Chebyshev distance

The Chebyshev distance equals the limit of Minkowski distance metric with \(p \to \infty\).


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 Chebyshev distance \(||u_i, v_j||_{\infty}\) for any pair of input vectors:

\[||u_i, v_j||_{\infty} = \max_l {|u_{il} - v_{jl}|},\]

where \(\quad 1 \leq i \leq n, \quad 1 \leq j \leq m, \quad 1 \leq l \leq k\).

Computation method: dense

The method defines Chebyshev 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: Chebyshev distance.