SVM with polynomial kernel visualization

This short video demonstrates how vectors of two classes that cannot be linearly separated in 2-D space,
can become linearly separated by a transformation function into a higher
dimensional space.

The transformation used is:
f([x y]) = [x y (x^2+y^2)]

If you would like a stand-alone file with a high-res version of this movie for academic purposes please contact me.

Category:

Howto & Style

Tags:

• svm
• polynomial
• linear
• science
• statistics
• mathmatics
• learning

[SoftwareEngineer3]

Thanks, very clear.

What would be the kernel for this transformation?

[udiprod]

Thanks.

The kernel is the dot product in the higher-dimensional space. In this case:

K( [x1 y1], [x2 y2] ) =

[x1 y1 x1^2+y1^2][x2 y2 x2^2 y2^2] =

x1x2+y1y2+(x1^2+y1^2)(x2^2+y2^­2)

[boulabiar]

good video,

you created it using any tools and languages ?

[udiprod]

Yes. I created it using Autodesk Maya. Thanks!

[cirimus]

Thank you for the inspiration, here's another one: ciri.be/blog/?p=593 based on yours.

[onlyneerya]

Very helpful, it was!

[viperbuller]

Very helpful, simple and clear! Nice! Thank you very much.

[loosupeter]

thank you , very informative when visualized

[oliverchess]

great for teaching, thank you for doing this.

[glapots]

Thank you. This explains it nicely. I just hope it comes up in my exam :)

[neozenith]

I use this video whenever I have to explain to people what I do. Thanks. :D

[AlejandroSolado]

very intensive. in 30 seconds you explain the intrinsic meaning.

Tanks

[Anjani1209]

||Hari Om||

Thanks

[Anjani1209]

||Hari Om||