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Bhattacharyya distance

Source: R/beta_div.r
bhattacharyya.Rd

Measures the similarity of two probability distributions.

Usage

bhattacharyya(counts, margin = 1L, pairs = NULL, cpus = n_cpus())

Arguments

counts

A numeric matrix of count data (samples \(\times\) features). Typically contains absolute abundances (integer counts), though proportions are also accepted.

margin

The margin containing samples. 1 if samples are rows, 2 if samples are columns. Ignored when counts is a special object class (e.g. phyloseq). Default: 1

pairs

Which combinations of samples should distances be calculated for? The default value (NULL) calculates all-vs-all. Provide a numeric or logical vector specifying positions in the distance matrix to calculate. See examples.

cpus

How many parallel processing threads should be used. The default, n_cpus(), will use all logical CPU cores.

Details

The Bhattacharyya distance is defined as: $$-\ln{\sum_{i=1}^{n}\sqrt{P_{i}Q_{i}}}$$

Where:

  • \(P_i\), \(Q_i\) : Proportional abundances of the \(i\)-th feature.

  • \(n\) : The number of features.

Base R Equivalent:

x <- ex_counts[1,]; p <- x / sum(x)
y <- ex_counts[2,]; q <- y / sum(y)
-log(sum(sqrt(p * q)))

Input Types

The counts parameter is designed to accept a simple numeric matrix, but seamlessly supports objects from the following biological data packages:

  • phyloseq

  • rbiom

  • SummarizedExperiment

  • TreeSummarizedExperiment

For large datasets, standard matrix operations may be slow. See vignette('performance') for details on using optimized formats (e.g. sparse matrices) and parallel processing.

References

Bhattacharyya, A. (1943). On a measure of divergence between two statistical populations defined by their probability distributions. Bulletin of the Calcutta Mathematical Society, 35, 99-109.

See also

beta_div(), vignette('bdiv'), vignette('bdiv_guide')

Other Abundance metrics: aitchison(), bray(), canberra(), chebyshev(), chord(), clark(), divergence(), euclidean(), gower(), hellinger(), horn(), jensen(), jsd(), lorentzian(), manhattan(), matusita(), minkowski(), morisita(), motyka(), psym_chisq(), soergel(), squared_chisq(), squared_chord(), squared_euclidean(), topsoe(), wave_hedges()

Examples

    bhattacharyya(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.1260663                    
#> Nose  1.8114121 1.6636016          
#> Stool 2.0200478 2.1276915 2.3040081