Improving k-nearest neighbour classification with distance functions based on receiver operating characteristics

The k-nearest neighbour (k-NN) technique, due to its interpretable nature, is a simple and very intuitively appealing method to address classification problems. However, choosing an appropriate distance function for k-NN can be challenging and an inferior choice can make the classifier highly vulnerable to noise in the data. In this paper, we propose a new method for determining a good distance function for k-NN. Our method is based on consideration of the area under the Receiver Operating Characteristics (ROC) curve, which is a well known method to measure the quality of binary classifiers. It computes weights for the distance function, based on ROC properties within an appropriate neighbourhood for the instances whose distance is being computed. We experimentally compare the effect of our scheme with a number of other well-known k-NN distance metrics, as well as with a range of different classifiers. Experiments show that our method can substantially boost the classification performance of the k-NN algorithm. Furthermore, in a number of cases our technique is even able to deliver better accuracy than state-of-the-art non k-NN classifiers, such as support vector machines.