Fig 1. Convergence to Gaussian for Manhattan and Euclidean distances for simulated standard uniform data with m = 100 instances and p = 10, 100, and 10000 attributes.

Convergence to Gaussian occurs rapidly with increasing p, and Gaussian is a good approximation for p as low as 10 attributes. The number of attributes in bioinformatics data is typically much larger, at least on the order of 10³. The Euclidean metric has stronger convergence to normal than Manhattan. P values from Shapiro-Wilk test, where the null hypothesis is a Gaussian distribution.