Robust Distance Measures for kNN Classification of Cancer Data.

The k-Nearest Neighbor (kNN) classifier represents a simple and very general approach to classification. Still, the performance of kNN classifiers can often compete with more complex machine-learning algorithms. The core of kNN depends on a "guilt by association" principle where classification is performed by measuring the similarity between a query and a set of training patterns, often computed as distances. The relative performance of kNN classifiers is closely linked to the choice of distance or similarity measure, and it is therefore relevant to investigate the effect of using different distance measures when comparing biomedical data. In this study on classification of cancer data sets, we have used both common and novel distance measures, including the novel distance measures Sobolev and Fisher, and we have evaluated the performance of kNN with these distances on 4 cancer data sets of different type. We find that the performance when using the novel distance measures is comparable to the performance with more well-established measures, in particular for the Sobolev distance. We define a robust ranking of all the distance measures according to overall performance. Several distance measures show robust performance in kNN over several data sets, in particular the Hassanat, Sobolev, and Manhattan measures. Some of the other measures show good performance on selected data sets but seem to be more sensitive to the nature of the classification data. It is therefore important to benchmark distance measures on similar data prior to classification to identify the most suitable measure in each case.