# Minkowski distance¶

The Minkowski distances are the set of distance metrics with different degree $$(p > 0)$$ and are widely used for distance computation in different algorithms. The most commonly used distance metric, Euclidean distance, is also a Minkowski distance with $$p = 2.0$$.

 Operation Computational methods dense dense

## Mathematical formulation¶

### Computing¶

Given a set $$U$$ of $$n$$ feature vectors $$u_1 = (u_{11}, \ldots, u_{1k}), \ldots, u_n = (u_{n1}, \ldots, u_{nk})$$ of dimension $$k$$ and a set $$V$$ of $$m$$ feature vectors $$v_1 = (v_{11}, \ldots, v_{1k}), \ldots, v_m = (v_{m1}, \ldots, v_{mk})$$ of dimension $$k$$, the problem is to compute the Minkowski distance $$||u_i, v_j||_{p}$$ for any pair of input vectors:

$||u_i, v_j||_{p} = \sum_{l=1}^{k} {({|u_{il} - v_{jl}|}^p)}^{1/p},$

where $$\quad 1 \leq i \leq n, \quad 1 \leq j \leq m, \quad p > 0$$.

### Computation method: dense¶

The method defines Minkowski distance metric, which is used in other algorithms for the distance computation. There are no separate computation mode to compute distance manually.

## Programming Interface¶

Refer to API Reference: Minkowski distance.