Find best match of two vectors with different length in R

Question

From two vectors (a, b) with increasing integers and eventually different lengths, I want to extract two vectors both with length n (=5) that lead to the smallest difference when subtracting a from b.

Example

a<-c(25,  89, 159, 224, 292, 358)

b<-c(1, 19,  93, 155, 230, 291)

Subtracting the following elements leads to the smallest difference:

c(25-19, 89-93, 159-155, 225-230, 291-292)

From a, 358 is excluded

From b, 1 is excluded.

The Problem: The length of the vectors can vary:

Examples

a<-c(25,  89, 159, 224, 292, 358)

b<-c(19,  93, 155, 230, 291)


a<-c(25,  89, 159, 224, 292, 358, 560)

b<-c(19,  93, 155, 230, 291)


a<-c(25,  89, 159, 224, 292, 358)

b<-c(1 , 5, 19,  93, 155, 230, 291)

Because I have to find this “best match” for >1000 vectors, I would like to built a function that takes as input the two vectors with different lengths and gives me as output the two vectors with length n=5 that lead to the smallest difference.

Answer 1

This works by brute force. The columns of combn.a and combn.b are the combinations of 5 elements from a and b . Each row of the two column data frame g is a pair of column numbers of combn.a and combn.b respectiively. f evaluates the sum of absolute differences of the a and b subsets corresponding to a row r of g . v is the distance values found, one per row of g , with ix being the row number in g having the least distance. From g[ix,] we can have the column numbers of the minimizer in comb.a and combn.b and from those we determine the corresponding a and b subsets.

align5 <- function(a, b) {
   combn.a <- combn(a, 5)
   combn.b <- combn(b, 5)
   g <- expand.grid(a = 1:ncol(combn.a), b = 1:ncol(combn.b))
   f <- function(r) sum(abs(combn.a[, r[1]] - combn.b[, r[2]]))
   v <- apply(g, 1, f)
   ix <- which.min(v)
   rbind( combn.a[, g[ix, 1] ], combn.b[,g[ix, 2] ] )
}

# test

a <- c(25,  89, 159, 224, 292, 358)
b <- c(1, 19,  93, 155, 230, 291)
align5(a, b)
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   25   89  159  224  292
## [2,]   19   93  155  230  291