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.
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1 Answer
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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