Timeline for Sparse approximate representation of a collection of vectors
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Feb 1, 2010 at 18:13 | vote | accept | Donald | ||
| Jan 29, 2010 at 23:28 | answer | added | Suresh Venkat | timeline score: 4 | |
| Jan 29, 2010 at 21:59 | history | edited | Yemon Choi |
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| Jan 29, 2010 at 19:58 | comment | added | Donald | I'm interested in the $\ell_1$ norm, not necessarily the $\ell_\infty$ norm (Hamming). I am willing to let $b_i \in \mathbb{R}^n$, so they are not necessarily the same. $||u-v||_1 = \sum_{i=1}^n|u_i-v_i|$. I'm thinking of values of $\epsilon = c\dot n$ for some constant $c < 1$, the smaller the better. Sonia -- I'm thinking of approximating the value of an exponentially sized set of functions over a domain given a polynomially sized set of evaluations (of possibly different functions) over the same domain. | |
| Jan 29, 2010 at 19:25 | comment | added | Sonia Balagopalan | Is there a particular reason why you want the size of $span(b_1,\ldots,b_k)$ to be roughly the same as the size of $C$, which is the dimension of the space. Just curious! | |
| Jan 29, 2010 at 19:14 | comment | added | Sonia Balagopalan | That's the Hamming metric which is also the same as the $L^1$ norm and counts the number of coordinates where they differ. So they differ at $\epsilon$ positions. I'm wondering what values of $\epsilon$ the OP has in mind though. The problem is interesting, but quite broad as it is. | |
| Jan 29, 2010 at 18:33 | comment | added | fedja |
Does $\|u-v\|<\varepsilon$ mean that $u$ and $v$ differ in at most $\varepsilon n$ positions or you normalize the norm in some other way?
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| Jan 29, 2010 at 16:08 | history | asked | Donald | CC BY-SA 2.5 |