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Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions.
On the transfer of masses
L. V. Kantorovich · 1942
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Hierarchical clustering schemes
S. C. Johnson · 1967
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What is random packing?
Anonymous · 1972
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Physics of amorphous materials
S. R. Elliott · 1983
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Harmonic analysis on semigroups
C. Berg, J. P. R. Christensen, and P. Ressel · 1984
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The quadtree and related hierarchical data structures
H. Samet · 1984
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Clustering to minimize the maximum intercluster distance
T. F. Gonzalez · 1985
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Optimal algorithms for approximate clustering
T. Feder and D. Greene · 1988
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Term-weighting approaches in automatic text retrieval
G. Salton and C. Buckley · 1988
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On the scaling of multidimensional matrices
J. Franklin and J. Lorenz · 1989
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Probabilistic approximation of metric spaces and its algorithmic applications
Y. Bartal · 1996
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On approximating arbitrary metrices by tree metrics
Y. Bartal · 1998
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Approximating a finite metric by a small number of tree metrics
M. Charikar, C. Chekuri, A. Goel, S. Guha, and S. Plotkin · 1998
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Linear assignment problems and extensions
R. E. Burkard and E. Cela · 1999
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Shape descriptors for non-rigid shapes with a single closed contour
L. J. Latecki, R. Lakamper, and T. Eckhardt · 2000
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The Earth Mover’s distance as a metric for image retrieval
Y. Rubner, C. Tomasi, and L. J. Guibas · 2000
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Algorithmic applications of low-distortion geometric embeddings
P. Indyk · 2001
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Fast image retrieval via embeddings
P. Indyk and N. Thaper · 2003
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Phylogenetics
C. Semple and M. Steel · 2003
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Topics in optimal transportation
C. Villani · 2003
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A tight bound on approximating arbitrary metrics by tree metrics
J. Fakcharoenphol, S. Rao, and K. Talwar · 2004
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Isometric embedding of finite ultrametric spaces in banach spaces
S. A. Shkarin · 2004
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Unifrac: a new phylogenetic method for comparing microbial communities
C. Lozupone and R. Knight · 2005
Cited alongside, same era.
Efficient kernel machines using the improved fast gauss transform
C. Yang, R. Duraiswami, and L. S. Davis · 2005
Cited alongside, same era.
Dna microarrays: design principles for maximizing ergodic, chaotic mixing
J.-M. Hertzsch, R. Sturman, and S. Wiggins · 2007
Cited alongside, same era.
Quantitative and qualitative β \beta diversity measures lead to different insights into factors that structure microbial communities
C. A. Lozupone, M. Hamady, S. T. Kelley, and R. Knight · 2007
Cited alongside, same era.
Persistent homology - a survey
H. Edelsbrunner and J. Harer · 2008
Cited alongside, same era.
Optimal transport: old and new
C. Villani · 2008
Cited alongside, same era.
Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
J. Solomon, F. De Goes, G. Peyre, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas · 2015
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Stochastic optimization for large-scale optimal transport
A. Genevay, M. Cuturi, G. Peyre, and F. Bach · 2016
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Sliced Wasserstein kernels for probability distributions
S. Kolouri, Y. Zou, and G. K. Rohde · 2016
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On valid optimal assignment kernels and applications to graph classification
N. M. Kriege, P.-L. Giscard, and R. Wilson · 2016
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Amplitude and phase variation of point processes
V. M. Panaretos, Y. Zemel, et al · 2016
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Persistence images: A stable vector representation of persistent homology
H. Adams, T. Emerson, M. Kirby, R. Neville, C. Peterson, P. Shipman, S. Chepushtanova, E. Hanson, F. Motta, and L. Ziegelmeier · 2017
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Kernel change-point analysis
Z. Harchaoui, E. Moulines, and F. R. Bach · 2009
Cited alongside, same era.
Automatic online tuning for fast gaussian summation
V. I. Morariu, B. V. Srinivasan, V. C. Raykar, R. Duraiswami, and L. S. Davis · 2009
Cited alongside, same era.
Fast and robust Earth Mover’s distances
O. Pele and M. Werman · 2009
Cited alongside, same era.
Libsvm: a library for support vector machines
C.-C. Chang and C.-J. Lin · 2011
Cited alongside, same era.
Sublinear time algorithms for Earth Mover’s distance
K. Do Ba, H. L. Nguyen, H. N. Nguyen, and R. Rubinfeld · 2011
Cited alongside, same era.
The phylogenetic Kantorovich–Rubinstein metric for environmental sequence samples
S. N. Evans and F. A. Matsen · 2012
Cited alongside, same era.
Later among the works it cites.
Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
J. Altschuler, J. Weed, and P. Rigollet · 2017
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Sliced Wasserstein kernel for persistence diagrams
M. Carriere, M. Cuturi, and S. Oudot · 2017
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Construction of non-asymptotic confidence sets in 2-Wasserstein space
J. Ebert, V. Spokoiny, and A. Suvorikova · 2017
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Practical data-dependent metric compression with provable guarantees
P. Indyk, I. Razenshteyn, and T. Wagner · 2017
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Approximating the quadratic transportation metric in near-linear time
J. Altschuler, F. Bach, A. Rudi, and J. Weed · 2018
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Massively scalable Sinkhorn distances via the Nystrom method
J. Altschuler, F. Bach, A. Rudi, and J. Weed · 2018
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Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn’s algorithm
P. Dvurechensky, A. Gasnikov, and A. Kroshnin · 2018
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Kernel method for persistence diagrams via kernel embedding and weight factor
G. Kusano, K. Fukumizu, and Y. Hiraoka · 2018
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Dynamical optimal transport on discrete surfaces
H. Lavenant, S. Claici, E. Chien, and J. Solomon · 2018
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Persistence Fisher kernel: A Riemannian manifold kernel for persistence diagrams
T. Le and M. Yamada · 2018
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Minimax statistical learning with Wasserstein distances
J. Lee and M. Raginsky · 2018
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Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
U. Şimşekli, A. Liutkus, S. Majewski, and A. Durmus · 2018
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Inference for empirical Wasserstein distances on finite spaces
M. Sommerfeld and A. Munk · 2018
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Scalable fair clustering
A. Backurs, P. Indyk, K. Onak, B. Schieber, A. Vakilian, and T. Wagner · 2019
Closest in time.
Scalable nearest neighbor search for optimal transport
Y. Dong, P. Indyk, I. Razenshteyn, and T. Wagner · 2019
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Computational optimal transport
G. Peyré and M. Cuturi · 2019
Closest in time.