Introduction
Many datasets can't be separated by a straight line. Picture red points clustered in the middle of a plot, surrounded by a ring of blue points. No straight street can separate them.
SVMs have a beautiful solution. Imagine the points are on a flat sheet of rubber. If you push the middle of the sheet up into a hill, the red points rise while the blue ring stays low — and now a flat plane can slice between them. In other words: move the data into a higher-dimensional space where a straight boundary works.
This topic shows two ways to do that: adding features explicitly, and the famous kernel trick, which gets the same result without ever computing the new features.