Timeline for What function could be a kernel?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2013 at 16:40 | comment | added | Mike Hughes | In the SVM domain, using a PSD kernel ensures the problem is convex, so the optimization achieves a unique, globally optimal solution. Without PSD-property, there's no guarantee that the solution found is anywhere near the best possible. But, yes there are several kernels (like the Sigmoid) that are not PSD but still successful in practice. A decent reference for this issue is: perso.lcpc.fr/tarel.jean-philippe/publis/jpt-icme05.pdf. | |
| Feb 12, 2013 at 16:31 | history | edited | Mike Hughes | CC BY-SA 3.0 |
deleted 12 characters in body
|
| Feb 12, 2013 at 16:27 | comment | added | Mike Hughes | @Peter: yes, you're right. It can be *semi-*definite, not just definite. Edited accordingly. | |
| Feb 12, 2013 at 16:26 | history | edited | Mike Hughes | CC BY-SA 3.0 |
added 30 characters in body
|
| Feb 12, 2013 at 14:12 | vote | accept | Gigili | ||
| Feb 12, 2013 at 11:00 | comment | added | Peter Bloem | As I understand it the second condition is only positive semi-definiteness. And from what I'm told, it's only necessary if you want to prove the convergence of the SVM algorithm. In practice, there are many kernels that are not PSD, but work well in practice. | |
| Feb 12, 2013 at 3:47 | history | edited | Mike Hughes | CC BY-SA 3.0 |
added 314 characters in body
|
| Feb 12, 2013 at 3:37 | history | answered | Mike Hughes | CC BY-SA 3.0 |