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Canberra distance

Source: R/beta_div.r
canberra.Rd

A weighted version of the Manhattan distance, sensitive to differences when both values are small.

Usage

canberra(
  counts,
  margin = 1L,
  norm = "none",
  pseudocount = NULL,
  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

norm

Normalize the incoming counts. Options are:

  • 'none': No transformation.

  • 'percent': Relative abundance (sample abundances sum to 1).

  • 'binary': Unweighted presence/absence (each count is either 0 or 1).

  • 'clr': Centered log ratio.

Default: 'none'.

pseudocount

Value added to counts to handle zeros when norm = 'clr'. Ignored for other normalization methods. See Pseudocount section.

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 Canberra distance is defined as: $$\sum_{i=1}^{n} \frac{|X_i - Y_i|}{X_i + Y_i}$$

Where:

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

  • \(n\) : The number of features.

Base R Equivalent:

x <- ex_counts[1,]
y <- ex_counts[2,]
sum(abs(x-y) / (x+y))

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.

Pseudocount

The pseudocount parameter is only relevant when norm = 'clr'.

Zeros are undefined in the centered log-ratio (CLR) transformation. If norm = 'clr', pseudocount is NULL (the default), and zeros are detected, the function uses half the minimum non-zero value (min(x[x>0]) / 2) and issues a warning.

To suppress the warning, provide an explicit value (e.g., 1).

Why this matters: The choice of pseudocount is not neutral; it acts as a weighting factor that can significantly distort downstream results, especially for sparse datasets. See Gloor et al. (2017) and Kaul et al. (2017) for open-access discussions on the mathematical implications, or Costea et al. (2014) for the impact on community clustering.

See aitchison for references.

References

Lance, G. N., & Williams, W. T. (1966). Computer programs for hierarchical polythetic classification ("similarity analyses"). The Computer Journal, 9(1), 60-64. doi:10.1093/comjnl/9.1.60

See also

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

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

    canberra(ex_counts)
#>         Saliva     Gums     Nose
#> Gums  2.342381                  
#> Nose  4.730955 5.218026         
#> Stool 5.970155 4.961746 5.227405