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Manhattan

Source: R/beta_div.r
manhattan.Rd

Manhattan beta diversity metric.

Usage

manhattan(counts, weighted = TRUE, pairs = NULL, cpus = n_cpus())

Arguments

counts

An OTU abundance matrix where each column is a sample, and each row is an OTU. Any object coercible with as.matrix() can be given here, as well as phyloseq, rbiom, SummarizedExperiment, and TreeSummarizedExperiment objects.

weighted

If TRUE, the algorithm takes relative abundances into account. If FALSE, only presence/absence is considered.

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.

Value

A dist object.

Calculation

In the formulas below, x and y are two columns (samples) from counts. n is the number of rows (OTUs) in counts.

$$D = \displaystyle \sum_{i = 1}^{n} |x_i - y_i|$$

  x <- c(4, 0, 3, 2, 6)
  y <- c(0, 8, 0, 0, 5)
  sum(abs(x-y))
  #>  18

References

Paul EB 2006. Manhattan distance. Dictionary of Algorithms and Data Structures. https://xlinux.nist.gov/dads/HTML/manhattanDistance.html

See also

Other beta_diversity: bray_curtis(), canberra(), euclidean(), generalized_unifrac(), gower(), jaccard(), kulczynski(), unweighted_unifrac(), variance_adjusted_unifrac(), weighted_normalized_unifrac(), weighted_unifrac()

Examples

    # Example counts matrix
    ex_counts
#>                   Saliva Gums Nose Stool
#> Streptococcus        162  793   22     1
#> Bacteroides            2    4    2   611
#> Corynebacterium        0    0  498     1
#> Haemophilus          180   87    2     1
#> Propionibacterium      1    1  251     0
#> Staphylococcus         0    1  236     1
    
    # Manhattan weighted distance matrix
    manhattan(ex_counts)
#>       Saliva Gums Nose
#> Gums     727          
#> Nose    1302 1841     
#> Stool    952 1487 1614
    
    # Manhattan unweighted distance matrix
    manhattan(ex_counts, weighted = FALSE)
#>       Saliva Gums Nose
#> Gums       1          
#> Nose       2    1     
#> Stool      3    2    1
    
    # Only calculate distances for A vs all.
    manhattan(ex_counts, pairs = 1:3)
#>       Saliva Gums Nose
#> Gums     727          
#> Nose    1302   NA     
#> Stool    952   NA   NA