Canberra and related distances
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) = ∑_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) = √{ \frac{1}{n} ∑_i ≤ft( \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)
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