Euclidean Distance

#Math

$\displaystyle \lVert \vec{x}\rVert_{2}=\sqrt{ \sum_{i}x_{i}^{2} }$

• Interestingly, for a given set of points $\displaystyle \vec{x}{i}$, the points that minimizes the sum of euclidean distances to $\displaystyle \vec{x}{i}$ is their mean

$\displaystyle d=\sqrt{ (x_{i}'-x_{i})^{2} }$

• Distance between two points
• Assuming Einstein notation
• $\displaystyle x_{i}$ refers to summing over all coordinate differences