Question

I have to create unique combination while allowing some mismatches. The following is an example:

set.seed (1234)
dataf <- data.frame (var1 = sample( c("A", "B", "-"),20, replace = T),
            var2 = sample( c("A"),20, replace = T),
            var3 = sample( c("B", "B", "B", "-"),20, replace = T),
            var4 = sample( c("A","A", "A",  "-"),20, replace = T),
            var5 = sample( c("A", "B", "A", "A", "-"),20, replace = T)
            )
 dataf

Rules:

(1) Generate Unique combinations:

     A B     A  B  B   - combination 1
    A  A     A  B  B    - combination 2
    B  B     B  A  A    - combination 3 
   so on ...

(2) Allow one (can be n) mismatch to create a category. For example:

A   B    A  B  B
A   A    A  B  B
B   A    A  B  B
B   A    B  B  B 
B   A    A  B  A

are same as there a single mismatch at different variables.

(3) “-” indicates missing values, can be treated as similar way as integers in matching means that one mismatch allowed.

A   B    A  B  B
 A   -    A  B  B
 A   B    A  -  B

However if there are two missing values then combination is declared unknown (-)

 A   B    A  B  B
 A   -    A  -  B
 A   B    A  -  -

The following is workout for the above data.

    var1 var2 var3 var4 var5       comb
1     A    A    B    -    -       -

2     B    A    B    A    A        1
3     B    A    B    A    A        1
4     B    A    B    A    A        1
5     -    A    B    A    A        1
6     B    A    B    A    -        1

7     A    A    B    A    B        2
8     A    A    B    A    B        2

9     B    A    B    A    A        1

10    B    A    -    A    -        -

11    -    A    B    A    A        1

12    B    A    B    -    -        -

13    A    A    B    A    A        2

14    -    A    B    -    A        -

15    A    A    B    A    A        2
16    -    A    B    A    A        2
17    A    A    B    A    B        2

18    A    A    -    A    A        3

19    A    A    B    A    B        2

20    A    A    -    A    A        3

Any idea ?

Answer 1

Here is how I would do it. The idea is create a distance matrix, so you can cluster your data into groups of rows that have a zero distance among them.

First, let’s remove (temporarily) the rows that have two or more dashes:

two.dashes <- apply(dataf, 1, function(x)sum(x == '-') >= 2)
subdata <- dataf[!two.dashes,]

Then, let’s compute a distance matrix.

mydist.fun <- function(i, j, x = subdata) {
   row.i <- x[i, ]
   row.j <- x[j, ]
   idx   <- row.i != '-' & row.j != '-'
   sum(row.i[idx] != row.j[idx])
}
rows.idx  <- seq_len(nrow(subdata))
rows.dist <- as.dist(outer(rows.idx, rows.idx, Vectorize(mydist.fun)))

Then, let’s use clustering to group your data. I am using a complete hierarchical clustering and cutting it at height = 0, i.e., it creates groups of points that all have a distance of zero among them.

hc <- hclust(rows.dist)
members <- cutree(hc, h = 0)

Let’s put everything together:

comb <- rep('-', nrow(dataf))
comb[!two.dashes] <- members
dataf$comb <- comb
dataf
#    var1 var2 var3 var4 var5 comb
# 1     A    A    B    -    -    -
# 2     B    A    B    A    A    1
# 3     B    A    B    A    A    1
# 4     B    A    B    A    A    1
# 5     -    A    B    A    A    1
# 6     B    A    B    A    -    1
# 7     A    A    B    A    B    2
# 8     A    A    B    A    B    2
# 9     B    A    B    A    A    1
# 10    B    A    -    A    -    -
# 11    -    A    B    A    A    1
# 12    B    A    B    -    -    -
# 13    A    A    B    A    A    3
# 14    -    A    B    -    A    -
# 15    A    A    B    A    A    3
# 16    -    A    B    A    A    1
# 17    A    A    B    A    B    2
# 18    A    A    -    A    A    3
# 19    A    A    B    A    B    2
# 20    A    A    -    A    A    3

This is exposing contradictions in your expected output. For example, row 7 and 13 should not belong to the same group. Also, there are rows with a single dash that could go to different groups, e.g. row 16.