correlation_distance {abdiv} | R Documentation |

The correlation and cosine distances, which are derived from the dot product of the two vectors.

correlation_distance(x, y) cosine_distance(x, y)

`x, y` |
Numeric vectors |

For vectors `x`

and `y`

, the cosine distance is defined as the
cosine of the angle between the vectors,

*d(x, y) = 1 - \frac{x \cdot y}{|x| |y|},*

where *|x|* is the
magnitude or L2 norm of the vector, *|x| = √{∑_i x_i^2}*.
Relation to other definitions:

Equivalent to the

`cosine()`

function in`scipy.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 (*x - \bar{x}*).
Relation to other definitions:

Equivalent to the

`correlation()`

function in`scipy.spatial.distance`

.Equivalent to the

`1 - mempearson`

calculator in Mothur.

The correlation or cosine distance. These are undefined if either
`x`

or `y`

contain all zero elements, that is, if *|x| = 0*
or *|y| = 0*. In this case, we return `NaN`

.

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)

[Package *abdiv* version 0.2.0 Index]