Paper Citation Record · LEDGER

Modified K-means Algorithm with Local Optimality Guarantees

As of 10 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2506.06990.

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

pith.paper-citation-record.v1
2506.06990 v2

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:56:39.658764Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

51 of 51 outbound references displayed

verified exact0
verified fuzzy36
unresolved15
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a5860d0d-0040-4b3a-91eb-96b3c2b7c74f · outbound

This paper cites write newline.

Modified K-means Algorithm with Local Optimality Guarantees write newline

Reference 1

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This paper cites an unresolved cited work.

Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 2

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Observation 3f2d8f4f-0e4d-411d-a4f5-6bdc806c13b2 · outbound

This paper cites NP-hardness of Euclidean sum-of-squares clustering.

Modified K-means Algorithm with Local Optimality Guarantees NP-hardness of Euclidean sum-of-squares clustering

Reference 3

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This paper cites and Vassilvitskii, S.

Modified K-means Algorithm with Local Optimality Guarantees and Vassilvitskii, S

Reference 4

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This paper cites F., Dick, T., and White, C.

Modified K-means Algorithm with Local Optimality Guarantees F., Dick, T., and White, C

Reference 5

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Observation cbcfed33-77de-498b-9406-91d11c45b6a6 · outbound

This paper cites S., Ghosh, J., and Lafferty, J.

Modified K-means Algorithm with Local Optimality Guarantees S., Ghosh, J., and Lafferty, J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:40.344018Z

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Observation 73e2a3a4-d95d-4ea3-a6f5-e48e0f5f37bd · outbound

This paper cites Toward Live Drum Separation Using Probabilistic Spectral Clustering Based on the Itakura-Saito Divergence.

Modified K-means Algorithm with Local Optimality Guarantees Toward Live Drum Separation Using Probabilistic Spectral Clustering Based on the Itakura-Saito Divergence

Reference 7

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This paper cites H., Bolte, J., and Teboulle, M.

Modified K-means Algorithm with Local Optimality Guarantees H., Bolte, J., and Teboulle, M

Reference 8

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This paper cites S., Sherali, H.

Modified K-means Algorithm with Local Optimality Guarantees S., Sherali, H

Reference 9

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 10

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Observation 4fb9551e-b195-4f9f-916d-4bfcbdc8cf65 · outbound

This paper cites On Clustering Time Series Using Euclidean Distance and Pearson Correlation.

Modified K-means Algorithm with Local Optimality Guarantees On Clustering Time Series Using Euclidean Distance and Pearson Correlation

Reference 11

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Source-reported events for the cited work

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Observation d2a6b1e2-2ee1-49b3-a88d-8a6fa3b4db4a · outbound

This paper cites Application of learning analytics using clustering data Mining for Students’ disposition analysis.

Modified K-means Algorithm with Local Optimality Guarantees Application of learning analytics using clustering data Mining for Students’ disposition analysis

Reference 12

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 13

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Observation 8d759a10-4e22-40c3-80f6-6416427328fa · outbound

This paper cites O., Chiang, M.

Modified K-means Algorithm with Local Optimality Guarantees O., Chiang, M

Reference 14

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 15

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Observation bbb81200-e578-4df1-9912-35096984474a · outbound

This paper cites and Gionis, A.

Modified K-means Algorithm with Local Optimality Guarantees and Gionis, A

Reference 16

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Observation 8e736355-c6ff-4984-87ee-cd48663909c2 · outbound

This paper cites Modeling wine preferences by data mining from physicochemical properties.

Modified K-means Algorithm with Local Optimality Guarantees Modeling wine preferences by data mining from physicochemical properties

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:40.205087Z

Source-reported events for the cited work

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Observation 43703509-b582-46fd-834b-d19e47cdf563 · outbound

This paper cites Visual Categorization with Bags of Keypoints.

Modified K-means Algorithm with Local Optimality Guarantees Visual Categorization with Bags of Keypoints

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:40.191185Z

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Observation 1dc73e3d-2583-44b3-b119-af106bac206a · outbound

This paper cites S., Mallela, S., and Kumar, R.

Modified K-means Algorithm with Local Optimality Guarantees S., Mallela, S., and Kumar, R

Reference 19

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Observation d654de51-f59a-4282-86b0-ce0946cbbd2e · outbound

This paper cites and Nielsen, F.

Modified K-means Algorithm with Local Optimality Guarantees and Nielsen, F

Reference 20

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Observation e80b8d68-1463-4897-b70c-cc0629f7c3b2 · outbound

This paper cites Using the Triangle Inequality to Accelerate k-Means.

Modified K-means Algorithm with Local Optimality Guarantees Using the Triangle Inequality to Accelerate k-Means

Reference 21

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Observation 0c6ebc82-5fe0-4ebc-b55f-5c63b5681759 · outbound

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:56:40.135397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0da92f85-e831-4fd6-8101-65e204c535ca · outbound

This paper cites Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D.

Modified K-means Algorithm with Local Optimality Guarantees Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D

Reference 23

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Source-reported events for the cited work

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Observation 192f2cc3-2208-4f31-8bd9-09ff5514a47c · outbound

This paper cites and Rozho n , V.

Modified K-means Algorithm with Local Optimality Guarantees and Rozho n , V

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:40.121329Z

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Observation fd4d5f96-a3b2-48ee-b4a1-3320fce67a09 · outbound

This paper cites and Elkan, C.

Modified K-means Algorithm with Local Optimality Guarantees and Elkan, C

Reference 25

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 26

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Observation 40488ba4-46fe-4dd1-b2e1-07668bc81463 · outbound

This paper cites and Saito, S.

Modified K-means Algorithm with Local Optimality Guarantees and Saito, S

Reference 27

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 28

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Observation d6f02f16-4dd8-4151-a481-304216fc7f27 · outbound

This paper cites M., Netanyahu, N.

Modified K-means Algorithm with Local Optimality Guarantees M., Netanyahu, N

Reference 29

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 30

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Observation cbab3833-9ab6-4df5-929a-112c20e781c5 · outbound

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Modified K-means Algorithm with Local Optimality Guarantees and Leibler, R

Reference 31

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Modified K-means Algorithm with Local Optimality Guarantees An Algorithm for Vector Quantizer Design

Reference 32

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Observation 314d1fb4-2c97-4a61-9671-d240e628a6e2 · outbound

This paper cites and Shih, Y.-Y.

Modified K-means Algorithm with Local Optimality Guarantees and Shih, Y.-Y

Reference 33

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This paper cites Least squares quantization in PCM.

Modified K-means Algorithm with Local Optimality Guarantees Least squares quantization in PCM

Reference 34

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 96959e81-d3d0-40bc-86f1-8f118c160ad0 · outbound

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 35

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0c972360-6929-4890-8336-bd9092176789 · outbound

This paper cites V., Tolledo, D., Machado, J., Baptista, L.

Modified K-means Algorithm with Local Optimality Guarantees V., Tolledo, D., Machado, J., Baptista, L

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.952702Z

Source-reported events for the cited work

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Observation 019a7077-9901-4e2e-8760-3fc18ff8df3a · outbound

This paper cites Student Engagement Level in e-Learning Environment: Clustering Using K-means.

Modified K-means Algorithm with Local Optimality Guarantees Student Engagement Level in e-Learning Environment: Clustering Using K-means

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.938702Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e3fbc128-1a83-4833-afa7-fcbfe0962e08 · outbound

This paper cites and Kanehisa, M.

Modified K-means Algorithm with Local Optimality Guarantees and Kanehisa, M

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.923835Z

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Observation 5e031b1e-fa28-4dba-ac76-4c8b127c7b47 · outbound

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Modified K-means Algorithm with Local Optimality Guarantees and Kanehisa, M

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.910145Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 16a11f81-164f-434b-a78a-a9a8d9fff51f · outbound

This paper cites and Ali, M.

Modified K-means Algorithm with Local Optimality Guarantees and Ali, M

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.896109Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9a0c7f5d-7b84-43fe-b4d8-a00a100b8893 · outbound

This paper cites numpy.argmin -- NumPy v2.2 Manual.

Modified K-means Algorithm with Local Optimality Guarantees numpy.argmin -- NumPy v2.2 Manual

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.880605Z

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Observation bca93dce-277b-49b9-985d-1e3d1c1cda6b · outbound

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Modified K-means Algorithm with Local Optimality Guarantees and Moore, A

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.865941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1c84f1e0-1618-4c31-adc4-fe87a6cd98ce · outbound

This paper cites and Xia, Y.

Modified K-means Algorithm with Local Optimality Guarantees and Xia, Y

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.852249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3628a17f-f2d9-40fc-96b2-22fa8e5382d1 · outbound

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Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 44

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Observation 4326f025-0ece-46cc-b023-2d73d40af7c4 · outbound

This paper cites The 20 newsgroups text dataset.

Modified K-means Algorithm with Local Optimality Guarantees The 20 newsgroups text dataset

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.823655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e9e88c0c-394b-45d0-9baf-610d0089f6e6 · outbound

This paper cites KMeans - scikit-learn documentation.

Modified K-means Algorithm with Local Optimality Guarantees KMeans - scikit-learn documentation

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.809410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 82baf603-b037-40bb-8b24-687444c810b3 · outbound

This paper cites an unresolved cited work.

Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:56:39.793680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e5b7ae7b-da59-414c-a7d2-1cca23b787e9 · outbound

This paper cites A Comparison of Document Clustering Techniques.

Modified K-means Algorithm with Local Optimality Guarantees A Comparison of Document Clustering Techniques

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.779702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b2a37703-9cff-4674-b3ad-aa5a2b0aa09d · outbound

This paper cites Kullback - - Leibler Divergence-Based Fuzzy C-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation.

Modified K-means Algorithm with Local Optimality Guarantees Kullback - - Leibler Divergence-Based Fuzzy C-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.764580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ec1e7e95-2a4f-4a05-9e22-1f2e03434562 · outbound

This paper cites and Song, M.

Modified K-means Algorithm with Local Optimality Guarantees and Song, M

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:39.746932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f0ff2b71-ec4d-48e1-bff9-de888b2b0221 · outbound

This paper cites an unresolved cited work.

Modified K-means Algorithm with Local Optimality Guarantees Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:56:39.729937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.