Hands-On Artificial Intelligence for IoT

Kernel trick

The previous method works fine when the input feature space is linearly separable. What should we do when it isn't? One simple way is to transform the data (X) into a higher dimensional space where it's linearly separable and find a maximal margin hyperplane in that high-dimensional space. Let's see how; our hyperplane in terms of α is as follows:

Let φ be the transform, then we can replace X by φ(X) and hence its dot product X^T X⁽ⁱ⁾ with a function K(X^T, X⁽ⁱ⁾) = φ(X)^T φ(X⁽ⁱ⁾) called kernel. So we now just preprocess the data by applying the transform φ and then find a linear separator in the transformed space as before.

The ...