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Squared Chi-Squared distance

Source: R/beta_div.r
squared_chisq.Rd

The squared version of the Chi-Squared distance.

Usage

squared_chisq(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 Squared \(\chi^2\) distance is defined as: $$\sum_{i=1}^{n}\frac{(P_i - Q_i)^2}{P_i + Q_i}$$

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

Cha, S.-H. (2007). Comprehensive survey on distance/similarity measures between probability density functions. International Journal of Mathematical Models and Methods in Applied Sciences, 1(4), 300–307.

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_chord(), squared_euclidean(), topsoe(), wave_hedges()

Examples

    squared_chisq(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.4240934                    
#> Nose  1.8915694 1.8927775          
#> Stool 1.9639806 1.9664677 1.9695393