Fetching the paper…
Reading the bibliography…
Numerous problems in machine learning are formulated as optimization with manifold constraints.
Multiplier and gradient methods
M. R. Hestenes · 1969
Earlier work this paper cites.
A method for nonlinear constraints in minimization problems
M. J. D. Powell · 1969
Earlier work this paper cites.
A dual algorithm for the solution of nonlinear variational problems via finite element approximation
D. Gabay and B. Mercier · 1976
Earlier work this paper cites.
Orthogonal Procrustes rotation for two or more matrices
J. M. F. Ten Berge · 1977
Earlier work this paper cites.
Computing discrete minimal surfaces and their conjugates
U. Pinkall and K. Polthier · 1993
Earlier work this paper cites.
Optimization techniques on Riemannian manifolds
S. T. Smith · 1994
Earlier work this paper cites.
The geometry of algorithms with orthogonality constraints
A. Edelman, T. A. Arias, and S. T. Smith · 1998
Earlier work this paper cites.
Subgradient algorithm on Riemannian manifolds
O. P. Ferreira and P. R. Oliveira · 1998
Earlier work this paper cites.
Laplacian eigenmaps and spectral techniques for embedding and clustering
M. Belkin and P. Niyogi · 2001
Earlier work this paper cites.
Computing the nearest correlation matrix – a problem from finance
N. J. Higham · 2002
Earlier work this paper cites.
On spectral clustering: Analysis and an algorithm
A. Y. Ng, M. I. Jordan, and Y. Weiss · 2002
Earlier work this paper cites.
Joint diagonalization on the oblique manifold for independent component analysis
P.-A. Absil and K. A. Gallivan · 2006
Earlier work this paper cites.
Robust Euclidean embedding
L. Cayton and S. Dasgupta · 2006
Earlier work this paper cites.
Trust-region methods on Riemannian manifolds
P-A Absil, Christopher G Baker, and K A Gallivan · 2007
Earlier work this paper cites.
Nonsmooth analysis on smooth manifolds
Y. Ledyaev and Q. Zhu · 2007
Earlier work this paper cites.
A unifying local convergence result for Newton’s method in Riemannian manifolds
F. Alvarez, J. Bolte, and J. Munier · 2008
Earlier work this paper cites.
1-bit compressive sensing
P. T. Boufounos and R. G. Baraniuk · 2008
Cited alongside, same era.
Numerical geometry of non-rigid shapes
A M Bronstein, M M Bronstein, and R Kimmel · 2008
Cited alongside, same era.
Graph implementations for nonsmooth convex programs
M. Grant and S. Boyd · 2008
Cited alongside, same era.
Optimization algorithms on matrix manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2009
Cited alongside, same era.
A gradient descent algorithm on the Grassman manifold for matrix completion
R. H. Keshavan and S. Oh · 2009
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikk, E. Chu, B. Peleato, and J. Eckstein · 2010
Cited alongside, same era.
Blind source separation with compressively sensed linear mixtures
M. Kleinsteuber and H. Shen · 2012
Later among the works it cites.
Functional maps: a flexible representation of maps between shapes
M Ovsjanikov, M Ben-Chen, J Solomon, A Butscher, and L J Guibas · 2012
Later among the works it cites.
Coupled quasi-harmonic bases
A. Kovnatsky, M. M. Bronstein, A. M. Bronstein, K. Glashoff, and R. Kimmel · 2013
Later among the works it cites.
Compressed modes for variational problems in mathematics and physics
V. Ozoliņš, R. Lai, R. Caflisch, and S. Osher · 2013
Later among the works it cites.
Exact and stable recovery of rotations for robust synchronization
L. Wang and A. Singer · 2013
Later among the works it cites.
A feasible method for optimization with orthogonality constraints
Z. Wen and W. Yin · 2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Low-rank optimization on the cone of positive semidefinite matrices
M. Journée, F. Bach, P.-A. Absil, and R. Sepulchre · 2010
Cited alongside, same era.
Online learning in the manifold of low-rank matrices
U. Shalit, D. Weinshall, and G. Chechik · 2010
Cited alongside, same era.
RTRMC: A Riemannian trust-region method for low-rank matrix completion
N. Boumal and P.-A. Absil · 2011
Cited alongside, same era.
Robust principal component analysis?
E. Candès, X. Li, Y. Ma, and J. Wright · 2011
Cited alongside, same era.
Blended intrinsic maps
V G Kim, Y Lipman, and T Funkhouser · 2011
Cited alongside, same era.
Linear regression under fixed-rank constraints: a Riemannian approach
G. Meyer, S. Bonnabel, and R. Sepulchre · 2011
Cited alongside, same era.
Probabilistic principal geodesic analysis
M. Zhang and P. T. Fletcher · 2013
Later among the works it cites.
A Riemannian subgradient algorithm for economic dispatch with valve-point effect
P. B. Borckmans, S. E. Selvan, N. Boumal, and P.-A. Absil · 2014
Later among the works it cites.
Manopt, a Matlab toolbox for optimization on manifolds
N. Boumal, B. Mishra, P.-A. Absil, and R. Sepulchre · 2014
Later among the works it cites.
Clustering on multi-layer graphs via subspace analysis on Grassmann manifolds
X. Dong, P. Frossard, P. Vandergheynst, and N. Nefedov · 2014
Later among the works it cites.
Functional map networks for analyzing and exploring large shape collections
Q. Huang, F. Wang, and L. Guibas · 2014
Later among the works it cites.
A splitting method for orthogonality constrained problems
R. Lai and S. Osher · 2014
Later among the works it cites.
Compressed manifold modes for mesh processing
T. Neumann, K. Varanasi, C. Theobalt, M. Magnor, and M. Wacker · 2014
Later among the works it cites.
Riemannian pursuit for big matrix recovery
M. Tan, I. W. Tsang, L. Wang, B. Vandereycken, and S. J. Pan · 2014
Later among the works it cites.
Multimodal diffusion geometry by joint diagonalization of Laplacians
D. Eynard, K. Glashoff, M. M. Bronstein, and A. M. Bronstein · 2015
Closest in time.
Functional correspondence by matrix completion
A. Kovnatsky, M. M. Bronstein, X. Bresson, and P. Vandergheynst · 2015
Closest in time.