The Euclidean Distance, or L2 norm, is the most common distance metric used in clustering. It measures the straight-line, or shortest, distance between observations in p-dimensional space. In two dimensions, the formula reduces to the commonly used Pythagorean theorem. For two observations x_{1} and x_{2}, the Euclidean Distance is computed by the following, where the superscript denotes the dimension from 1 to n: