Timeline for Fitting a simplex to set of almost orthogonal vectors
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7 at 14:59 | vote | accept | user103464 | ||
| Dec 5, 2023 at 22:59 | comment | added | user103464 | Nice, do you have a citation for this or something I could reference? | |
| Dec 4, 2023 at 17:06 | comment | added | David E Speyer | I believe the more general statement should be that, if the distances are within $r$ of $\sqrt{2}$ (or, the dot products are within $r'$ of $0$), then the distance to the simplex is $O(\sqrt{d} r)$ (or $O(\sqrt{d} r')$) and this cannot be improved. If $r > 1/\sqrt{d}$, this is a trivial bound. | |
| Dec 4, 2023 at 16:05 | comment | added | user103464 | Thanks a lot, I will update the status of the problem and accept the answer. I think I was also interested in the version of the question where the points are mapped to the simplex at distance $o(1)$ (rather than specifically $O(1/\sqrt{d})$. Maybe I should just ask a fresh question about this. | |
| Nov 29, 2023 at 21:28 | history | edited | David E Speyer | CC BY-SA 4.0 |
added 1 character in body
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| Nov 29, 2023 at 21:14 | history | answered | David E Speyer | CC BY-SA 4.0 |