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Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.
Fundamenta Mathematicae 20
Bochner, S.: Integration von funktionen, deren werte die elemente eines vektorraumes sind · 1933
Earlier work this paper cites.
Journal of Multivariate Analysis 4
Perlman, M.D.: Jensen’s inequality for a convex vector-valued function on an infinite-dimensional space · 1974
Earlier work this paper cites.
Elsevier Science & Technology Books (1983)
Kallenberg, O.: Random measures · 1983
Earlier work this paper cites.
John Wiley & Sons (1986)
Hall, M.: Combinatorial theory (2nd ed) · 1986
Earlier work this paper cites.
Graduate Texts in Mathematics. Springer-Verlag (1995)
Kechris, A.: Classical descriptive set theory · 1995
Earlier work this paper cites.
Mathematische Nachrichten 254
Cascales, B., Raja, M.: Measurable selectors for the metric projection · 2003
Earlier work this paper cites.
Springer Science & Business Media (2003)
Schrijver, A.: Combinatorial optimization: polyhedra and efficiency, vol. 24 · 2003
Earlier work this paper cites.
58. American Mathematical Soc. (2003)
Villani, C.: Topics in optimal transportation · 2003
Earlier work this paper cites.
No. v. 1 in Measure Theory. Springer Berlin Heidelberg (2007)
Bogachev, V.: Measure theory · 2007
Earlier work this paper cites.
Discrete & Computational Geometry 37
Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams · 2007
Earlier work this paper cites.
Springer Science & Business Media (2008)
Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows: in metric spaces and in the space of probability measures · 2008
Earlier work this paper cites.
Springer Science & Business Media (2008)
Villani, C.: Optimal transport: old and new, vol. 338 · 2008
Earlier work this paper cites.
Economic Theory 42
Carlier, G., Ekeland, I.: Matching for teams · 2010
Earlier work this paper cites.
Foundations of computational mathematics 10
Cohen-Steiner, D., Edelsbrunner, H., Harer, J., Mileyko, Y.: Lipschitz functions have Lp-stable persistence · 2010
Earlier work this paper cites.
American Mathematical Soc. (2010)
Edelsbrunner, H., Harer, J.: Computational topology: an introduction · 2010
Earlier work this paper cites.
Archive for rational mechanics and analysis 195
Figalli, A.: The optimal partial transport problem · 2010
Earlier work this paper cites.
Journal de mathématiques pures et appliquées 94
Figalli, A., Gigli, N.: A new transportation distance between non-negative measures, with applications to gradients flows with dirichlet boundary conditions · 2010
Earlier work this paper cites.
SIAM Journal on Mathematical Analysis 43
Agueh, M., Carlier, G.: Barycenters in the Wasserstein space · 2011
Earlier work this paper cites.
Inverse Problems 27
Mileyko, Y., Mukherjee, S., Harer, J.: Probability measures on the space of persistence diagrams · 2011
Earlier work this paper cites.
Mathematical Physics, Analysis and Geometry 14
Nielsen, L.: Weak convergence and Banach space-valued functions: improving the stability theory of feynman’s operational calculi · 2011
Earlier work this paper cites.
Wiley Series in Probability and Statistics. Wiley (2013)
Billingsley, P.: Convergence of probability measures · 2013
Earlier work this paper cites.
In: Advances in Neural Information Processing Systems, pp. 2292–2300 (2013)
Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport · 2013
Cited alongside, same era.
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley (2013)
Folland, G.: Real analysis: modern techniques and their applications · 2013
Cited alongside, same era.
Phys. Rev. E 87
Kramar, M., Goullet, A., Kondic, L., Mischaikow, K.: Persistence of force networks in compressed granular media · 2013
Cited alongside, same era.
arXiv preprint arXiv:1307.8300 (2013)
Turner, K.: Means and medians of sets of persistence diagrams · 2013
Cited alongside, same era.
Foundations of Computational Mathematics 14
Blumberg, A.J., Gal, I., Mandell, M.A., Pancia, M.: Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces · 2014
Cited alongside, same era.
Probability Theory and Related Fields pp. 1–17 (2016)
Le Gouic, T., Loubes, J.M.: Existence and consistency of Wasserstein barycenters · 2016
Later among the works it cites.
Journal of Machine Learning Research 18
Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., Chepushtanova, S., Hanson, E., Motta, F., Ziegelmeier, L.: Persistence images: a stable vector representation of persistent homology · 2017
Later among the works it cites.
The Annals of Applied Probability 27
Bobrowski, O., Kahle, M., Skraba, P., et al.: Maximally persistent cycles in random geometric complexes · 2017
Later among the works it cites.
Journal of Symbolic Computation 78
Bubenik, P., Dłotko, P.: A persistence landscapes toolbox for topological statistics · 2017
Later among the works it cites.
In: 34th International Conference on Machine Learning (2017)
Carrière, M., Cuturi, M., Oudot, S.: Sliced Wasserstein kernel for persistence diagrams · 2017
Later among the works it cites.
URL https://github.com/rflamary/POT
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In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2014)
Li, C., Ovsjanikov, M., Chazal, F.: Persistence-based structural recognition · 2014
Cited alongside, same era.
Discrete & Computational Geometry 52
Turner, K., Mileyko, Y., Mukherjee, S., Harer, J.: Fréchet means for distributions of persistence diagrams · 2014
Cited alongside, same era.
Information and Inference: A Journal of the IMA 3
Turner, K., Mukherjee, S., Boyer, D.M.: Persistent homology transform for modeling shapes and surfaces · 2014
Cited alongside, same era.
ESAIM: Mathematical Modelling and Numerical Analysis 49
Carlier, G., Oberman, A., Oudet, E.: Numerical methods for matching for teams and Wasserstein barycenters · 2015
Cited alongside, same era.
Computer Graphics Forum 34
Carrière, M., Oudot, S.Y., Ovsjanikov, M.: Stable topological signatures for points on 3d shapes · 2015
Cited alongside, same era.
In: International Conference on Machine Learning, pp. 2143–2151 (2015)
Chazal, F., Fasy, B., Lecci, F., Michel, B., Rinaldo, A., Wasserman, L.: Subsampling methods for persistent homology · 2015
Cited alongside, same era.
arXiv preprint arXiv:1510.02502 (2015)
Chen, Y.C., Wang, D., Rinaldo, A., Wasserman, L.: Statistical analysis of persistence intensity functions · 2015
Cited alongside, same era.
Flamary, R., Courty, N.: POT python optimal transport library (2017) · 2017
Later among the works it cites.
Journal of Experimental Algorithmics (JEA) 22
Kerber, M., Morozov, D., Nigmetov, A.: Geometry helps to compare persistence diagrams · 2017
Later among the works it cites.
The Journal of Machine Learning Research 18
Kusano, G., Fukumizu, K., Hiraoka, Y.: Kernel method for persistence diagrams via kernel embedding and weight factor · 2017
Later among the works it cites.
2017-86 (2017)
Peyré, G., Cuturi, M.: Computational optimal transport · 2017
Later among the works it cites.
Bulletin of Mathematical Sciences 7
Santambrogio, F.: Euclidean, metric, and Wasserstein gradient flows: an overview · 2017
Later among the works it cites.
Information and Media Technologies 12
Umeda, Y.: Time series classification via topological data analysis · 2017
Later among the works it cites.
Journal of Applied and Computational Topology pp. 1–37 (2018)
Bubenik, P., Vergili, T.: Topological spaces of persistence modules and their properties · 2018
Later among the works it cites.
In: International Conference on Artificial Intelligence and Statistics, pp. 1608–1617 (2018)
Genevay, A., Peyre, G., Cuturi, M.: Learning generative models with sinkhorn divergences · 2018
Later among the works it cites.
arXiv preprint arXiv:1805.05032 (2018)
Goel, A., Trinh, K.D., Tsunoda, K.: Asymptotic behavior of Betti numbers of random geometric complexes · 2018
Later among the works it cites.
The Annals of Applied Probability 28
Hiraoka, Y., Shirai, T., Trinh, K.D., et al.: Limit theorems for persistence diagrams · 2018
Later among the works it cites.
In: Advances in Neural Information Processing Systems (2018)
Lacombe, T., Cuturi, M., Oudot, S.: Large scale computation of means and clusters for persistence diagrams using optimal transport · 2018
Later among the works it cites.
arXiv preprint arXiv:1807.07054 (2018)
Schweinhart, B.: Weighted persistent homology sums of random Čech complexes · 2018
Later among the works it cites.
In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 617–635 (2018)
Som, A., Thopalli, K., Natesan Ramamurthy, K., Venkataraman, V., Shukla, A., Turaga, P.: Perturbation robust representations of topological persistence diagrams · 2018
Later among the works it cites.
Journal of Applied and Computational Topology 3
Divol, V., Polonik, W.: On the choice of weight functions for linear representations of persistence diagrams · 2019
Closest in time.
Journal of Machine Learning Research 20
Hofer, C.D., Kwitt, R., Niethammer, M.: Learning representations of persistence barcodes · 2019
Closest in time.