skbio.stats.composition.clr#

skbio.stats.composition.clr(mat, axis=-1, validate=True)[source]#

Perform centre log ratio (CLR) transformation.

This function transforms compositions from Aitchison geometry to the real space. The \(clr\) transform is both an isometry and an isomorphism defined on the following spaces:

\[clr: S^D \rightarrow U\]

where \(U= \{x :\sum\limits_{i=1}^D x = 0 \; \forall x \in \mathbb{R}^D\}\)

It is defined for a composition \(x\) as follows:

\[clr(x) = \ln\left[\frac{x_1}{g_m(x)}, \ldots, \frac{x_D}{g_m(x)}\right]\]

where \(g_m(x) = (\prod\limits_{i=1}^{D} x_i)^{1/D}\) is the geometric mean of \(x\).

Parameters:
matarray_like of shape (…, n_components, …)

A matrix of positive proportions.

axisint, optional

Axis along which CLR transformation will be performed. Each vector on this axis is considered as a composition. Default is the last axis (-1).

validatebool, default True

Check if the matrix consists of strictly positive values.

Returns:
ndarray of shape (…, n_components, …)

CLR-transformed matrix.

See also

clr_inv

Examples

>>> import numpy as np
>>> from skbio.stats.composition import clr
>>> x = np.array([.1, .3, .4, .2])
>>> clr(x)
array([-0.79451346,  0.30409883,  0.5917809 , -0.10136628])
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