# Better classification performance when using an RBF kernel function in high dimensional space?

I'm learning about SVM's and understand that boosting something into a higher dimension can sometimes help separate the data better. However, if I were to perform 1 nearest neighbor with the RBF kernel, is it possible that the classification performance is better in the higher dimensional space than the lower dimensional space?

## 1 Answer

In general RRF kernels perform better but they are prone to over-fitting. In addition you must also perform free parameter selection. In the paper Kernel Nearest-Neighbor Algorithm that is to my knowledge the first paper on kernel -KNN the following is stated:

"If samples distribute arbitrarily, conventional nearest-neighbor algorithm may not obtain satisfactory result. However, mapping to a high dimensional space, the kernel nearest-neighbor algorithm can work better and obtain good results."

The paper used polynomial kernels due to free parameter issues but mapping to a high dimensional space was helpful.