composition_stats.multiplicative_replacement

composition_stats.multiplicative_replacement(mat, delta=None)

Replace all zeros with small non-zero values

It uses the multiplicative replacement strategy [1] , replacing zeros with a small positive \(\delta\) and ensuring that the compositions still add up to 1.

Parameters

mat: array_like

a matrix of proportions where rows = compositions and columns = components each composition (row) must add up to unity (see closure())

delta: float, optional

a small number to be used to replace zeros If delta is not specified, then the default delta is \(\delta = \frac{1}{N^2}\) where \(N\) is the number of components

Returns

numpy.ndarray, np.float64

A matrix of proportions where all of the values are nonzero and each composition (row) adds up to 1

Raises

ValueError

Raises an error if negative proportions are created due to a large delta.

Notes

This method will result in negative proportions if a large delta is chosen.

References

1

J. A. Martin-Fernandez. “Dealing With Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation”

Examples

>>> import numpy as np
>>> from composition_stats import multiplicative_replacement
>>> X = np.array([[.2,.4,.4, 0],[0,.5,.5,0]])
>>> multiplicative_replacement(X)
array([[ 0.1875,  0.375 ,  0.375 ,  0.0625],
       [ 0.0625,  0.4375,  0.4375,  0.0625]])