How do I compare each element in a list with each other element and outpt the results as a pairwise comparison matrix in R?

Question

I am trying to automate the process of calculating Jaccard's index of similarity for every possible pair of sites surveyed in a recent vegetation study.

Below is a dummy list in the format of my data, where x, y, and z are discrete survey sites, and function jaccard().

x <- c("sp1","sp2","sp3")
y <- c("sp2","sp3","sp4")
z <- c("sp3","sp4","sp5")
dummy_list <- list(x,y,z)

jaccard <- function(a, b) {
intersection = length(intersect(a, b))
union = length(a) + length(b) - intersection
return (intersection/union) }

I want to pass each pairwise comparison (x-y, x-z, y-z) to jaccard() and output a matrix of calculated Jaccard indicies. How can I achieve this?

Answer 1

We could first Vectorize your jaccard function and then use outer:

x <- c("sp1","sp2","sp3")
y <- c("sp2","sp3","sp4")
z <- c("sp3","sp4","sp5")

dummy_list <- setNames(list(x, y, z), c("x","y","z"))

jaccard <- function(a, b) {
  intersection = length(intersect(a, b))
  union = length(a) + length(b) - intersection
  return (intersection/union)
}

vjaccard <- Vectorize(jaccard)

outer(dummy_list, dummy_list, FUN = "vjaccard")
#>     x   y   z
#> x 1.0 0.5 0.2
#> y 0.5 1.0 0.5
#> z 0.2 0.5 1.0

^{Created on 2022-03-02 by the reprex package (v2.0.1)}

Answer 2

jaccard <- function(List) {
  ln <- combn(List, 2,function(x){
    n <- length(intersect(x[[1]], x[[2]]))
    m <- length(unlist(x))
    n/(m-n)})
  structure(ln, Size = length(ln), Diag = FALSE, class = 'dist')
}

jaccard(dummy_list)
    1   2
2 0.5    
3 0.2 0.5

Answer 3

We can use the following base R approach (without using the jaccard function but following the same definition)

> dummy_list <- list(x = x, y = y, z = z)

> 1 / (outer(lengths(dummy_list), lengths(dummy_list), `+`) / crossprod(table(stack(dummy_list))) - 1)
    x   y   z
x 1.0 0.5 0.2
y 0.5 1.0 0.5
z 0.2 0.5 1.0