Machine Learning in Java - Second Edition

Euclidean distances

In Euclidean space, with the n dimension, the distance between two elements is based on the locations of the elements in such a space, which is expressed as p-norm distance. Two commonly used distance measures are L2- and L1-norm distances.

L2-norm, also known as Euclidean distance, is the most frequently applied distance measure that measures how far apart two items in a two-dimensional space are. It is calculated as follows:

L1-norm, also known as Manhattan distance, city block distance, and taxicab norm, simply sums the absolute differences in each dimension, as follows: