Timeline for Corresponding RKHS of Common Kernels
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2016 at 23:31 | vote | accept | j__ | ||
| Feb 12, 2016 at 22:42 | comment | added | pAt84 | By using the kernel function, e.g. alex.smola.org/papers/1999/MikSchSmoMuletal99.pdf Wikipedia also has an article about it. Just google a litte. | |
| Feb 12, 2016 at 22:09 | comment | added | j__ | that's a really interesting comment! Although I can't quite see how I would perform pca in the RKHS if it was say infinite dimensional. Any suggestions of how to approach this? | |
| Feb 12, 2016 at 22:03 | comment | added | pAt84 | If this were the case you might get there very easily with PCA, which can be performed in the RKHS as well, using a kernel. | |
| Feb 12, 2016 at 20:50 | comment | added | j__ | thanks, I was thinking a little along that direction already. For examples, if we have 10 points we know they live in at most 10 dimensions and could we as such write these this subspace analytically (even as a infinite series). | |
| Feb 12, 2016 at 20:45 | comment | added | pAt84 | Be aware though. These RKHS are usually high-dimensional as you have already noticed. The human understanding of such high-dimensional spaces is usually completely off: people still expect clusters like they often see them in 2D but the matter of the fact is that we can not understand a high-dimensional RKHS like the one of the polynomial kernel. Instead thinking of clusters, it is often better to think of manifolds in the RKHS, i.e. your data only populates a sub-space of the RKHS. Maybe if you take this direction you will actually get the gist of it faster than heading straight for it. | |
| Feb 12, 2016 at 20:27 | comment | added | j__ | Thanks for the pointers - very useful! I am trying to understand the relationship between the RKHS of different kernels and it seemed like a good place to start. | |
| Feb 12, 2016 at 20:21 | history | answered | pAt84 | CC BY-SA 3.0 |