Skip to contents

Chord distance

Source: R/beta_div.r
chord.Rd

Euclidean distance between normalized vectors.

Usage

chord(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 Chord distance is defined as: $$\sqrt{\sum_{i=1}^{n} \left(\frac{X_i}{\sqrt{\sum_{j=1}^{n} X_j^2}} - \frac{Y_i}{\sqrt{\sum_{j=1}^{n} Y_j^2}}\right)^2}$$

Where:

  • \(X_i\), \(Y_i\) : Absolute counts of the \(i\)-th feature.

  • \(n\) : The number of features.

Base R Equivalent:

x <- ex_counts[1,]
y <- ex_counts[2,]
sqrt(sum(((x / sqrt(sum(x ^ 2))) - (y / sqrt(sum(y ^ 2))))^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

Orlóci, L. (1967). An agglomerative method for classification of plant communities. Journal of Ecology, 55(1), 193-206. doi:10.2307/2257725

See also

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

Other Abundance metrics: aitchison(), bhattacharyya(), bray(), canberra(), chebyshev(), 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

    chord(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.7126859                    
#> Nose  1.3939318 1.3874634          
#> Stool 1.4067198 1.4093819 1.4104270