Charting a Manifold

Keywords

Manifold (fluid mechanics), Invertible matrix, Manifold alignment, Coordinate system, Curse of dimensionality

References

• A global geometric framework for nonlinear dimensionality reduction.Joshua B. Tenenbaum, Vin de Silva, John Langford — 2000
• Nonlinear dimensionality reduction by locally linear embedding.Sam T. Roweis, Lawrence K. Saul — 2000
• The Isomap Algorithm and Topological StabilityMukund Balasubramanian, Eric L. Schwartz — 2002
• Modeling the manifolds of images of handwritten digitsGeoffrey E. Hinton, Peter Dayan, Michael Revow — 1997
• Global Coordination of Local Linear ModelsSam T. Roweis, Lawrence K. Saul, Geoffrey E. Hinton — 2001
• Dimension Reduction by Local Principal Component AnalysisNandakishore Kambhatla, Todd K. Leen — 1997
• Non-Linear Dimensionality ReductionDavid DeMers, Garrison W. Cottrell — 1992
• Nonlinear Image Interpolation using Manifold LearningChristoph Bregler, Stephen M. Omohundro — 1994
• Segmentation using eigenvectors: a unifying viewYaakov Weiss — 1999
• Regularized Principal ManifoldsAlex Smola, S. Mika, B. Schölkopf — 1999
• A Variational Approach to Recovering a Manifold from Sample PointsJosé Gomes, A. Mojsilovic — 2002

Cited by

• Advances in dissimilarity-based data visualisationAndrej Gisbrecht — 2015
• Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and VisualizationKerstin Bunte, Sven Haase, Sven Haase — 2011
• Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves AnalysisMaría Montserrat Serrallonga y Sivilla — 2016
• Multifactor analysis for face recognition based on factor-dependent geometryMarios Savvides, Sung Won Park — 2011
• Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High DimensionsMiles Crosskey — 2014
• Unsupervised Feature Learning and Deep Learning: A Review and New PerspectivesYoshua Bengio, Aaron Courville, Pascal Vincent — 2012
• Visual exploration of multivariate data in breast cancer by dimensional reductionClaudio Varini — 2006
• Methods for estimation of intrinsic dimensionalityZakiah I. Kalantan — 2014
• Nonlinear Manifold Learning for Data StreamM.H.C. Law, Nan Zhang, Anil K. Jain — 2004
• Bayesian and Information-Theoretic Learning of High Dimensional DataMinhua Chen — 2012
• Discovering Shared Structure in Manifold LearningYoshua Bengio, Martin Monperrus — 2004
• Experiments with Massively Parallel Constraint SolvingLucas Bordeaux, Youssef Hamadi, Horst Samulowitz — 2009
• Manifold Learning for Natural Image Sets, Doctoral Dissertation August 2006Richard Souvenir — 2006
• Semisupervised alignment of manifoldsJihun Ham, Daniel D. Lee, Lawrence K. Saul — 2005
• Non-Negative Matrix Factorization Based Algorithms to Cluster Frequency Basis Functions for Monaural Sound Source Separation.Rajesh Jaiswal — 2013
• Three-dimensional free form surface reconstruction from occluding contours in a sequence of images or videoDavid B. Cooper, Kongbin Kang — 2004
• Classification et modélisation de sorties fonctionnelles de codes de calcul : application aux calculs thermo-hydrauliques accidentels dans les réacteurs à eau pressurisés (REP)Benjamin Auder — 2011
• A HYBRID BUSINESS FAILURE PREDICTION MODEL USING LOCALLY LINEAR EMBEDDING AND SUPPORT VECTOR MACHINESFengyi Lin, Ching Chiang Yeh, Meng Yuan Lee — 2013
• Advancing the Effectiveness of Non-Linear Dimensionality Reduction TechniquesMichael S. Gashler — 2012
• Numerische Methoden zur Analyse hochdimensionaler DatenDennis Heinen — 2014

Related papers

• Unsupervised Learning of Image Manifolds by Semidefinite ProgrammingKilian Q. Weinberger, Lawrence K. Saul — 2004
• Stochastic Neighbor EmbeddingGeoffrey E. Hinton, Sam T. Roweis — 2002
• Maximum Likelihood Estimation of Intrinsic DimensionElizaveta Levina, Peter J. Bickel — 2004
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional dataDavid L. Donoho, Carrie Grimes — 2003
• Global Versus Local Methods in Nonlinear Dimensionality ReductionVin D. Silva, Joshua B. Tenenbaum — 2002
• Automatic Alignment of Local RepresentationsYee Whye Teh, Sam T. Roweis — 2002
• Locality Preserving ProjectionsXiaofei He, Partha Niyogi — 2003
• Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral ClusteringYoshua Bengio, Jean-françcois Paiement, Pascal Vincent — 2003
• Nonlinear Component Analysis as a Kernel Eigenvalue ProblemBernhard Schölkopf, Alexander J. Smola, Klaus‐Robert Müller — 1998