Statistical Measures of Distance

Measures of statistical distance are widely used in techniques such as clustering and classification, when we wish to identify objects that are in some sense similar to each other. The choice of distance between data points is an important one, and there are a large number of measures to choose from. In this paper we present some of the most commonly used measures of distance and compare their usefulness when analyzing data sets with different properties. They include general metrics such as the Minkowski, which includes the classic Euclidian, the Chebyshev, the Manhattan, and the Hamming distance. We present the Mahalanobis metric, which is similar to the Euclidian but corrects for strong structure in the data. In addition, we present the concept of correlation as a distance measure, covering the properties of the Pearson and Spearman correlations.