Radial Basis Function Kernel

The radial basis function kernel, or RBF kernel, is a widely used kernel function in machine learning, most often applied inside support vector machines to let a linear classifier separate data that is not linearly separable in its original space. It is defined as K(x, x prime) equals exp of negative the squared Euclidean distance between x and x prime divided by 2 sigma squared, where sigma is an adjustable width parameter, sometimes reparameterized as gamma equals 1 over 2 sigma squared. Because its value decreases smoothly with distance, ranging from one when the two points coincide down toward zero as they grow far apart, the RBF kernel has a natural interpretation as a measure of similarity between points, and it corresponds to an underlying feature space of infinitely many dimensions.