Tag Archives: function basis

A Story of Basis and Kernel – Part II: Reproducing Kernel Hilbert Space

Author: Changyue Song

1. Opening Words

In the previous blog, the function basis was briefly discussed. We began with viewing a function as an infinite vector, and then defined the inner product of functions. Similar to \( \mathcal{R}^n \) space, we can also find orthogonal function basis for a function space.

This blog will move a step further discussing about kernel functions and reproducing kernel Hilbert space (RKHS). Kernel methods have been widely used in a variety of data analysis techniques. The motivation of kernel method arises in mapping a vector in \( \mathcal{R}^n \) space as another vector in a feature space.… Read more