Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment

Zhenyue Zhang, Hongyuan Zha

Type: Preprint

Publication Date: 2002-01-01

Citations: 551

DOI: https://doi.org/10.48550/arxiv.cs/0212008

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Manifold learning and unwrapping using density ridges	2016	Shaker
+ PDF Chat	Manifold learning and optimization using tangent space proxies	2025	Ryan A. Robinett Lorenzo Orecchia Samantha J. Riesenfeld
+	Dimension Reduction: A Guided Tour	2009	Christopher J. C. Burges
+	$O(k)$-Equivariant Dimensionality Reduction on Stiefel Manifolds	2023	Andrew Lee Harlin Lee José A. Perea Nikolas Schonsheck Madeleine Weinstein
+	Nonlinear dimensionality reduction using probabilistic principal surfaces	2000	Kuiyu Chang Joydeep Ghosh
+	Tangent bundle Manifold Learning for image analysis	2013	Alexander Kuleshov Alexander Bernstein
+	LDLE: Low Distortion Local Eigenmaps	2021	Dhruv Kohli Alexander Cloninger Gal Mishne
+ PDF Chat	Inductive Global and Local Manifold Approximation and Projection	2024	Jungeum Kim Xiao Wang
+	Tangent Bundle Manifold Learning via Grassmann&Stiefel Eigenmaps	2012	Alexander Bernstein Alexander Kuleshov
+	Metric Learning on Manifolds	2011	Dominique Perrault-Joncas Marina Meil
+	Isometric Correction for Manifold Learning	2010	Behrouz Behmardi Raviv Raich
+	Tangent Bundle Manifold Learning via Grassmann&Stiefel Eigenmaps	2012	Alexander Bernstein Alexander Kuleshov
+	Manifold Learning via Manifold Deflation	2020	Daniel Ting Michael I. Jordan
+	Non-isometric manifold learning	2007	Piotr Dollár Vincent Rabaud Serge Belongie
+	Principal subbundles for dimension reduction	2023	Morten Akhøj James Benn Erlend Grong Stefan Sommer Xavier Pennec
+ PDF Chat	Tangent-based manifold approximation with locally linear models	2014	Sofia Karygianni Pascal Frossard
+	Manifold unwrapping using density ridges	2016	Jonas Nordhaug Myhre Matineh Shaker Devrim Kaba Robert Jenssen Deniz Erdoğmuş
+ PDF Chat	Uniform Manifold Approximation with Two-phase Optimization	2022	Hyeon Jeon Hyung-Kwon Ko Soohyun Lee Jaemin Jo Jinwook Seo
+	Manifold learning: what, how, and why	2023	Marina Meilă Hanyu Zhang
+ PDF Chat	Manifold Learning: What, How, and Why	2023	Marina Meilă Hanyu Zhang

Works That Cite This (102)

Action	Title	Year	Authors
+ PDF Chat	Nonlinear supervised dimensionality reduction via smooth regular embeddings	2018	Cem Örnek Elif Vural
+ PDF Chat	Curvature-aware manifold learning	2018	Yangyang Li
+ PDF Chat	Quadratic projection based feature extraction with its application to biometric recognition	2016	Yan Yan Hanzi Wang Si Chen Xiaochun Cao David Zhang
+ PDF Chat	Multiview Hessian regularized logistic regression for action recognition	2014	Weifeng Liu Hongli Liu Dapeng Tao Yanjiang Wang Ke Lü
+	Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature	2016	Anna Little Mauro Maggioni Lorenzo Rosasco
+ PDF Chat	Estimating the mean manifold of a deformable object from noisy observations	2016	Ziv Yavo Joseph M. Francos Ignacio Santamarı́a Louis L. Scharf
+	Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian	2007	Peter W. Jones Mauro Maggioni Raanan Schul
+	Diffusion Representations	2015	Moshe Salhov Amit Bermanis Guy Wolf Amir Averbuch
+	A Tangent Distance Preserving Dimensionality Reduction Algorithm	2019	Xu Zhao Zongli Jiang
+	Multiview Hessian regularized logistic regression for action recognition	2014	W. Liu H. Liu Dapeng Tao Y. Wang Ke Lü

Works Cited by This (3)

Action	Title	Year	Authors
+	The Elements of Statistical Learning	2001	Trevor Hastie J. Friedman Robert Tibshirani
+	Applied Functional Data Analysis	2003	Henry W. Altland
+	Topology representing networks	1994	Thomas Martinetz Klaus Schulten