| bray_curtis {abdiv} | R Documentation |
The Bray-Curtis distance is the Manhattan distance divided by the sum of both vectors.
bray_curtis(x, y)
x, y |
Numeric vectors |
For two vectors x and y, the Bray-Curtis distance is defined
as
d(x, y) = \frac{\sum_i |x_i - y_i|}{\sum_i x_i + y_i}.
The Bray-Curtis distance is connected to many other distance measures in this package; we try to list some of the more important connections here. Relation to other definitions:
Equivalent to vegdist() with method = "bray".
Equivalent to the braycurtis() function in
scipy.spatial.distance for positive vectors. They take the
absolute value of x_i + y_i in the denominator.
Equivalent to the braycurtis and odum calculators in
Mothur.
Equivalent to D_{14} = 1 - S_{17} in
Legendre & Legendre.
The Bray-Curtis distance on proportions is equal to half the Manhattan distance.
The Bray-Curtis distance on presence/absence vectors is equal to the Sorenson index of dissimilarity.
The Bray-Curtis distance between x and y. The
Bray-Curtis distance is undefined if the sum of all elements in x
and y is zero, in which case we return NaN.
x <- c(15, 6, 4, 0, 3, 0)
y <- c(10, 2, 0, 1, 1, 0)
bray_curtis(x, y)
# For proportions, equal to half the Manhattan distance
bray_curtis(x / sum(x), y / sum(y))
manhattan(x / sum(x), y / sum(y)) / 2