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Paper Citation Record · LEDGER

Number of Clusters in a Dataset: A Regularized K-means Approach

As of 17 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2505.22991.

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

pith.paper-citation-record.v1
2505.22991 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:04:49.908419Z

measured 40 of 40 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

40 of 40 outbound references displayed

  • verified exact3
  • verified fuzzy25
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ac6cb70e-07b4-4a01-a5a7-51435822af86 · outbound

This paper cites Ahmadian, A.

Number of Clusters in a Dataset: A Regularized K-means Approach Ahmadian, A

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:57.040194Z

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 2331970d-6861-49fb-97c6-b0a3ac560784 · outbound

This paper cites Recovering the number of clusters in data sets with noise features using feature rescaling factors.

Number of Clusters in a Dataset: A Regularized K-means Approach Recovering the number of clusters in data sets with noise features using feature rescaling factors

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.537027Z

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=2026-08-07T13:04:46.354500Z digest=sha256:221dbe69beac3df76d25e4d7f11b83261f4ec6bbe89d33e7ea90383ce94d5225

Observation 4ae7a1a0-ef0e-4e28-b508-9e4e1f1cb31f · outbound

This paper cites Anderson.

Number of Clusters in a Dataset: A Regularized K-means Approach Anderson

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.780620Z

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 b85bde29-6036-4d23-9822-f94ac7dc2dde · outbound

This paper cites Arthur and S.

Number of Clusters in a Dataset: A Regularized K-means Approach Arthur and S

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.578366Z

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=2026-08-07T13:04:46.524886Z digest=sha256:8dc051a1e2f6af4758c8c795899ff7b17e9ddd1ce335528ea42d17af53468988

Observation 8676e443-3973-4c40-af0a-e71be77c6ddf · outbound

This paper cites Bachem, M.

Number of Clusters in a Dataset: A Regularized K-means Approach Bachem, M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.383246Z

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 e37c3b49-59a6-45d3-8b3e-1938a4defbf9 · outbound

This paper cites Recombinator-k-means: An evolutionary algorithm that exploits k-means++ for recombination.

Number of Clusters in a Dataset: A Regularized K-means Approach Recombinator-k-means: An evolutionary algorithm that exploits k-means++ for recombination

Reference 6

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.343281Z

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 b781a6e6-24c5-48a8-960a-618d178b1afe · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:56.204151Z

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 9c8cccc1-6ac7-4b9a-9ae1-1ceb6f6cafaf · outbound

This paper cites Bozdogan.

Number of Clusters in a Dataset: A Regularized K-means Approach Bozdogan

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.045127Z

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=2026-08-07T13:04:46.850708Z digest=sha256:0942d4e874dea3ab7cb630b1ebb044a8e292da87812b1cb60abf52b4c66c37e0

Observation e2d0a4eb-d8b1-422c-81cc-94935036b515 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.909023Z

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=2026-08-07T13:04:46.950897Z digest=sha256:7146e2d9aab987cecd21de7ee0b9cba0c585f13227f843830fe798219e4627c0

Observation 37ebfc11-1248-415d-89a3-416630563a27 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.749909Z

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 8e14bf0f-b22b-4d4b-bf02-e4fe8be5a365 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.610450Z

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=2026-08-07T13:04:47.080718Z digest=sha256:ff2c8f3363a5f2e420db870702bf12ae1aa899d20dff40bfbdc4241a02d0714f

Observation 89e101c3-810e-4604-a668-773cb0faf63c · outbound

This paper cites Frank and A.

Number of Clusters in a Dataset: A Regularized K-means Approach Frank and A

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.449685Z

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=2026-08-07T13:04:47.176034Z digest=sha256:3ec2724ebde676e93fbd7691e6ab7120aa50603e287e58b6dcfeb9a57f24ad8c

Observation f51c542e-fa1a-43d9-abb3-c6bc5dbf752a · outbound

This paper cites Franti and S.

Number of Clusters in a Dataset: A Regularized K-means Approach Franti and S

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.341184Z

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=2026-08-07T13:04:47.306298Z digest=sha256:e038158780267613c53f819532ba898fd744649f54f45d27688c47f0c4ad40ca

Observation af31801a-022b-4e70-95b4-2ada1605414e · outbound

This paper cites Estimating the number of clusters using cross-validation.

Number of Clusters in a Dataset: A Regularized K-means Approach Estimating the number of clusters using cross-validation

Reference 14

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.166207Z

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=2026-08-07T13:04:47.375125Z digest=sha256:e39e65d0157a126dd66b9d703fbb98a4b61c278d84551bc8dabfe477f5a2ea57

Observation 7781a075-326e-4b6f-9b1e-0eba3f421b2d · outbound

This paper cites Fujita, D.Y.

Number of Clusters in a Dataset: A Regularized K-means Approach Fujita, D.Y

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.201123Z

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=2026-08-07T13:04:47.447948Z digest=sha256:ed5ebb709aee96710f05f2f3df0a8d057a40d87ab23ac3c1874ad7d20b4437e7

Observation 54f94ea9-1b68-4183-af6f-5ab531ac2a38 · outbound

This paper cites Gersho and R.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Gersho and R.M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.916750Z

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 83c4920e-0a62-4bf2-89a3-cbd58bb09ffd · outbound

This paper cites Gradshteyn and I.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Gradshteyn and I.M

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.623552Z

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=2026-08-07T13:04:47.629266Z digest=sha256:11847047a5cebbc360821bc35d6bc205a689bc45f5cb1479d9b4462b69d460b7

Observation bb90cbb5-6ec5-43a9-9bdd-9b0b85cbef69 · outbound

This paper cites Jain and R.C.

Number of Clusters in a Dataset: A Regularized K-means Approach Jain and R.C

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.397606Z

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 6dc91853-8d6a-403c-9640-caa4e1be9fb4 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:54.253593Z

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=2026-08-07T13:04:47.823525Z digest=sha256:1cf797b35be91ab6609a44179e2bd98a7068c0e49e962d715642e7b4209dcb4f

Observation b67a5435-0600-45cc-918a-1f3a2ed54411 · outbound

This paper cites Kamgar-Parsi, J.A.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi, J.A

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.081866Z

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 976491ad-9bb2-4c9c-ba14-438e6597f885 · outbound

This paper cites Kamgar-Parsi and B.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.939115Z

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 390b87ee-6de7-4a71-acc1-d84f43c7e40b · outbound

This paper cites Kamgar-Parsi and B.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi and B

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.774354Z

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 9c929101-eacb-42a2-ad4f-48097213f8e1 · outbound

This paper cites Kanungo, D.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Kanungo, D.M

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.594233Z

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 1c74d2cb-b5d3-4836-839a-40d059e3b552 · outbound

This paper cites Krzanowski and Y .T.

Number of Clusters in a Dataset: A Regularized K-means Approach Krzanowski and Y .T

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.446122Z

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=2026-08-07T13:04:48.336835Z digest=sha256:80a45108dc6408744c3b1a7ce2d5edf504ae8e8ce38819b2c1624b14524c3a02

Observation 41a943df-8e10-4e75-b813-3cb92d5e3689 · outbound

This paper cites Kulis and M.I.

Number of Clusters in a Dataset: A Regularized K-means Approach Kulis and M.I

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.279488Z

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=2026-08-07T13:04:48.426491Z digest=sha256:82eac2af99d71f464a1596fb2ff8ed3dd8ff8ea251055ac680d0a79bcb12dc87

Observation 904b4134-c232-4cf7-980a-fbd3f394cf57 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:53.135386Z

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 16ea8d4a-8334-4245-8ab2-e26b9d0fbcd5 · outbound

This paper cites Linde, A.

Number of Clusters in a Dataset: A Regularized K-means Approach Linde, A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.982499Z

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 bf11d1d8-6875-4ab8-900f-e17e4ce6c713 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.808925Z

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 f978c8cc-16d5-4788-ae8a-39530d4d149a · outbound

This paper cites Manning, P.

Number of Clusters in a Dataset: A Regularized K-means Approach Manning, P

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.609981Z

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 c55e8309-7a0f-40ff-9808-95bb437d26fd · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.398137Z

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 d1673e53-8254-4e59-bb55-2a5ba42ef029 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.199872Z

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=2026-08-07T13:04:48.996040Z digest=sha256:b62dbfcc8c60735d4fd483b7b6e09477318ed0e4dfc72dd065515b2ef0b2c521

Observation b8ad7e33-ac5d-4ff3-831d-cc6efc3dfd3f · outbound

This paper cites Rousseeuw.

Number of Clusters in a Dataset: A Regularized K-means Approach Rousseeuw

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.062568Z

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=2026-08-07T13:04:49.110768Z digest=sha256:a3f09c9ca597d8505d912f759044987a4e29ddffa88ee315cf857126fcd2fdc1

Observation 4258a392-3b4e-416f-812c-aa496985d357 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:51.877418Z

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=2026-08-07T13:04:49.174032Z digest=sha256:bfc3ca474d7a6d55ca4008cda41a00f86d3388de4567a2eee6ab6bfc8aea8ade

Observation 123cae2c-1753-465b-8cf7-ee960fd47608 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:51.704890Z

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=2026-08-07T13:04:49.280298Z digest=sha256:a448b98e85529066692dd6ff11d6cc2de0c8b325a8be9484efdf670466e43711

Observation acb9d018-5573-443d-b527-62dcc1a8a65c · outbound

This paper cites Sugar and G.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Sugar and G.M

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.529523Z

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=2026-08-07T13:04:49.395973Z digest=sha256:e98ad4c1393b7d906e0b42d350c75b2dad803504f00e7217454f7c1c5cc1834b

Observation 81bad8a1-c601-4d40-9f8f-b1cb21f1407b · outbound

This paper cites Szczypi´nski, M.

Number of Clusters in a Dataset: A Regularized K-means Approach Szczypi´nski, M

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.380172Z

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=2026-08-07T13:04:49.475300Z digest=sha256:a1558d1771847b39989bb9d137498d1016479bd447fe41e36c0e6090b1f54a6d

Observation 3121c814-4aeb-43b3-a5f1-75d44b1d3534 · outbound

This paper cites Tibshirani, G.

Number of Clusters in a Dataset: A Regularized K-means Approach Tibshirani, G

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.179870Z

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=2026-08-07T13:04:49.585977Z digest=sha256:0109c768f7761ccee157095259380040b24b0c3257c8bc15d5bca0c1f2ba233e

Observation e83ff1ef-e072-49e8-8893-5ab57b22eb48 · outbound

This paper cites Vidal, Y.

Number of Clusters in a Dataset: A Regularized K-means Approach Vidal, Y

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.016328Z

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=2026-08-07T13:04:49.667631Z digest=sha256:0070cfe88995c99e5d181cafd26113fa1102700d0889608e23f0681c2b118435

Observation 2516949b-7000-449e-a9d0-06848c811e98 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:50.881453Z

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=2026-08-07T13:04:49.758918Z digest=sha256:d6d374a8455f9a35439852cd88dc2bb8520deed4bddec069ab980f3401c6f76e

Observation 99b44445-a15a-49a1-afd5-3a46ca1bcb53 · outbound

This paper cites (A-4) With repeated use of (A-3), Eq.

Number of Clusters in a Dataset: A Regularized K-means Approach (A-4) With repeated use of (A-3), Eq

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:50.708599Z

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=2026-08-07T13:04:49.908419Z digest=sha256:2a852c1821142372ba1d508b02df23ebdbb577d08a35a756fba77b8779bb478b

Pith citing papers

No inbound Pith citation observations are available.