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 \(p = 2.0\).


Computational methods



Mathematical formulation#


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.