# Asymmetric distance measure in k-NN classifier?

What is the problem with an asymmetric distance measure in k-NN classifier?

I think it will not cause problem, so long as I compute the distance consistently, say always from test_data to labeled_data.

It has to be symmetric. The reason is because, KNN can be viewed as a non-parametric kernel density estimation problem. In the estimation problem you get a term of the form $K(x-x_{i})$ and $K$ is a Kernel which has to be symmetric (see http://en.wikipedia.org/wiki/Variable_kernel_density_estimation)