I am reading Tom Mitchell's Machine Learning. In section 8.2.3, he defines: Kernel function is the function of distance that is used to determine the weight of each training example. In other words, the kernel function is the function $K$ such that $w_i = K(d(x_i, x_q))$. However, when we talk about SVMs we have a kernel function $K(x,y) = \phi(x) \cdot \phi(y)$. Is kernel function (when talking about locally weighted regression or maybe k-NN) just a totally different thing from kernel function (SVMs)?