# Adaptive Gamma in RBF Kernel

The RBF Kernel is defined by

$$K(x,y)=\exp(-\gamma ||x-y||^2)$$

Wouldnt it be better to find a suited gamma value for each dimension?

$$K(x,y)=\exp(-\sum_i \gamma_i * (x_i-y_i)^2 )$$

This would add more weight to more important dimensions.

In fact there are several papers dealing with a weighted RBF kernel, here is one (see Chapter 3.1) for those who are interested:

Kernel Learning in Support Vector Machines using Dual-Objective Optimization

Chapter 3.1: Weighted Radial Basis Function Kernels https://www.ai.rug.nl/~mwiering/GROUP/ARTICLES/SVM_kernel_opt.pdf