Minkowski Distance

The $L_p$ distance (aka Minkowski Distance) is a generalization with different $p$ coefficient of the Euclidean ($p=2$), Manhattan ($p=1$) and Chebyshev ($p=\infty$) distances.

$$\Vert x-y{\Vert }_p={\left(\sum _{i=1}^d(x_i-y_i{)}^p\right)}^{\frac{1}{p}}$$

$L_p$ distance in $R^2$ with different values for $p$.

Note

Note that the number of dimensions $k$ for points in ${\mathbb{R}}^k$ and the $p$ coefficient are two different things.