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Topsoe distance

Source: R/beta_div.r
topsoe.Rd

A symmetric divergence measure based on the Jensen-Shannon divergence.

Usage

topsoe(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 Topsoe distance is defined as: $$\sum_{i=1}^{n}P_i\ln\left(\frac{2P_i}{P_i + Q_i}\right) + \sum_{i=1}^{n}Q_i\ln\left(\frac{2Q_i}{P_i + Q_i}\right)$$

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)
sum(p * log(2 * p / (p+q)), q * log(2 * y / (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

Topsoe, F. (2000). Some inequalities for information divergence and related measures of discrimination. IEEE Transactions on Information Theory, 46(4), 1602-1609. doi:10.1109/18.850703

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(), matusita(), minkowski(), morisita(), motyka(), psym_chisq(), soergel(), squared_chisq(), squared_chord(), squared_euclidean(), wave_hedges()

Examples

    topsoe(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.2275073                    
#> Nose  1.2639597 1.2553101          
#> Stool 1.3288072 1.3353573 1.3430006