Bray Curtis distance, or Sorensen distance, is a normalization method that is commonly used in botany, ecology and environmental science field. It views the space as grid similar to the city block distance. The Bray curtis distance has a nice property that if all coordinates are postive, its value is between zero and one. Zero bray curtis represent exact similar coordinate. If both objects are in the zero coordinates, the Bray curtis distance is undefined. The normalization is done using absolute difference divided by the summation.
Formula: , or equivalent formula
Try to experiment with your own input values using the interactive program of Bray Curtis Distance below.
Input coordinate values of ObjectA and ObjectB (the coordinate are numbers only), then press "Get Sorensen Distance" button. The program will directly calculate when you type the input.
For example:
Point A has coordinate (0, 3, 4, 5) and point B has coordinate (7, 6, 3, 1).


Features 




cost 
time 
weight 
incentive 

Object A 
0 
3 
4 
5 

Object B 
7 
6 
3 
1 
The Bray Curtis distance or Sorensen distance between point A and B is
The pattern of Bray Curtis distance in 2dimension is quadrilateral. The figure below is drawn with a sink at the center. Compare this shape with the 2D shape of Canberra distance.
See also: Bray Curtis normalization, Canberra distance, City Block Distance
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Similarity Measurement. http:\people.revoledu.comkardi tutorialSimilarity