R - Divide each value in matrix by maximum value of its row/column

Question

I'm trying to transform the values in a matrix by dividing each value by the lesser of the maximum values of its column or row name. I am having trouble because I don't know how to query the row/column for a particular value from inside a larger function.

A small cut of the data looks like this: a weighted (symmetrical) adjacency matrix, mat:

              Acousmatic Acoustic Afro-beat Alternative Ambient
  Acousmatic         125       11         3           3       1
  Acoustic            11   112398      1810       24216    3824
  Afro-beat            3     1810     10386        1220     298
  Alternative          3    24216      1220      103286    2838
  Ambient              1     3824       298        2838   20400

As an example, I want to transform the value of "Alternative-Acoustic" (24216) by finding the maximum value for "Acoustic" given by its diagonal (112398) and the maximum value for "Alternative" given by its diagonal (103286), and by dividing "Alternative-Acoustic" (24216) by the lesser of those two numbers. So in this case, the lesser would be "Alternative," so I want to transform the "Alternative-Acoustic" value with 24216/103286=~.2345.

I want to automatically perform this transformation for all values in this matrix, which would result in a matrix with values ranging from 0-1 with the diagonals as all 1's.

I tried the following in many different iterations with "mat" as both a matrix and a data frame, but I do not know how to correctly query the row and column maximums for each value in the matrix. This is using nonexistent functions ('colmax' and 'rowmax'), but I think it most clearly expresses what I want to do:

transformedmat <- apply(mat,1:2, function(x) x/min(colmax(x),rowmax(x)))

I also tried to write an embedded function, but that ended poorly, and I'm wondering if there's a simpler solution:

rescalemat <- function(mat){
    apply(mat, 1, function(x){
    colmax<-apply(mat, 2, function(x) max(x))
    rowmax<-apply(mat, 1, function(x) max(x))
    x/min(colmax,rowmax)
    mat
})
}

Any help would be greatly appreciated.

Thanks.

Answer 1

try this:

A1 = mat/apply(mat,1,max)
A2 = t(t(mat)/apply(mat,2,max))
result = ifelse(A1>A2,A1,A2)

Answer 2

Unless I've missed something, this approach looks valid too:

res = diag(mat)
#names(res) = colnames(mat)       
mat / outer(res, res, pmin) 

#            Acousmatic  Acoustic  Afro.beat Alternative    Ambient
#Acousmatic       1.000 0.0880000 0.02400000   0.0240000 0.00800000
#Acoustic         0.088 1.0000000 0.17427306   0.2344558 0.18745098
#Afro-beat        0.024 0.1742731 1.00000000   0.1174658 0.02869247
#Alternative      0.024 0.2344558 0.11746582   1.0000000 0.13911765
#Ambient          0.008 0.1874510 0.02869247   0.1391176 1.00000000

Where mat is:

mat = structure(c(125L, 11L, 3L, 3L, 1L, 11L, 112398L, 1810L, 24216L, 
3824L, 3L, 1810L, 10386L, 1220L, 298L, 3L, 24216L, 1220L, 103286L, 
2838L, 1L, 3824L, 298L, 2838L, 20400L), .Dim = c(5L, 5L), .Dimnames = list(
    c("Acousmatic", "Acoustic", "Afro-beat", "Alternative", "Ambient"
    ), c("Acousmatic", "Acoustic", "Afro.beat", "Alternative", 
    "Ambient")))