Timeline for Does the plane clustered to minimize sum distances^2 to clusters centers ( inertia / "K-means") produce hexagonal clusters / hexagonal lattice?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 15, 2020 at 15:59 | history | edited | Adam P. Goucher | CC BY-SA 4.0 |
amend typo in paper publication year
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| Jul 14, 2020 at 21:01 | vote | accept | Alexander Chervov | ||
| Jul 14, 2020 at 21:01 | comment | added | Alexander Chervov | Thank you very much for your comments ! | |
| Jul 14, 2020 at 18:22 | comment | added | Adam P. Goucher | @AlexanderChervov Yes, the hexagonal lattice is the unique optimal solution. This is implied by the proof given here, together with the observation that equality holds in (3) if and only if the polygon in question is regular. dmg.tuwien.ac.at/gruber/gruber_arbeiten/short1.pdf | |
| Jul 14, 2020 at 18:11 | comment | added | Adam P. Goucher | @AlexanderChervov In terms of surveys, you'll want to get hold of a copy of the book Sphere Packings, Lattices and Groups by Conway and Sloane; my entire answer is basically just paraphrasing relevant parts of Chapter 2. | |
| Jul 14, 2020 at 17:41 | comment | added | Alexander Chervov | Let me clarify one point about dimension 2, does the hexagonal lattice is THE ONLY solution, or the there can be some other ? | |
| Jul 14, 2020 at 17:18 | comment | added | Alexander Chervov | Thank you very much for your excellent answer ! If it would be possible to suggest references on the dimension 3 and higher cases - that would be very kind of you . The paper by Toth, unfortunatelt is behind the pay-wall, if it possible to suggest some later references, may be just surveys - that would be great... | |
| Jul 14, 2020 at 14:37 | history | edited | Adam P. Goucher | CC BY-SA 4.0 |
diacritical mark on the surname of László Fejes Tóth
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| Jul 14, 2020 at 8:27 | history | answered | Adam P. Goucher | CC BY-SA 4.0 |