Distance metrics for instance-based learning

Examination of three different distance metrics is examined and experimental comparisons using data from three domains: malignant cancer classification, heart disease diagnosis, and diabetes prediction indicate that the Manhattan distance metric works works quite well, although not better than the Euclidean metric that has become a standard for machine learning experiments.

Abstract

Instance-based learning techniques use a set of stored training instances to classify new examples. The most common such learning technique is the nearest neighbor method, in which new instances are classified according to the closest training instance. A critical element of any such method is the metric used to determine distance between instances. Euclidean distance is by far the most commonly used metric; no one, however, has systematically considered whether a different metric, such as Manhattan distance, might perform equally well on naturally occurring data sets. Some evidence from psychological research indicates that Manhattan distance might be preferable in some circumstances. This paper examines three different distance metrics and presents experimental comparisons using data from three domains: malignant cancer classification, heart disease diagnosis, and diabetes prediction. The results of these studies indicate that the Manhattan distance metric works works quite well, although not better than the Euclidean metric that has become a standard for machine learning experiments. Because the nearest neighbor technique provides a good benchmark for comparisons with other learning algorithms, the results below include a number of such comparisons, which show that nearest neighbor, using any distance metric, compares quite well to other machine learning techniques.