Paper Citation Record · LEDGER

Accelerating Spectral Clustering under Fairness Constraints

As of 8 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2506.08143.

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

pith.paper-citation-record.v1
2506.08143 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:24:58.775022Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

15 of 15 outbound references displayed

verified exact1
verified fuzzy10
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2d45e53f-2b79-4d41-a37a-20723341ec0f · outbound

This paper cites The results show that our algorithm outperforms the compared ones in terms of computational time for all tested sample sizes and cluster sizes.

Accelerating Spectral Clustering under Fairness Constraints The results show that our algorithm outperforms the compared ones in terms of computational time for all tested sample sizes and cluster sizes

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.954938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e1e3fbf3-c46a-450d-9ad4-28124bdc5627 · outbound

This paper cites an unresolved cited work.

Accelerating Spectral Clustering under Fairness Constraints Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:24:58.967791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 573b7a8e-4342-4649-9ab8-c28ad852f5bb · outbound

This paper cites an unresolved cited work.

Accelerating Spectral Clustering under Fairness Constraints Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:24:58.901931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2e2baf97-2be5-4a70-81f2-eef82c2f207e · outbound

This paper cites However, extending the fairlet analysis, which relies on the k-median and k-center cost of the fairlet decomposition, to the spectral setting is not trivial.

Accelerating Spectral Clustering under Fairness Constraints However, extending the fairlet analysis, which relies on the k-median and k-center cost of the fairlet decomposition, to the spectral setting is not trivial

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.888875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 34b7f76a-230b-4a50-8869-ae9db936f846 · outbound

This paper cites an unresolved cited work.

Accelerating Spectral Clustering under Fairness Constraints Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:24:58.875424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9792886e-01e3-4f43-b556-ef4ec8572768 · outbound

This paper cites Since polynomial functions possess derivatives of all orders, each ψij is smooth (i.e., C ∞).

Accelerating Spectral Clustering under Fairness Constraints Since polynomial functions possess derivatives of all orders, each ψij is smooth (i.e., C ∞)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.862523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ed93f143-da00-4c01-a2b2-c88e653b2c41 · outbound

This paper cites Therefore, the only linear combination of the gradients ∇xψij(¯x)that equals zero is the trivial one, which proves thatC(¯x)is linearly independent.

Accelerating Spectral Clustering under Fairness Constraints Therefore, the only linear combination of the gradients ∇xψij(¯x)that equals zero is the trivial one, which proves thatC(¯x)is linearly independent

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.848914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eeadac17-afab-4818-832c-363d916b81cd · outbound

This paper cites Proof of Proposition 3.2 Proof.Expandingϕ(M H)to recover the expression of the augmented Lagrangian shows thatH7→ϕ(M H)is convex as long asα <1.

Accelerating Spectral Clustering under Fairness Constraints Proof of Proposition 3.2 Proof.Expandingϕ(M H)to recover the expression of the augmented Lagrangian shows thatH7→ϕ(M H)is convex as long asα <1

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.835939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 536b3c8b-1a56-4770-ac1c-595cd729d1cd · outbound

This paper cites Rösner, C.

Accelerating Spectral Clustering under Fairness Constraints Rösner, C

Reference 1987

Resolution: unresolved; no resolver link, observed 2026-08-07T05:24:58.725926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb249449-3be0-427f-a68c-e322f8ec3938 · outbound

This paper cites P., Schwarting, W., Bhatia, S.

Accelerating Spectral Clustering under Fairness Constraints P., Schwarting, W., Bhatia, S

Reference 2008

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.980183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a85c85be-42c6-4fdf-9ee4-981d3260292f · outbound

This paper cites The parameters τ and µ are set to 2 16 Accelerating Spectral Clustering under Fairness Constraints Table 10: Description of the real-world datasets used for the experiments.

Accelerating Spectral Clustering under Fairness Constraints The parameters τ and µ are set to 2 16 Accelerating Spectral Clustering under Fairness Constraints Table 10: Description of the real-world datasets used for the experiments

Reference 2011

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.927600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c71b234a-a336-4b3f-b3f4-b1d11befc547 · outbound

This paper cites The K-modes algorithm for clustering.

Accelerating Spectral Clustering under Fairness Constraints The K-modes algorithm for clustering

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:24:58.822355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e1201dc7-e217-4876-8ec1-f33f80a2235b · outbound

This paper cites Evaluating the fairness of discriminative foundation models in computer vision.

Accelerating Spectral Clustering under Fairness Constraints Evaluating the fairness of discriminative foundation models in computer vision

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.992471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7d6ce241-f88a-454b-a0e0-acfff2903467 · outbound

This paper cites Another related work is (Zhang & Wang, 2024).

Accelerating Spectral Clustering under Fairness Constraints Another related work is (Zhang & Wang, 2024)

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.914193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4a318b3f-579c-41a9-99c9-bcca5bd063bd · outbound

This paper cites These plots show that our method produces assignments comparable to exact algorithms (o-FSC,s-FSC).

Accelerating Spectral Clustering under Fairness Constraints These plots show that our method produces assignments comparable to exact algorithms (o-FSC,s-FSC)

Reference 7500

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:24:58.941541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.