Paper Citation Record · LEDGER

On the Wasserstein Geodesic Principal Component Analysis of probability measures

As of 8 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2506.04480.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.04480 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:47:38.509206Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:34:53.419120Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-15T13:10:49.323330Z

Reference resolution

44 of 44 outbound references displayed

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External citation measurements

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Outbound references

Observation 5ec72545-fb44-4178-9ef7-2344b966b2df · outbound

This paper cites Barycenters in the Wasserstein space.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Barycenters in the Wasserstein space

Reference 1

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This paper cites A user’s guide to optimal transport.

On the Wasserstein Geodesic Principal Component Analysis of probability measures A user’s guide to optimal transport

Reference 2

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Observation 4611b3e4-35c4-4b40-8c28-3780e4b19ead · outbound

This paper cites Gradient flows: in metric spaces and in the space of probability measures.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Gradient flows: in metric spaces and in the space of probability measures

Reference 3

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Observation 5b253270-6a22-4b14-8fe0-2ea59371268b · outbound

This paper cites On the Bures–Wasserstein distance between positive definite matrices.

On the Wasserstein Geodesic Principal Component Analysis of probability measures On the Bures–Wasserstein distance between positive definite matrices

Reference 4

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Observation b9b835ed-e872-4a8b-8222-ba191c608f9f · outbound

This paper cites Geodesic PCA in the Wasserstein space by convex PCA.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Geodesic PCA in the Wasserstein space by convex PCA

Reference 5

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Observation 01c01f0d-e271-4eef-af9f-dcb5196f8607 · outbound

This paper cites Distribution’s template estimate with Wasserstein metrics.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Distribution’s template estimate with Wasserstein metrics

Reference 6

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Observation 191ea7b5-c2b1-44b6-a801-852f2725dc9e · outbound

This paper cites An introduction to optimization on smooth manifolds.

On the Wasserstein Geodesic Principal Component Analysis of probability measures An introduction to optimization on smooth manifolds

Reference 7

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Observation dd191bb0-11dd-48ee-8c96-05490d7142cf · outbound

This paper cites Polar factorization and monotone rearrangement of vector-valued functions.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Polar factorization and monotone rearrangement of vector-valued functions

Reference 8

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Observation 4ea654ea-f6e2-47e3-b61b-a3fcf39efe11 · outbound

This paper cites Populations of unlabelled networks: Graph space geometry and generalized geodesic principal components.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Populations of unlabelled networks: Graph space geometry and generalized geodesic principal components

Reference 9

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Observation 1080c809-7265-4c22-8d4f-387cd6b4f4fc · outbound

This paper cites Geodesic PCA versus log-PCA of histograms in the Wasserstein space.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Geodesic PCA versus log-PCA of histograms in the Wasserstein space

Reference 10

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Observation 2eabf528-d039-43b5-a4f3-2e46c0985e59 · outbound

This paper cites Groups of diffeomorphisms and the motion of an incompressible fluid.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Groups of diffeomorphisms and the motion of an incompressible fluid

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:43.811057Z

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Observation be926572-4d68-4f74-89fd-de04380138a2 · outbound

This paper cites Thomas Fletcher, Conglin Lu, and Sarang Joshi.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Thomas Fletcher, Conglin Lu, and Sarang Joshi

Reference 12

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Observation 5431cd4b-be64-499f-821a-3f0d07091009 · outbound

This paper cites Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifolds.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifolds

Reference 13

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Observation 2d26f248-ba87-41ae-9609-9be5bf47754f · outbound

This paper cites Riemannian proximal gradient methods.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Riemannian proximal gradient methods

Reference 14

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Observation 54a36925-1159-4b92-aa2c-efe6a851cd16 · outbound

This paper cites Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:43.366114Z

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Observation 967b7209-c835-4d12-ac40-1edfcd5f85e4 · outbound

This paper cites Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces

Reference 16

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Observation 1cb13d48-cb23-46b3-9b45-7bf65546ae69 · outbound

This paper cites Geometric hydrodynamics and infinite-dimensional Newton’s equations.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Geometric hydrodynamics and infinite-dimensional Newton’s equations

Reference 17

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Observation 59afcb0f-5b07-44c7-a206-d3fdee402990 · outbound

This paper cites A geometric study of Wasserstein spaces: Euclidean spaces.

On the Wasserstein Geodesic Principal Component Analysis of probability measures A geometric study of Wasserstein spaces: Euclidean spaces

Reference 18

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Observation 91c1f1fd-0bca-49d9-b960-f5da24230d1d · outbound

This paper cites MNIST handwritten digit database.

On the Wasserstein Geodesic Principal Component Analysis of probability measures MNIST handwritten digit database

Reference 19

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This paper cites Gluing methods for quantitative stability of optimal transport maps.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Gluing methods for quantitative stability of optimal transport maps

Reference 20

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Observation dbfcb270-d4a9-4938-81ab-3f4f16d15884 · outbound

This paper cites Eigenvalue continuity and Gersgorin’s theorem.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Eigenvalue continuity and Gersgorin’s theorem

Reference 21

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Observation 950c8be9-b5b6-411e-956d-ce202f82ddc3 · outbound

This paper cites Improved SQP and SLSQP algorithms for feasible path-based process optimisation.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Improved SQP and SLSQP algorithms for feasible path-based process optimisation

Reference 22

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Observation 05d5484c-e26e-44f3-88b2-6eb069e71744 · outbound

This paper cites Wasserstein Riemannian geometry of Gaussian densities.Information Geometry, 1:137–179, 2018.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Wasserstein Riemannian geometry of Gaussian densities.Information Geometry, 1:137–179, 2018

Reference 23

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Observation 67fea233-603c-43d7-bc72-009ccd0124b9 · outbound

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On the Wasserstein Geodesic Principal Component Analysis of probability measures A convexity principle for interacting gases

Reference 24

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Observation 4a0f2fe0-9329-4c62-b7e9-4298812c7ecf · outbound

This paper cites Geomstats: A Python package for Riemannian geometry in machine learning.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Geomstats: A Python package for Riemannian geometry in machine learning

Reference 25

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This paper cites Geometry of matrix decompositions seen through optimal transport and information geometry.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Geometry of matrix decompositions seen through optimal transport and information geometry

Reference 26

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This paper cites Mémoire sur la théorie des déblais et des remblais.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Mémoire sur la théorie des déblais et des remblais

Reference 27

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This paper cites The geometry of dissipative evolution equations: the porous medium equation.

On the Wasserstein Geodesic Principal Component Analysis of probability measures The geometry of dissipative evolution equations: the porous medium equation

Reference 28

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Unresolved cited work

Reference 29

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Ramsay and Bernard W

Reference 30

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Landscape pictures dataset

Reference 31

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Observation cc1ba8cd-f98b-4047-b85f-7e71f51f8e79 · outbound

This paper cites On inequalities for moments and the covariance of monotone functions.

On the Wasserstein Geodesic Principal Component Analysis of probability measures On inequalities for moments and the covariance of monotone functions

Reference 32

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Observation 139e6471-c572-43b3-acbd-aacaf91de3b3 · outbound

This paper cites Principal geodesic analysis for probability measures under the optimal transport metric.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Principal geodesic analysis for probability measures under the optimal transport metric

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:40.695280Z

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Observation d18b0c9f-ad51-4fab-8059-c3b2b0151be7 · outbound

This paper cites Optimization over Geodesics for Exact Principal Geodesic Analysis.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Optimization over Geodesics for Exact Principal Geodesic Analysis

Reference 34

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This paper cites Optimization over geodesics for exact principal geodesic analysis.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Optimization over geodesics for exact principal geodesic analysis

Reference 35

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This paper cites Wasserstein geometry of Gaussian measures.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Wasserstein geometry of Gaussian measures

Reference 36

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This paper cites Riemannian and stratified geometries on covariance and correlation matrices.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Riemannian and stratified geometries on covariance and correlation matrices

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:40.275533Z

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This paper cites Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:40.167810Z

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Observation f285e365-56b5-4b28-9071-f0ebe356d587 · outbound

This paper cites A linear optimal transportation framework for quantifying and visualizing variations in sets of images.

On the Wasserstein Geodesic Principal Component Analysis of probability measures A linear optimal transportation framework for quantifying and visualizing variations in sets of images

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:47:39.982997Z

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Observation 08b46323-6334-4805-9151-28cba27c52d6 · outbound

This paper cites 3d shapenets: A deep representation for volumetric shapes, 2015.

On the Wasserstein Geodesic Principal Component Analysis of probability measures 3d shapenets: A deep representation for volumetric shapes, 2015

Reference 40

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Observation 19e4cd56-e71e-4693-8bb1-3ecb0225a351 · outbound

This paper cites Inexact Riemannian Gradient Descent Method for Nonconvex Optimization.

On the Wasserstein Geodesic Principal Component Analysis of probability measures Inexact Riemannian Gradient Descent Method for Nonconvex Optimization

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:47:38.696983Z

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Unresolved cited work

Reference 42

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Unresolved cited work

Reference 43

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On the Wasserstein Geodesic Principal Component Analysis of probability measures Unresolved cited work

Reference 44

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Pith citing papers

Observation dcf91036-3ea9-4967-a3e6-42bed5da11ea · inbound

PCA of probability measures: Sparse and Dense sampling regimes cites this paper.

PCA of probability measures: Sparse and Dense sampling regimes On the Wasserstein Geodesic Principal Component Analysis of probability measures

Reference 32

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Shape-constrained density estimation with Wasserstein projection cites this paper.

Shape-constrained density estimation with Wasserstein projection On the Wasserstein Geodesic Principal Component Analysis of probability measures

Reference 38

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Source-reported events for the cited work

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