio Segovia-Dominguez, Yuzhou Chen, Cuneyt G. Akcora, Zhiwei Zhen, Murat Kantarcioglu, Yulia R. Gel, Baris Coskunuzer
Graph Representation Learning Topological Data Analysis Manifold Learning Persistent Homology Free Counterpart

January 12, 2024

Deep Manifold Transformation for Protein Representation Learning
Bozhen Hu, Zelin Zang, Cheng Tan, Stan Z. Li
Manifold Learning Protein Language Model Protein Representation Learning Protein Representation

January 2, 2024

Scalable manifold learning by uniform landmark sampling and constrained locally linear embedding
Dehua Peng, Zhipeng Gui, Wenzhang Wei, Huayi Wu
Dimensionality Reduction Manifold Learning Low Dimensional Structure Landmark Retrieval

December 22, 2023

Compressing Image-to-Image Translation GANs Using Local Density Structures on Their Learned Manifold
Alireza Ganjdanesh, Shangqian Gao, Hirad Alipanah, Heng Huang
Generative Adversarial Network Manifold Learning Image to Image GAN Compression

December 21, 2023

Probing Biological and Artificial Neural Networks with Task-dependent Neural Manifolds
Michael Kuoch, Chi-Ning Chou, Nikhil Parthasarathy, Joel Dapello, James J. DiCarlo, Haim Sompolinsky, SueYeon Chung
Neural Network Manifold Learning Linear Probing Mechanistic Study Neural Geometry