Fetching the paper…
Reading the bibliography…
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and point processes.
Les éléments aléatoires de nature quelconque dans un espace distancié
M. Fréchet · 1948
Earlier work this paper cites.
Sur la distance de deux lois de probabilité
M. Fréchet · 1957
Earlier work this paper cites.
Convex analysis
R. T. Rockafellar · 1970
Earlier work this paper cites.
Bounds for the determinant of the sum of hermitian matrices
M. Fiedler · 1971
Earlier work this paper cites.
Generalized Procrustes analysis
J. C. Gower · 1975
Earlier work this paper cites.
Riemannian center of mass and mollifier smoothing
H. Karcher · 1977
Earlier work this paper cites.
Some asymptotic theory for the bootstrap
P. J. Bickel and D. A. Freedman · 1981
Earlier work this paper cites.
The Fréchet distance between multivariate normal distributions
D. Dowson and B. Landau · 1982
Earlier work this paper cites.
The distance between two random vectors with given dispersion matrices
I. Olkin and F. Pukelsheim · 1982
Earlier work this paper cites.
Random measures
O. Kallenberg · 1986
Earlier work this paper cites.
Structural image restoration through deformable templates
Y. Amit, U. Grenander, and M. Piccioni · 1991
Earlier work this paper cites.
Procrustes methods in the statistical analysis of shape
C. Goodall · 1991
Earlier work this paper cites.
The regularity of mappings with a convex potential
L. A. Caffarelli · 1992
Earlier work this paper cites.
Optimal coupling of multivariate distributions and stochastic processes
J. A. Cuesta-Albertos, L. Rüschendorf, and A. Tuero-Diaz · 1993
Earlier work this paper cites.
On a generalization of cyclic monotonicity and distances among random vectors
M. Knott and C. S. Smith · 1994
Earlier work this paper cites.
Mean size-and-shapes and mean shapes: a geometric point of view
H. Le · 1995
Earlier work this paper cites.
Morphometric tools for landmark data: geometry and biology
F. L. Bookstein · 1997
Earlier work this paper cites.
Optimal transportation plans and convergence in distribution
J. A. Cuesta-Albertos, C. Matrán, and A. Tuero-Diaz · 1997
Earlier work this paper cites.
A convexity principle for interacting gases
R. J. McCann · 1997
Earlier work this paper cites.
Statistical shape analysis
I. L. Dryden and K. V. Mardia · 1998
Earlier work this paper cites.
Optimal maps for the multidimensional Monge–Kantorovich problem
W. Gangbo and A. Świȩch · 1998
Earlier work this paper cites.
On the consistency of procrustean mean shapes
H. Le · 1998
Earlier work this paper cites.
Nonparametric validation of similar distributions and assessment of goodness of fit
A. Munk and C. Czado · 1998
Earlier work this paper cites.
A geometrical approach to monotone functions in ℝ n \mathbb{R}^{n}
G. Alberti and L. Ambrosio · 1999
Earlier work this paper cites.
Convergence of probability measures
P. Billingsley · 1999
Earlier work this paper cites.
A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
Earlier work this paper cites.
Locating Fréchet means with application to shape spaces
H. Le · 2001
Cited alongside, same era.
Steepest descent algorithms in a space of measures
I. Molchanov and S. Zuyev · 2002
Cited alongside, same era.
On the n n -coupling problem
L. Rüschendorf and L. Uckelmann · 2002
Cited alongside, same era.
A comparison of normalization methods for high density oligonucleotide array data based on variance and bias
B. M. Bolstad, R. A. Irizarry, M. Åstrand, and T. P. Speed · 2003
Cited alongside, same era.
Topics in Optimal Transportation
C. Villani · 2003
Cited alongside, same era.
On hadamard differentiability in k-sample semiparametric models?with applications to the assessment of structural relationships
G. Freitag and A. Munk · 2005
Cited alongside, same era.
An introduction to copulas
R. B. Nelsen · 2013
Later among the works it cites.
Optimal transportation with infinitely many marginals
B. Pass · 2013
Later among the works it cites.
A linear optimal transportation framework for quantifying and visualizing variations in sets of images
W. Wang, D. Slepčev, S. Basu, J. A. Ozolek, and G. K. Rohde · 2013
Later among the works it cites.
Fast computation of Wasserstein barycenters
M. Cuturi and A. Doucet · 2014
Later among the works it cites.
Convex Analysis
S. Krantz · 2014
Later among the works it cites.
Synthesizing and mixing stationary Gaussian texture models
G.-S. Xia, S. Ferradans, G. Peyré, and J.-F. Aujol · 2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
On the convergence of some Procrustean averaging algorithms
D. Groisser · 2005
Cited alongside, same era.
Real Analysis: Measure Theory, Integration & Hilbert Spaces
E. M. Stein and R. Shakarchi · 2005
Cited alongside, same era.
Principal component analysis for riemannian manifolds, with an application to triangular shape spaces
S. Huckemann and H. Ziezold · 2006
Cited alongside, same era.
Towards a coherent statistical framework for dense deformable template estimation
S. Allassonnière, Y. Amit, and A. Trouvé · 2007
Cited alongside, same era.
Gradient flows in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
Cited alongside, same era.
The one-and multi-sample problem for functional data with application to projective shape analysis
A. Munk, R. Paige, J. Pang, V. Patrangenaru, and F. Ruymgaart · 2008
Cited alongside, same era.
J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré · 2015
Later among the works it cites.
Distribution’s template estimate with Wasserstein metrics
E. Boissard, T. Le Gouic, J.-M. Loubes, et al · 2015
Later among the works it cites.
Sliced and Radon Wasserstein barycenters of measures
N. Bonneel, J. Rabin, G. Peyré, and H. Pfister · 2015
Later among the works it cites.
Numerical methods for matching for teams and wasserstein barycenters
G. Carlier, A. Oberman, and É. Oudet · 2015
Later among the works it cites.
Theoretical foundations of functional data analysis, with an introduction to linear operators
T. Hsing and R. Eubank · 2015
Later among the works it cites.
An efficient linear programming method for optimal transportation
A. M. Oberman and Y. Ruan · 2015
Later among the works it cites.
Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis
V. Patrangenaru and L. Ellingson · 2015
Later among the works it cites.
Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
J. Solomon, F. De Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas · 2015
Later among the works it cites.
A fixed-point approach to barycenters in Wasserstein space
P. C. Álvarez-Esteban, E. del Barrio, J. A. Cuesta-Albertos, and C. Matrán · 2016
Later among the works it cites.
Discrete Wasserstein barycenters: Optimal transport for discrete data
E. Anderes, S. Borgwardt, and J. Miller · 2016
Later among the works it cites.
Wasserstein barycentric coordinates: histogram regression using optimal transport
N. Bonneel, G. Peyré, and M. Cuturi · 2016
Later among the works it cites.
A smoothed dual approach for variational wasserstein problems
M. Cuturi and G. Peyré · 2016
Later among the works it cites.
Existence and consistency of Wasserstein barycenters
T. Le Gouic and J.-M. Loubes · 2016
Later among the works it cites.
Amplitude and phase variation of point processes
V. M. Panaretos and Y. Zemel · 2016
Later among the works it cites.
Limit laws of the empirical wasserstein distance: Gaussian distributions
T. Rippl, A. Munk, and A. Sturm · 2016
Later among the works it cites.
Fast dictionary learning with a smoothed wasserstein loss
A. Rolet, M. Cuturi, and G. Peyré · 2016
Later among the works it cites.
Inference for empirical wasserstein distances on finite spaces
M. Sommerfeld and A. Munk · 2016
Later among the works it cites.
Fréchet means in Wasserstein space: gradient descent and Procrustes analysis
Y. Zemel and V. M. Panaretos · 2016
Later among the works it cites.
From sparse to dense functional data and beyond
X. Zhang, J.-L. Wang, et al · 2016
Later among the works it cites.
C. Tameling, M. Sommerfeld, and A. Munk · 2017
Closest in time.