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We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes.
Some metric inequalities in the space of matrices
K. Fan and A. J. Hoffman · 1955
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Probability inequalities for sums of bounded random variables
W. Hoeffding · 1963
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The Index Theorem and the Heat Equation
P. Gilkey · 1974
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Closest unitary, orthogonal and hermitian operators to a given operator
J. B. Keller · 1975
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Computing the polar decomposition with applications
N. J. Higham · 1986
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Noncommutative Harmonic Analysis
M. E. Taylor · 1986
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Least-squares fitting of two 3-D point sets
K. S. Arun, T. S. Huang, and S. D. Blostein · 1987
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Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction
M. van Heel · 1987
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Representation Theory: A First Course
W. Fulton and J. Harris · 1991
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A common-lines based method for determining orientations for N ≥ 3 N\geq 3 particle projections simultaneously
P.A. Penczek, J. Zhu, and J. Frank · 1996
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Nonlinear dimensionality reduction by locally linear embedding
S. T. Roweis and L. K. Saul · 2000
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A Global Geometric Framework for Nonlinear Dimensionality Reduction
J. B. Tenenbaum, V. de Silva, and J. C. Langford · 2000
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Single-particle electron cryo-microscopy: towards atomic resolution
M. van Heel, B. Gowen, R. Matadeen, E.V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan · 2000
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The Mathematics of Computerized Tomography
F. Natterer · 2001
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Laplacian eigenmaps for dimensionality reduction and data representation
M. Belkin and P. Niyogi · 2003
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The global approach to Quantum field theory
B. DeWitt · 2003
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Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
D. L. Donoho and C. Grimes · 2003
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Diffusion maps
R. R. Coifman and S. Lafon · 2006
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Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State
J. Frank · 2006
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High dimensional statistical inference and random matrices
I. M. Johnstone · 2006
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Riemannian Geometry
P. Petersen · 2006
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From graph to manifold Laplacian: The convergence rate
A. Singer · 2006
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Convergence of Laplacian eigenmaps
M. Belkin and P. Niyogi · 2007
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Covariance regularization by thresholding
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The non-linear statistics of high-contrast patches in natural images
A. B. Lee, K. S. Pedersen, and D. Mumford · 2003
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Heat kernels and Dirac operators
N. Berline, E. Getzler, and M. Vergne · 2004
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Diffusion maps and geometric harmonics
S. Lafon · 2004
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Towards a theoretical foundation for Laplacian-based manifold methods
M. Belkin and P. Niyogi · 2005
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From graphs to manifolds - weak and strong pointwise consistency of graph Laplacians
M. Hein, J. Audibert, and U. von Luxburg · 2005
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Robust principal component analysis?
E. J. Candes, X. Li, Y. Ma, and J. Wright
Cited in the paper.
P. J. Bickel and E. Levina · 2008
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On the local behavior of spaces of natural images
G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian · 2008
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On consistency and sparsity for principal components analysis in high dimensions
I. M. Johnstone and A. Y. Lu · 2009
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Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD
A. V. Little, J. Lee, Y.M. Jung, and M. Maggioni · 2009
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Some remarks on diffusion distances
M. J. Goldberg and S. Kim · 2010
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