| canberra {abdiv} | R Documentation |
The Canberra distance and Clark's coefficient of divergence are measures that use the absolute difference over the sum for each element of the vectors.
canberra(x, y)
clark_coefficient_of_divergence(x, y)
x, y |
Numeric vectors |
For vectors x and y, the Canberra distance is defined as
d(x, y) = \sum_i \frac{|x_i - y_i|}{x_i + y_i}.
Elements where
x_i + y_i = 0 are not included in the sum. Relation of
canberra() to other definitions:
Equivalent to R's built-in dist() function with
method = "canberra".
Equivalent to the vegdist() function with
method = "canberra", multiplied by the number of entries where
x > 0, y > 0, or both.
Equivalent to the canberra() function in
scipy.spatial.distance for positive vectors. They take the
absolute value of x_i and y_i in the denominator.
Equivalent to the canberra calculator in Mothur, multiplied
by the total number of species in x and y.
Equivalent to D_{10} in Legendre & Legendre.
Clark's coefficient of divergence involves summing squares and taking a square root afterwards:
d(x, y) = \sqrt{
\frac{1}{n} \sum_i \left( \frac{x_i - y_i}{x_i + y_i} \right)^2
},
where n is the number of elements where x > 0, y > 0, or
both. Relation of clark_coefficient_of_divergence() to other
definitions:
Equivalent to D_{11} in Legendre & Legendre.
The Canberra distance or Clark's coefficient of divergence. If every
element in x and y is zero, Clark's coefficient of
divergence is undefined, and we return NaN.
x <- c(15, 6, 4, 0, 3, 0)
y <- c(10, 2, 0, 1, 1, 0)
canberra(x, y)
clark_coefficient_of_divergence(x, y)