Chebyshev Distance - L∞ norm (maximum coordinate difference)

Overview

d ≥ 0; d=0 iff a=b. Chebyshev Distance is symmetric.

Output

distance, lower is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Similarity assessment, clustering

How it works

1. 1

   Compute the Chebyshev Distance between vectors a and b.

   $$d_{\infty }(\mathbf{a},\mathbf{b})=\underset{j=1}{\overset{n}{\max }}|a_j-b_j|$$

   Roy 1991 (Chebyshev / L∞ distance; pending PDF page verification)

Edge cases and pitfalls

• Only the worst-case criterion gap determines the distance - all other gaps are ignored.

Works with

How to cite