Timeline for How can I embed an N-points metric space to a hypercube with low distortion?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2010 at 5:05 | vote | accept | pacificmoth | ||
| Apr 15, 2010 at 15:55 | |||||
| Jan 9, 2010 at 5:04 | comment | added | pacificmoth | If, by any chance, you find the ref, please do let me know. I kinda like the idea of converting l_1 to a hamming space by concatenation. Thanks. | |
| Jan 9, 2010 at 4:52 | comment | added | Suresh Venkat | The usual way to convert l_1 to a hamming space is by writing the coordinates in unary and then concatenating them. This is potentially nasty if the values are large. Generally this can be fixed if the value ranges aren't large by scaling, but I'm also convinced there's a direct embedding into the hypercube that I can't find a ref for. | |
| Jan 9, 2010 at 4:28 | comment | added | pacificmoth | This is a fairly educating answer. I appreciate it. But the thing here is that I have to restrict the assignment of points to the vertices instead of any vector inside the hypercube. So it isn't really embedding to $\ell_1$ space. Or, maybe you could show me how to move those points to the vertices after embedding without much distortion, that would be cool. | |
| Jan 8, 2010 at 21:47 | history | answered | Suresh Venkat | CC BY-SA 2.5 |