Comprehensive matching across a list of vectors - r

Question

I am trying to match between all available combinations of vectors.
For example, i have 4 vectors:
a<-c(1,2,3,4)
b<-c(1,2,6,7)
c<-c(1,2,8,9)
d<-c(3,6,8,2)
The intended output should be able to tell me:
similarity between a & b: 1, 2
similarity between a & c: 1, 2
similarity between a & d: 2, 3
similarity between b & c: 1, 2
similarity between b & d: 2, 6
similarity between c & d: 2, 8
similarity between a & b & c: 1, 2
similarity between b & c & d: 2
similarity between a & c & d: 2
similarity between a & b & d: 2
similarity between a & b & c & d: 2
Does R have a function that does such comparison/ matching?
For simplicity, the number of vectors is set at 4 for now. I am in fact dealing with 100s of vectors and would like to match/intersect/compare between all possible combinations of vectors. For example with 4 vectors, there will be a possible 4C2+4C3+4C4=11 available combinations. With 100 vectors, there will be a possible 100C100+ 100C99+100C98+...+100C2 available combinations
thanks in advance

Answer 1

intersect seems to do what you want. It only does pairs of vectors at a time though eg
intersect(a, b) # 1 2
intersect(b, intersect(c, d)) # 2
If you want a shorthand to intersect more than 2, try Reduce (?Reduce)
# intersection of a/b/c/d
Reduce(intersect, list(a, b, c, d), a)
# intersection of b/c/d
Reduce(intersect, list(b, c, d), b)
Reduce will successively apply intersect to the list and the result of the previous intersect call, starting with intersect(b, b) (the init argument I just set to one of the vectors to be intersected, as the intersection of a set with itself is the set).
If you wanted a way to go through all (pairs, tuples, quadruples) of (a, b, c, d) and return the intersection, you could try
generate all combinations of (a, b, c, d) in lengths 2 (pairs), 3 (tuples), 4 (quadruples)
combos = lapply(2:4, combn, x=c('a', 'b', 'c', 'd'), simplify=F)
# [[1]]
# [[1]][[1]]
# [1] "a" "b"
# [[1]][[2]]
# [1] "a" "c"
# ...
# [[2]]
# [[2]][[1]]
# [1] "a" "b" "c"
# [[2]][[2]]
# [1] "a" "b" "d"
# ...
# [[3]]
# [[3]][[1]]
# [1] "a" "b" "c" "d"
Flatten it out to just a list of character vectors
combos = unlist(combos, recursive=F)
# [[1]]
# [1] "a" "b"
# ...
# [[10]]
# [1] "b" "c" "d"
# [[11]]
# [1] "a" "b" "c" "d"
For each set, call Reduce as specified above. We can use (e.g.) get("a") to get the variable a; or mget(c("a", "b", "c") to get the variables a, b, c in a list. If your variables are columns in a dataframe, then you can modify appropriately.
intersects = lapply(combos, function (varnames) {
Reduce(intersect, mget(varnames, inherits=T), get(varnames[1]))
})
# add some labels for clarity.
# You will probably actually want to /do/ something with the
# resulting intersections rather than this.
names(intersects) <- sapply(combos, paste, collapse=", ")
intersects
# $`a, b`
# [1] 1 2
# $`a, c`
# [1] 1 2
# ...
# $`a, b, c, d`
# [1] 2
You will need to modify to suit how your data is in R; e.g. columns of a dataframe vs named vectors in the workspace and so on.
You might also just prefer a for loop from step 3. onwards rather than all the *apply depending on what you want to do with the result. (Plus, if you have many vectors, holding all the intersections simultaneously in memory might not be a good idea anyway).