## Chebyshev Distance

Chebyshev distance is also called Maximum value distance. It examines the absolute magnitude of the differences between coordinates of a pair of objects. This distance can be used for both ordinal and quantitative variables.

Other name : Tchebyschev Distance (due to translation)

Formula

Experiment with the interactive program below. Suppose you need to walk from location A to location B. There are two paths. Using path-1, you need to walk 3 km, while using path 2, you need to walk 4 km. What is the Chebyshev Distance from location A to location B? Put A = (0, 0) to indicate the origin and B = (3, 4), the Chebyshev distance represents the maximum length of walking distance from location A to location B through any paths . If you have the third dimension, it may represent the height and the fourth dimension can represent any other factors such as satisfaction, comfortability, etc.

Input coordinate values of Object-A and Object-B (the coordinate are numbers only), then press "Get Chebyshev Distance" button. The program will directly calculate when you type the input.

Features Object A Object B

## Example

 Features cost time weight incentive Object A 0 3 4 5 Object B 7 6 3 -1

Point A has coordinate (0, 3, 4, 5) and point B has coordinate (7, 6, 3, -1).

The Chebyshev Distance between point A and B is

The pattern of Chebyshev distance in 2-dimension is square. When the sink is on the center, it forms concentric squares around the center.

Chebyshev distance is a special case of Minkowski distance with (take a limit)

Preferable reference for this tutorial is

Teknomo, Kardi (2015) Similarity Measurement. http:\people.revoledu.comkardi tutorialSimilarity