Conformal transformation of the metric for k-nearest neighbors classification

The paper introduces a new method for improving the nearest neighbors classifier. Our approach is based on the idea of replacing the constant metric with a variable and conformally equivalent one that is data dependent, and therefore it is more informative. We define a family of conformal transformations that, under some assumptions, induces distance functions that are efficiently computable. Using the intuition that the distances between points near a class boundary should be larger, a simple method for selecting a transformation is proposed. We perform experiments on two datasets. The first set of experiments are with a sentiment prediction dataset, and in this case our method offers some improvements over the standard k-NN algorithm. In the second empirical analysis, we apply the method to a news categorisation problem. In this case the results are mixed. We conclude with a discussion of the advantages and weaknesses of the method, and propose a number of possible improvements.