Mathematical Set Up Suppose we have a training matrix \(X\) with \(n\) observations and \(d\) features \[ X = \begin{pmatrix} x_{11} & x_{12} & \ldots & x_{1d}\\ x_{21} & x_{22} & \ldots & x_{2d} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n1} & x_{n2} & \ldots & x_{nd} \end{pmatrix} =\begin{pmatrix} {\bf{x}}_1^\top \\ {\bf{x}}_2^\top \\ \vdots \\ {\bf{x}}_n^\top \end{pmatrix} \in\mathbb{R}^{n\times d} \] and that we want to do a feature transform of this data using the Radial Basis Function.
