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Matusita distance

Source: R/beta_div.r
matusita.Rd

A distance measure closely related to the Hellinger distance.

Usage

matusita(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 Matusita distance is defined as: $$\sqrt{\sum_{i=1}^{n}\left(\sqrt{P_i} - \sqrt{Q_i}\right)^2}$$

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)
sqrt(sum((sqrt(p) - sqrt(q)) ^ 2))

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

Matusita, K. (1955). Decision rules, based on the distance, for problems of fit, two samples, and estimation. The Annals of Mathematical Statistics, 26(4), 631-640. doi:10.1214/aoms/1177728422

See also

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

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

Examples

    matusita(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.4867106                    
#> Nose  1.2935044 1.2732200          
#> Stool 1.3170808 1.3273191 1.3417468