correlation_distance {abdiv} | R Documentation |
Correlation and cosine distance
Description
The correlation and cosine distances, which are derived from the dot product of the two vectors.
Usage
correlation_distance(x, y)
cosine_distance(x, y)
Arguments
x , y |
Numeric vectors |
Details
For vectors x
and y
, the cosine distance is defined as the
cosine of the angle between the vectors,
where is the
magnitude or L2 norm of the vector,
.
Relation to other definitions:
Equivalent to the
cosine()
function inscipy.spatial.distance
.
The correlation distance is simply equal to one minus the Pearson
correlation between vectors. Mathematically, it is equivalent to the cosine
distance between the vectors after they are centered ().
Relation to other definitions:
Equivalent to the
correlation()
function inscipy.spatial.distance
.Equivalent to the
1 - mempearson
calculator in Mothur.
Value
The correlation or cosine distance. These are undefined if either
x
or y
contain all zero elements, that is, if
or
. In this case, we return
NaN
.
Examples
x <- c(2, 0)
y <- c(5, 5)
cosine_distance(x, y)
# The two vectors form a 45 degree angle, or pi / 4
1 - cos(pi / 4)
v <- c(3.5, 0.1, 1.4)
w <- c(3.3, 0.5, 0.9)
correlation_distance(v, w)
1 - cor(v, w)