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Paper Citation Record · LEDGER

A Flag Decomposition for Hierarchical Datasets

As of 16 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2502.07782.

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

pith.paper-citation-record.v1
2502.07782 v2

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T11:42:21.421924Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

67 of 67 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9820bcd3-48d8-49ad-8964-7bb17fc24f5d · outbound

This paper cites Gen- eralized Weiszfeld algorithms for lq optimization.IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(4):728–745, 2014.

A Flag Decomposition for Hierarchical Datasets Gen- eralized Weiszfeld algorithms for lq optimization.IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(4):728–745, 2014

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a6265aa2-d834-43cb-9a53-0bd86412d43b · outbound

This paper cites Bandos, Lorenzo Bruzzone, and Gustavo Camps- Valls.

A Flag Decomposition for Hierarchical Datasets Bandos, Lorenzo Bruzzone, and Gustavo Camps- Valls

Reference 2

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raw_fallback, observed 2026-08-08T11:42:22.359557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4f0b8121-5a6d-4989-ba84-841ad032e5bc · outbound

This paper cites Block modified Gram–Schmidt algorithms and their analysis.SIAM Journal on Matrix Analysis and Applications, 40(4):1257–1290, 2019.

A Flag Decomposition for Hierarchical Datasets Block modified Gram–Schmidt algorithms and their analysis.SIAM Journal on Matrix Analysis and Applications, 40(4):1257–1290, 2019

Reference 3

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 3ee5daa4-71cd-4f08-8b3f-26118c41bd80 · outbound

This paper cites Weiszfeld’s method: Old and new results.Journal of Optimization Theory and Appli- cations, 164:1–40, 2015.

A Flag Decomposition for Hierarchical Datasets Weiszfeld’s method: Old and new results.Journal of Optimization Theory and Appli- cations, 164:1–40, 2015

Reference 4

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raw_fallback, observed 2026-08-08T11:42:22.333206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.150853Z digest=sha256:55ff88f204128f74c41fa9a8f6abcfd2f1c84f4ff61fa27f92854a49b8797b90

Observation 6876ffd7-c7af-48c4-8e58-ff21d1ce78df · outbound

This paper cites Belhumeur, Joao P Hespanha, and David J.

A Flag Decomposition for Hierarchical Datasets Belhumeur, Joao P Hespanha, and David J

Reference 5

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.319827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.155512Z digest=sha256:346476f2462142e22f46c3b8de9d2e3659d42729e66563c5a8b2afd63aa42b23

Observation c15b1a85-09ff-4396-88e8-bc62b26edef3 · outbound

This paper cites Numerical methods for computing angles between linear subspaces.Mathematics of computation, 27(123):579–594, 1973.

A Flag Decomposition for Hierarchical Datasets Numerical methods for computing angles between linear subspaces.Mathematics of computation, 27(123):579–594, 1973

Reference 6

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raw_fallback, observed 2026-08-08T11:42:22.305505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.159967Z digest=sha256:7d94e7dadb715a454fc3d705e0bd27d3b391c589958db9209eca28f166e710b5

Observation 89c4cb3b-34b2-41fa-a1c8-bd9d2dd1b151 · outbound

This paper cites Introduction to hierarchical matrices with applications.En- gineering analysis with boundary elements, 27(5):405–422,.

A Flag Decomposition for Hierarchical Datasets Introduction to hierarchical matrices with applications.En- gineering analysis with boundary elements, 27(5):405–422,

Reference 7

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.291921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.164885Z digest=sha256:9e3a742e934640ca2b7b7aae3af4c4d37976cce69f40b375c77c30032079dc4b

Observation 3f0d0dfe-ab29-4edd-b5cc-079459b3fcea · outbound

This paper cites Manopt, a Matlab toolbox for optimization on manifolds.JMLR, 15(1):1455–1459, 2014.

A Flag Decomposition for Hierarchical Datasets Manopt, a Matlab toolbox for optimization on manifolds.JMLR, 15(1):1455–1459, 2014

Reference 8

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.277818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4d97c0a9-1c6d-445a-8b88-d4e5773f28af · outbound

This paper cites Shape spaces of nonlinear flags.

A Flag Decomposition for Hierarchical Datasets Shape spaces of nonlinear flags

Reference 9

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raw_fallback, observed 2026-08-08T11:42:22.264489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 3a3cb21c-b88a-4ef9-ade2-495cac6ed5a5 · outbound

This paper cites SIAM, 1997.

A Flag Decomposition for Hierarchical Datasets SIAM, 1997

Reference 10

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation fd8878c7-8e81-4686-92f4-c239d2aae6dd · outbound

This paper cites A flag representation for finite collec- tions of subspaces of mixed dimensions.Linear Algebra and its Applications, 451:15–32, 2014.

A Flag Decomposition for Hierarchical Datasets A flag representation for finite collec- tions of subspaces of mixed dimensions.Linear Algebra and its Applications, 451:15–32, 2014

Reference 11

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raw_fallback, observed 2026-08-08T11:42:22.237561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation d8238c0a-e0cc-43d2-9d1e-fe2ed96e59dc · outbound

This paper cites The ge- ometry of algorithms with orthogonality constraints.SIAM Journal on Matrix Analysis and Applications, 20(2):303– 353, 1998.

A Flag Decomposition for Hierarchical Datasets The ge- ometry of algorithms with orthogonality constraints.SIAM Journal on Matrix Analysis and Applications, 20(2):303– 353, 1998

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.185961Z digest=sha256:d93efadaa03b43cd95da0c4966d471448814150c669a5228dfdd3a36a6e1732d

Observation cd533446-a464-446d-bc03-235e9bbecaf1 · outbound

This paper cites A review on the selection criteria for the truncated SVD in Data Science applications.Journal of Computational Mathematics and Data Science, 5, 2022.

A Flag Decomposition for Hierarchical Datasets A review on the selection criteria for the truncated SVD in Data Science applications.Journal of Computational Mathematics and Data Science, 5, 2022

Reference 13

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.210570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation fe1a5f80-fb90-4a3e-b20f-d34db7257255 · outbound

This paper cites The geometric median on riemannian manifolds with application to robust atlas estimation.NeuroImage, 45(1): S143–S152, 2009.

A Flag Decomposition for Hierarchical Datasets The geometric median on riemannian manifolds with application to robust atlas estimation.NeuroImage, 45(1): S143–S152, 2009

Reference 14

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.197107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.194132Z digest=sha256:b901f59f319eb8dfa97f51c01758f40c25e1a40d16f441655ad7fce92e04932a

Observation e335ab07-cd70-44ee-a012-d7a3d215989e · outbound

This paper cites Subspace averaging and order determina- tion for source enumeration.IEEE Transactions on Signal Processing, 67(11):3028–3041, 2019.

A Flag Decomposition for Hierarchical Datasets Subspace averaging and order determina- tion for source enumeration.IEEE Transactions on Signal Processing, 67(11):3028–3041, 2019

Reference 15

Resolution
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raw_fallback, observed 2026-08-08T11:42:22.183886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 691059ca-9912-46db-9db3-f9d1e87f0cd6 · outbound

This paper cites an unresolved cited work.

A Flag Decomposition for Hierarchical Datasets Unresolved cited work

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4d6959e6-9734-429d-993f-b38882606197 · outbound

This paper cites A block Householder– based algorithm for the QR decomposition of hierarchical matrices.SIAM Journal on Matrix Analysis and Applica- tions, 45(2):847–874, 2024.

A Flag Decomposition for Hierarchical Datasets A block Householder– based algorithm for the QR decomposition of hierarchical matrices.SIAM Journal on Matrix Analysis and Applica- tions, 45(2):847–874, 2024

Reference 17

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raw_fallback, observed 2026-08-08T11:42:22.157802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.206423Z digest=sha256:7272e8d69b8b5f63e5bf2a228d3dc8e49db5b034d734b3a8eea19b7fac5d7e18

Observation bcdab1fc-7a77-4475-a1ab-d0838ea8d270 · outbound

This paper cites an unresolved cited work.

A Flag Decomposition for Hierarchical Datasets Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-08T11:42:22.144249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.210421Z digest=sha256:424763f0fe280ec85b818d4e3f89237568d072759ad4f8542920f2acaa67dc24

Observation 9e8b409a-f8ac-4c50-b602-e0c53907a66b · outbound

This paper cites Stability analysis and improvement of the block Gram–Schmidt algorithm.SIAM journal on scientific and statistical computing, 12(5):1058– 1073, 1991.

A Flag Decomposition for Hierarchical Datasets Stability analysis and improvement of the block Gram–Schmidt algorithm.SIAM journal on scientific and statistical computing, 12(5):1058– 1073, 1991

Reference 19

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.131047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 565cd1a9-ce36-4417-b78b-80d68c71928e · outbound

This paper cites Learning multiple layers of features from tiny images.Technical report, 2009.

A Flag Decomposition for Hierarchical Datasets Learning multiple layers of features from tiny images.Technical report, 2009

Reference 20

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.116875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 1f514c48-8042-456b-8a57-3d3d37343e6f · outbound

This paper cites Imagenet classification with deep convolutional neural net- works.Advances in neural information processing systems, 25, 2012.

A Flag Decomposition for Hierarchical Datasets Imagenet classification with deep convolutional neural net- works.Advances in neural information processing systems, 25, 2012

Reference 21

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.103354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.222766Z digest=sha256:c3a62cbd83f2e608cc9a947a892f7a9a0ddeaa67ca31da2eea074ee6f18b0640

Observation a6426fe0-a946-4435-9642-7b04e38a1133 · outbound

This paper cites Sage, 1978.

A Flag Decomposition for Hierarchical Datasets Sage, 1978

Reference 22

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.089589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.226678Z digest=sha256:a24dc5ed38d4c982d923d4a457bafa354a2c2341cd40d349054a35043082bea4

Observation 3fe5a1f0-819c-4d21-8351-f98d1dc0bcd2 · outbound

This paper cites A scalable second order method for ill-conditioned matrix completion from few samples.

A Flag Decomposition for Hierarchical Datasets A scalable second order method for ill-conditioned matrix completion from few samples

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.075917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation e03840f7-38e9-4119-bb64-8e4ec6826683 · outbound

This paper cites Iteratively reweighted least squares for basis pursuit with global linear convergence rate.Advances in Neural In- formation Processing Systems, 34:2873–2886, 2021.

A Flag Decomposition for Hierarchical Datasets Iteratively reweighted least squares for basis pursuit with global linear convergence rate.Advances in Neural In- formation Processing Systems, 34:2873–2886, 2021

Reference 24

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raw_fallback, observed 2026-08-08T11:42:22.062234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.235025Z digest=sha256:1b69ef2f3075c3e95b79efb4920f66d06c84d3d381601f9a280468ecb2ee9d4c

Observation 0da5c211-283f-4b1d-9c82-2a7a63e342d9 · outbound

This paper cites Hierarchy, complexity, society.

A Flag Decomposition for Hierarchical Datasets Hierarchy, complexity, society

Reference 25

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.048428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.239104Z digest=sha256:75512b179ea7836187c491e993f82b3a264ffd907a67e5ff00493d67f9873cad

Observation 825636b4-f51d-4a77-80b3-5cc0e600b273 · outbound

This paper cites Hypersdfusion: Bridging hierarchical structures in language and geometry for enhanced 3d text2shape genera- tion.

A Flag Decomposition for Hierarchical Datasets Hypersdfusion: Bridging hierarchical structures in language and geometry for enhanced 3d text2shape genera- tion

Reference 26

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.034986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.243215Z digest=sha256:785a9131f26159d83108d54cf1bf583934f695c9904398f87788710d7e442c82

Observation 0405fe7a-5068-4e9a-b574-0619b8f2e6d6 · outbound

This paper cites Fast, robust and non-convex subspace recovery.Information and Inference: A Journal of the IMA, 7(2):277–336, 2018.

A Flag Decomposition for Hierarchical Datasets Fast, robust and non-convex subspace recovery.Information and Inference: A Journal of the IMA, 7(2):277–336, 2018

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.021258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.247548Z digest=sha256:97b9b2443eb978be635075dbaf97a38679e577b7a372047e4513039d5027fc5d

Observation 214c33f3-17da-461a-94cb-f9cebb462bdb · outbound

This paper cites An overview of robust sub- space recovery.Proceedings of the IEEE, 106(8), 2018.

A Flag Decomposition for Hierarchical Datasets An overview of robust sub- space recovery.Proceedings of the IEEE, 106(8), 2018

Reference 28

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:22.007444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.251760Z digest=sha256:5022e8aa271102f4d1f9c412136163953de4882efdc0dd04bf2081f72df497b4

Observation ca698e2e-0d22-42ae-b327-200bc867dc61 · outbound

This paper cites Robust computation of linear models by convex re- laxation.Foundations of Computational Mathematics, 15: 363–410, 2015.

A Flag Decomposition for Hierarchical Datasets Robust computation of linear models by convex re- laxation.Foundations of Computational Mathematics, 15: 363–410, 2015

Reference 29

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verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.993713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.256167Z digest=sha256:2441f4d7f0cb4d65f0f6eb65c8c630563aa07b90d337615a5d88efa39b53c234

Observation 47511b9c-1a0b-498d-a08e-97e5e60cc1a3 · outbound

This paper cites Robust recovery of subspace structures by low-rank representation.IEEE transactions on pattern anal- ysis and machine intelligence, 35(1):171–184, 2012.

A Flag Decomposition for Hierarchical Datasets Robust recovery of subspace structures by low-rank representation.IEEE transactions on pattern anal- ysis and machine intelligence, 35(1):171–184, 2012

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.980184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.260184Z digest=sha256:5a46d1193505f46a65e790df1a9e226a2cc42ffa08aaf90e4cd2025748e3eac8

Observation c4a0333d-c6a9-47b1-9b14-48e2d4dca4b5 · outbound

This paper cites Mouton, 1966.

A Flag Decomposition for Hierarchical Datasets Mouton, 1966

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.966834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.264196Z digest=sha256:a707c9ffa726aaad500410bcb3f0978b251c46d7bbc67277a42ca0585f1acc0a

Observation 727d0075-f6d8-439b-b976-a12af277cbac · outbound

This paper cites Self- organizing mappings on the flag manifold with applications to hyper-spectral image data analysis.Neural Computing and Applications, 34(1):39–49, 2022.

A Flag Decomposition for Hierarchical Datasets Self- organizing mappings on the flag manifold with applications to hyper-spectral image data analysis.Neural Computing and Applications, 34(1):39–49, 2022

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.953493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.268388Z digest=sha256:8421fd8b1cc1fb1ebe97afaf15276c6468433bee354cfba6cb08f9d1b6c232df

Observation be35b7d5-9d8f-4ed9-b593-3b4374da9272 · outbound

This paper cites Chordal averaging on flag manifolds and its applications.

A Flag Decomposition for Hierarchical Datasets Chordal averaging on flag manifolds and its applications

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.939683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.272410Z digest=sha256:fa60bc7f905a4d6017cebe80320ea55321ee5fbf6e77c7cdb58605328befaff3

Observation b09dfbf0-f369-4239-b647-c93f15203e02 · outbound

This paper cites The flag median and FlagIRLS.

A Flag Decomposition for Hierarchical Datasets The flag median and FlagIRLS

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.926257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.276383Z digest=sha256:5505b6f1e323ddd1041567e369fc27990830070bcb98d911e139d83a3fb645e6

Observation 6a6c0194-3888-4bac-abef-9c286e9f017b · outbound

This paper cites Module representatives for refining gene co-expression modules.Physical Biology, 20 (4):045001, 2023.

A Flag Decomposition for Hierarchical Datasets Module representatives for refining gene co-expression modules.Physical Biology, 20 (4):045001, 2023

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.912880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.280372Z digest=sha256:4488e14170307f2b6ba36e843b66b7613fa64489d88071553be9c5a7b285b622

Observation 04d3f657-3c8e-4f8a-b015-e6837767d3af · outbound

This paper cites Fun with Flags: Robust principal directions via flag mani- folds.

A Flag Decomposition for Hierarchical Datasets Fun with Flags: Robust principal directions via flag mani- folds

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.899211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.284474Z digest=sha256:a79c4d5a3d54026432d258ace71426c09e9957b2be9b1eb62f67369292ab0678

Observation 9fc990c9-064e-481b-9605-8d3a37a2b029 · outbound

This paper cites PhD thesis, Colorado State University, 2023.

A Flag Decomposition for Hierarchical Datasets PhD thesis, Colorado State University, 2023

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.885186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.288642Z digest=sha256:87653d851208ca864e8f8a5e3fa1fedf34f21d016b95cf786b14d5ca3426cfd8

Observation 1e5dbbc0-e4e7-4a58-af84-4ff0b137323c · outbound

This paper cites Finding the subspace mean or median to fit your need.

A Flag Decomposition for Hierarchical Datasets Finding the subspace mean or median to fit your need

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.871230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.292802Z digest=sha256:7e4d482ee4603edfe288f12985211f184aa22175bdfc0e24a112dbb022faf16d

Observation b578f5f7-b25b-48d0-bc75-5b2bb5aed988 · outbound

This paper cites On a minimum enclosing ball of a collection of linear subspaces.Linear Algebra and its Applications, 625:248–278, 2021.

A Flag Decomposition for Hierarchical Datasets On a minimum enclosing ball of a collection of linear subspaces.Linear Algebra and its Applications, 625:248–278, 2021

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.857658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.297065Z digest=sha256:88a4fbec4f730e875fbb6e68c74f109934222f618329ef15215bacbbdbabc9e2

Observation fe948f21-21d9-4fac-8073-e5ab2c1bd6f1 · outbound

This paper cites Automated flower classification over a large number of classes.

A Flag Decomposition for Hierarchical Datasets Automated flower classification over a large number of classes

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.844089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.301273Z digest=sha256:c183b855c9ea70c7f111ac0f82acaceaefb2e83c0297976340317f18f51dda7a

Observation f47b0c28-5b9d-4426-9091-813277671eda · outbound

This paper cites Riemannian optimization method on generalized flag mani- folds for complex and subspace ICA.

A Flag Decomposition for Hierarchical Datasets Riemannian optimization method on generalized flag mani- folds for complex and subspace ICA

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.830507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.305613Z digest=sha256:bcd3729ebab20d364c42bc2fa410ac1ae0ec48d26392ca0e262c9dc5c54c5656

Observation e9e239b0-a48a-4584-b72c-a839394237b2 · outbound

This paper cites Riemannian optimization method on generalized flag man- ifolds for complex and subspace ICA.

A Flag Decomposition for Hierarchical Datasets Riemannian optimization method on generalized flag man- ifolds for complex and subspace ICA

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.817105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.309772Z digest=sha256:f0f598ef3ee773868712d0efc5a67cee194cf114dc328cee7f988965eaad520e

Observation 6d6fe2d4-c99b-46a1-aa9f-8d4076f290ef · outbound

This paper cites Riemannian optimization method on the flag manifold for independent subspace analysis.

A Flag Decomposition for Hierarchical Datasets Riemannian optimization method on the flag manifold for independent subspace analysis

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.803379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.313783Z digest=sha256:d6f2a7fb3a2dad6478b4b24e3241891b9bb204ab55b9897367ee1cce2fe92044

Observation 1e9e57a7-ada8-4e94-b7b6-187ed4bf2dea · outbound

This paper cites Flag manifolds for subspace ICA prob- lems.

A Flag Decomposition for Hierarchical Datasets Flag manifolds for subspace ICA prob- lems

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.789451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.318256Z digest=sha256:fa51f47b574bef2639786ba351aab4686da8b16aa5a5f41e147786816a4afc71

Observation 259f9d89-2fec-464b-911a-1a9412523ceb · outbound

This paper cites Natural conjugate gradient on complex flag manifolds for complex independent subspace analysis.

A Flag Decomposition for Hierarchical Datasets Natural conjugate gradient on complex flag manifolds for complex independent subspace analysis

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.776039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.322116Z digest=sha256:a8e3a00a55d9c8c7ac9c72383b9ea690904b062cbd97ac28d8dbc82304212c94

Observation b9b42840-b930-458e-819e-d5227a131995 · outbound

This paper cites Beyond low rank+ sparse: Multiscale low rank matrix decomposition.IEEE journal of selected topics in signal processing, 10(4), 2016.

A Flag Decomposition for Hierarchical Datasets Beyond low rank+ sparse: Multiscale low rank matrix decomposition.IEEE journal of selected topics in signal processing, 10(4), 2016

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.760988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.326204Z digest=sha256:532ec96f25439585a877087b052ba7ced99a8e42ca4a65833e43500559ab7a55

Observation cd3077b8-753e-4197-956e-cc829acfce77 · outbound

This paper cites Barycentric subspace analysis on manifolds.

A Flag Decomposition for Hierarchical Datasets Barycentric subspace analysis on manifolds

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.747188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.330351Z digest=sha256:7c2ba6f2a1f4aa383a7e2b2efe34bf2cba95b42671fe74d942db62e65c6306bc

Observation ee350675-9e19-45eb-916a-7bdd1a5df7e6 · outbound

This paper cites Flag orbit codes and their expansion to Stiefel codes.

A Flag Decomposition for Hierarchical Datasets Flag orbit codes and their expansion to Stiefel codes

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.733322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.334379Z digest=sha256:46a9b380dd18107974e9db770cb61d1eaff7ef5a85f29e0b3059240728b4a1f2

Observation 1e166e07-991d-4af0-b86d-757db5d5e052 · outbound

This paper cites Columbia University Press, 1985.

A Flag Decomposition for Hierarchical Datasets Columbia University Press, 1985

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.719288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.338539Z digest=sha256:b4620ba1e132b2d8d85a9678605c96f720fb8a976db1efb669ad2b16090dda95

Observation e20284c5-de9c-43f4-bfea-954801fa5633 · outbound

This paper cites Adaptive subspaces for few-shot learn- ing.

A Flag Decomposition for Hierarchical Datasets Adaptive subspaces for few-shot learn- ing

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.705444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.342705Z digest=sha256:7738794720f3526c5009f5e8aea5f2d0bc7c5988d02f9ace30d57d7f97053447

Observation 054f06fd-7937-499a-892b-f9ecc030b075 · outbound

This paper cites Prototypical networks for few-shot learning.Advances in neural informa- tion processing systems, 30, 2017.

A Flag Decomposition for Hierarchical Datasets Prototypical networks for few-shot learning.Advances in neural informa- tion processing systems, 30, 2017

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.691170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.347067Z digest=sha256:af98a95a84a59c41234a5344866d8b1d405f7a6c0ad4fa93c2fb089ae8a7f4d9

Observation 30342bc8-73d2-4d0f-83ff-7fcbd8265fba · outbound

This paper cites Rethinking the Rieman- nian logarithm on flag manifolds as an orthogonal alignment problem.

A Flag Decomposition for Hierarchical Datasets Rethinking the Rieman- nian logarithm on flag manifolds as an orthogonal alignment problem

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.677115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.351314Z digest=sha256:3b331b0519dba5377db32b709d3d75a6763d3410f08cdfbf118267d5028f6597

Observation af7fd7de-1e51-4352-8a97-b59da91c4459 · outbound

This paper cites The curse of isotropy: from principal components to principal subspaces, 2024.

A Flag Decomposition for Hierarchical Datasets The curse of isotropy: from principal components to principal subspaces, 2024

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.663419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.355375Z digest=sha256:55cbda6de620bc71943d92688a5bb6902967796c581b09844f96750727d21b53

Observation c0637cfb-24de-44c0-94d8-e00bae40723f · outbound

This paper cites Nested subspace learning with flags, 2025.

A Flag Decomposition for Hierarchical Datasets Nested subspace learning with flags, 2025

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.649519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.359346Z digest=sha256:b93bf46404c3f50440e8cc0b771d012aebe31f09d70914a46e513cf9695f7cd7

Observation 324e2524-ac25-450c-a4d7-8c7b3ea7f6a8 · outbound

This paper cites Representing part-whole hierarchies in foundation models by learning localizability composability and decomposability from anatomy via self supervision.

A Flag Decomposition for Hierarchical Datasets Representing part-whole hierarchies in foundation models by learning localizability composability and decomposability from anatomy via self supervision

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.634960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.363411Z digest=sha256:4f1b6a139bd13c2a18c65721ff1d74dc2e64a864b8b0bcdb328cceddad0afb02

Observation b76a961c-8abe-4723-b5e9-a85dc41cb592 · outbound

This paper cites Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation.

A Flag Decomposition for Hierarchical Datasets Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-08T11:42:21.367473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-08T11:42:21.367473Z digest=sha256:6960559b82a1a5396463736d6fb226b3114643bdf08709dbbbf4c058ed8a00c6

Observation 396da05c-112e-4587-9486-b4a862b14ca8 · outbound

This paper cites Dual principal component pursuit.Journal of Machine Learning Research, pages 1—- 50, 2018.

A Flag Decomposition for Hierarchical Datasets Dual principal component pursuit.Journal of Machine Learning Research, pages 1—- 50, 2018

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.621242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.371510Z digest=sha256:20a3ef71fc826ff13461ce6d5b56571114879bd4bc04cf7b1791a38ee58fb60c

Observation f3564188-1713-4722-8288-1165a0f01865 · outbound

This paper cites Fast, blind, and accurate: Tuning-free sparse re- gression with global linear convergence.

A Flag Decomposition for Hierarchical Datasets Fast, blind, and accurate: Tuning-free sparse re- gression with global linear convergence

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.606642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.375120Z digest=sha256:3d9a84724388a40763aa13ac0abf1e69706cc794cbc5a90b45094b0a689d2a9d

Observation b6956aac-306e-4a33-858d-f80f3f53c7f0 · outbound

This paper cites Hd- cnn: hierarchical deep convolutional neural networks for large scale visual recognition.

A Flag Decomposition for Hierarchical Datasets Hd- cnn: hierarchical deep convolutional neural networks for large scale visual recognition

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.592087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.379791Z digest=sha256:8f8f4fb4001632819a9f27d388e169d72e16fdea943e0ec646ec1d1d7ef3590d

Observation 79ba8b24-b2e0-43c7-add1-0080a40ab274 · outbound

This paper cites Optimiza- tion on flag manifolds.Mathematical Programming, 194(1): 621–660, 2022.

A Flag Decomposition for Hierarchical Datasets Optimiza- tion on flag manifolds.Mathematical Programming, 194(1): 621–660, 2022

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.577568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.383503Z digest=sha256:898c6e5110a9d7232d72b1445966c43be46423b0676bdc268d3d4f910393c1b6

Observation 450706b0-ffd7-47b7-a41b-5129a7ee407f · outbound

This paper cites A novel m-estimator for ro- bust PCA.The Journal of Machine Learning Research, 15 (1):749–808, 2014.

A Flag Decomposition for Hierarchical Datasets A novel m-estimator for ro- bust PCA.The Journal of Machine Learning Research, 15 (1):749–808, 2014

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.563211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.390478Z digest=sha256:5647bf46f82a4ff2fbbbeff15980309571edb4b6bcdc319e950a649a432f8587

Observation 4fd345eb-b8cb-4dfa-8513-2a85bd07fbcd · outbound

This paper cites By way of contradiction, assumeC j =0.

A Flag Decomposition for Hierarchical Datasets By way of contradiction, assumeC j =0

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.548571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.400685Z digest=sha256:40f423e95643210124cc0ea1972e6d54301fe7260cd5f548a411a2682c9125ca

Observation 53dc41b5-5c8f-4681-9f7a-dacfedc79ae2 · outbound

This paper cites It suffices to show Q⊤ j Q:j−1 = [Q⊤ j Q1|Q⊤ j Q2| · · · |Q⊤ j Qj−1] =0(23) which is equivalent to showing[Q j]is orthogonal to [Q1,Q 2,.

A Flag Decomposition for Hierarchical Datasets It suffices to show Q⊤ j Q:j−1 = [Q⊤ j Q1|Q⊤ j Q2| · · · |Q⊤ j Qj−1] =0(23) which is equivalent to showing[Q j]is orthogonal to [Q1,Q 2,

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.532466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.404977Z digest=sha256:f8653503c66a0aeb94ccc95c6cabc466b35581e1b94cd5cce4b609801626458e

Observation bb158827-1a3e-4858-b68b-b2fcc808f334 · outbound

This paper cites an unresolved cited work.

A Flag Decomposition for Hierarchical Datasets Unresolved cited work

Reference 64

Resolution
unresolved
raw_fallback, observed 2026-08-08T11:42:21.516786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.409833Z digest=sha256:a6ed99e8b88b10652cb48c24d2ee831e360bce5d74f5d0f552661b11ab370fc7

Observation 0e4281af-fb86-48c2-89a8-4f786cc8c9fb · outbound

This paper cites Using Eq.

A Flag Decomposition for Hierarchical Datasets Using Eq

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.503113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.414051Z digest=sha256:8a037db17bd27343a4dad810947aa8ebf9279ab62c0fc0d92b95bd42a97cdd46

Observation 08c8266a-4efe-42eb-868e-c388550b99a6 · outbound

This paper cites By the induction hypothesis (5),Q i ∈ St(mi, n)fori= 1,2,.

A Flag Decomposition for Hierarchical Datasets By the induction hypothesis (5),Q i ∈ St(mi, n)fori= 1,2,

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T11:42:21.488228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.418072Z digest=sha256:0687b22b173d813c500992497dbc0bad51bc22727ae0f7299d3353a7479e62d0

Observation 08876b78-3ba9-4f55-ab20-dcec33c0efe4 · outbound

This paper cites an unresolved cited work.

A Flag Decomposition for Hierarchical Datasets Unresolved cited work

Reference 67

Resolution
unresolved
raw_fallback, observed 2026-08-08T11:42:21.473960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T11:42:21.421924Z digest=sha256:5e999774ac54c9a376857b5daa96cb5bb11f6892233f66419784cc7d2c0986b9

Pith citing papers

No inbound Pith citation observations are available.