Timeline for Johnson-Lindenstrauss lemma preserves angles
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Apr 1, 2020 at 22:16 | comment | added | usul | @keyboardAnt I only skimmed it myself. It seems like they need the isosceles argument too, but I didn't get intuition for why. | |
| Apr 1, 2020 at 18:34 | comment | added | keyboardAnt | @usul, thank you for your reply. As far as I understood from "reading" the paper you referred to (challenging for me), it seems like the paper used a right angle isosceles triangle (not only right angle). Is it necessary? Because from your answer I understand that the requirement for the isosceles property isn't a key ingredient of the proof. Best regards | |
| Apr 1, 2020 at 15:55 | comment | added | usul | Put $y$ at the origin and project $z$ onto $x$; call this point $w$. Now $zwy$ is a right triangle. The projection approximately preserves the lengths of all the edges of this triangle. And one can show that the angle at $w$ is still close to 90 degrees, i.e. the dot product of $(y-w)$ and $(z-w)$ is very small. These seem to be key ingredients the paper is using to show the angle at $x$ is approximately preserved. | |
| Apr 1, 2020 at 15:20 | comment | added | usul | There is a full proof in the paper cited in those notes, "Dimensionality Reductions That Preserve Volumes and Distance to Affine Spaces, and Their Algorithmic Applications" by Magen, 2002. | |
| Apr 1, 2020 at 14:41 | history | edited | keyboardAnt | CC BY-SA 4.0 |
added 873 characters in body
|
| Apr 1, 2020 at 14:12 | history | edited | keyboardAnt | CC BY-SA 4.0 |
added 157 characters in body
|
| Apr 1, 2020 at 10:20 | history | edited | keyboardAnt | CC BY-SA 4.0 |
added 22 characters in body
|
| Apr 1, 2020 at 9:26 | history | edited | Martin Sleziak |
added a top-level tag; https://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
|
|
| Apr 1, 2020 at 0:31 | answer | added | Andreas Blass | timeline score: 2 | |
| Mar 31, 2020 at 19:45 | comment | added | keyboardAnt | @MartinSleziak, thanks. | |
| Mar 31, 2020 at 19:45 | comment | added | keyboardAnt | @PaulSiegel, could you please elaborate? Best regards | |
| Mar 31, 2020 at 19:40 | history | edited | LSpice | CC BY-SA 4.0 |
Unicode -> TeX
|
| Mar 31, 2020 at 19:36 | history | edited | YCor |
edited tags
|
|
| Mar 31, 2020 at 19:16 | comment | added | Paul Siegel | Isn't this just a continuity argument? The ratio inside the $arccos$ depends continuously on $a$, $b$, and $c$, and $arccos$ itself is continuous, so the result follows from the definition of continuity. | |
| Mar 31, 2020 at 18:42 | comment | added | Martin Sleziak | I will point out that the tag (geometry) is deprecated on MathOverflow, see the tag-info. Perhaps you (or some other users) might be able to choose other suitable tag. | |
| Mar 31, 2020 at 18:41 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added 4 characters in body
|
| Mar 31, 2020 at 18:22 | history | edited | keyboardAnt | CC BY-SA 4.0 |
added 113 characters in body
|
| Mar 31, 2020 at 18:13 | history | edited | keyboardAnt | CC BY-SA 4.0 |
added 184 characters in body
|
| Mar 31, 2020 at 18:10 | review | First posts | |||
| Mar 31, 2020 at 19:57 | |||||
| Mar 31, 2020 at 18:06 | history | asked | keyboardAnt | CC BY-SA 4.0 |