Canberra distance

The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966[1] and refined in 1967[2] by G. N. Lance and W. T. Williams. It is similar to the Manhattan distance. It is mostly used for data scattered around the origin.

Contents

Formal description

The Canberra distance, d^{CAD}, between two vectors \mathbf{p}, \mathbf{q} in an n-dimensional real vector space is given as follows:

d^{{CAD}}(\mathbf{p}, \mathbf{q}) = \sum_{i=1}^n \frac{|p_i-q_i|}{|p_i|%2B|q_i|},

where

\mathbf{p}=(p_1,p_2,\dots,p_n)\text{ and }\mathbf{q}=(q_1,q_2,\dots,q_n)\,

are vectors.

See also

Notes

  1. ^ Lance, G. N.; Williams, W. T. (1966). "Computer programs for hierarchical polythetic classification ("similarity analysis").". Computer Journal 9 (1): 60–64. doi:10.1093/comjnl/9.1.60. 
  2. ^ Lance, G. N.; Williams, W. T. (1967). "Mixed-data classificatory programs I.) Agglomerative Systems". Australian Computer Journal: 15–20. 

References