Linearly Separable? No? For me it is! A Brief introduction to Kernel Methods

This is a crash-introduction to kernel methods and the best thing to do is starting with a very simple question? Is this bidimensional set linearly separable? Of course, the answer is yes, it is. Why? A dataset defined in a subspace Ω ⊆ ℜn is linearly separable if there exists a (n-1)-dimensional hypersurface that is able to separate all points belonging to a class from the others. Let’s consider the problem from another viewpoint, supposing, for simplicity, to work in 2D. We have defined an hypothetical separating line and we have also set an arbitrary point O as an origin. Let’s now draw the vector w, orthogonal to the line and pointing in one of the two sub-spaces. Let’s now consider the inner product between w and a random point x0:  how can we decide if it’s on the side pointed by w? Simple, the inner product is proportional to the cosine of […]