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| = \sqrt{\sum_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]