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Chebyshev Distance

Chebyshev Distance

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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

For 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.
2D Chebyshev distance

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

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Preferable reference for this tutorial is

Teknomo, Kardi. Similarity Measurement. http:\\people.revoledu.com\kardi\ tutorial\Similarity\

 

 

 

 
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