How to get the closest element in a vector for every element in another vector without duplicates?

Question

I got this code which create two vectors and for each element from a I want to get the closest element in b :

a = rnorm(100)
b = rnorm(100)
c = vapply(a, function(x) which.min(abs(b - x)), 1)
table(duplicated(c))

FALSE  TRUE 
   61    39 

As you can see this method is prompt to give a lot of duplicates which is normal but I would like to not have duplicates. I thought of deleting occurence from b once an index has been selected but I don't know how to do it under vapply .

Answer 1

The closest match you are going to get is by sorting the vectors and then pairing them off. The following permuation on b should allow you to do that.

p <- order(b)[order(order(a))] # order on b and then back transform the ordering of a

sum(abs(a-b[p]))
[1] 20.76788

Clearly, allowing duplicates does make things much closer:

sum(abs(a-b[c]))
[1] 2.45583

Answer 2

I believe this is the best you can get: sum(abs(sort(a) - sort(b)))

I am using data.table to preserve the original sorting of a :

require(data.table)

set.seed(1)

a <- rnorm(100)
b <- rnorm(100)

sum(abs(a - b))
sum(abs(sort(a) - sort(b)))

dt <- data.table(a = a, b = b)
dt[, id := .I]

# sort dt by a
setkey(dt, a)

# sort b
dt[, b := sort(b)]

# return to original order
setkey(dt, id)

dt
dt[, sum(abs(a - b))]

This solution gives better result if compared to Chase's solution:

dt2 <- as.data.table(foo(a,b))
dt2[, sum(abs(a - bval))]
dt[, sum(abs(a - b))]

Result:

> dt2[, sum(abs(a - bval))]
[1] 24.86731
> dt[, sum(abs(a - b))]
[1] 20.76788

Answer 3

This is very bad programming, but may work and is vectorized...

   a <- rnorm(100)
   b <- rnorm(100)
   #make a copy of b (you'll see why)
   b1<-b
   res<- vapply(a, function(x) {ret<-which.min(abs(b1 - x));b1[ret]<<-NA;return(ret)}, 1)

Answer 4

This can almost certainly be improved upon through vectorization, but appears to work and may get the job done:

set.seed(1)
a = rnorm(5)
b = rnorm(5)

foo <- function(a,b) {

  out <- cbind(a, bval = NA)

  for (i in seq_along(a)) {
    #which value of B is closest?
    whichB <- which.min(abs(b - a[i]))
    #Assign that value to the bval column
    out[i, "bval"] <- b[whichB]
    #Remove that value of B from being chosen again
    b <- b[-whichB]
  }

  return(out)

}

#In action
foo(a,b)
---
              a       bval
[1,] -0.6264538 -0.8204684
[2,]  0.1836433  0.4874291
[3,] -0.8356286 -0.3053884
[4,]  1.5952808  0.7383247
[5,]  0.3295078  0.5757814