How to calculate the euclidean distance in R between two matrices each with unequal dimensions

Question

How to calculate the euclidean distance in R between Matrix A and Matrix B as per below:

I have two matrices that is Matrix A and Matrix B

Matrix A:

     [,1][,2]
[1,]   1   1   
[2,]   1   2   
[3,]   2   1   
[4,]   2   2   
[5,]   10  1   
[6,]   10  2   
[7,]   11  1   
[8,]   11  2   
[9,]   5   5   
[10,]  5   6

Matrix B:

     [,1][,2][,3][,4][,5][,6]
[1,]   2   1   5   5  10   1
[2,]   1   1   2   1  10   1
[3,]   5   5   5   6  11   2
[4,]   2   2   5   5  10   1
[5,]   2   1   5   6  5    5
[6,]   2   2   5   5  11   1
[7,]   2   1   5   5  10   1
[8,]   1   1   5   6  11   1
[9,]   2   1   5   5  10   1
[10,]  5   6   11  1  10   2


I want the Result matrix (euclidean distance) to be as per below:

        [1,]  [,2]  [,3]

    [1,] 1.00  5.66  9.00
    [2,] 1.00  1.41
    [3,]
    [4,]
    [5,]
    [7,]
    [8,]
    [9,]
    [10]

For every row in Matrix A, calculate the euclidean distance to every two column in each row Matrix B.

For example, to get the answer for the following in result matrix:

        [,1]
    [1,]

The calculation is:

    A(1,1) - From Matrix A
    B(2,1) - From Matrix B

    = sqrt((xA -xB)^2 + (yA -yB)^2)
    = sqrt((1-2)^2 + (1-1)^2)
    = 1.00

    xA and yA from Matrix A
    xB and yB from Matrix B

To get the answer for the following in result matrix:

        [,2]
    [1,] 5.66

The calculation is:

    A(1,1) - From Matrix A
    B(5,5) - From Matrix B

    = sqrt((xA -xB)^2 + (yA -yB)^2)
    = sqrt((1-5)^2 + (1-5)^2)
    = 5.66

To get the answer for the following in result matrix:

        [,3]
    [1,] 9.00

The calculation is:

    A(1,1) - From Matrix A
    B(10,1) - From Matrix B

    = sqrt((xA -xB)^2 + (yA -yB)^2)
    = sqrt((1-10)^2 + (1-1)^2)
    = 9.00

Currently, my codes below only works if Matrix A and B are of equal dimensions:

    distance <- function(MatrixA, MatrixB) {
      resultMatrix <- matrix(NA, nrow=dim(MatrixA)[1], ncol=dim(MatrixB)[1])
      for(i in 1:nrow(MatrixB)) {
         resultMatrix[,i] <- sqrt(rowSums(t(t(MatrixA)-MatrixB[i,])^2))
      }
         resultMatrix
      }

Are you asking for the correct approach (in psuedocode) or the complete code itself? Ideally, you should ask for help with the approach, give the coding a try, and ask for corrections afterwards. I can help with the approach if you like. — Brishna Batool
Hi @BrishnaBatool i have the code but it only works if Matrix A and B are of the same dimensions. I will edit my question and insert the codes. For now yes I would love to know your approach. Any help would be greatly appreciated! — DataMiningStudent

Brishna Batool Brishna Batool · Accepted Answer · 2018-01-05T08:49:17

You just need to change your for loop, so it calculates for each row all three columns of the result matrix:

for(i in 1:nrow(matA)) 
{
  resultMatrix[i,1] <- sqrt(rowSums((t(MatrixA[i,])-MatrixB[i,1:2])^2))
  resultMatrix[i,2] <- sqrt(rowSums((t(MatrixA[i,])-MatrixB[i,3:4])^2))
  resultMatrix[i,3] <- sqrt(rowSums((t(MatrixA[i,])-MatrixB[i,5:6])^2))

}

Generalized for an arbitrary number of columns:

for(i in 1:nrow(MatrixA)) 
{
  for(j in 1:((dim(MatrixB)[2])/2)) 
  {  
    k = (j * 2) - 1
    resultMatrix[i,j] <- sqrt(rowSums((t(MatrixA[i,])-MatrixB[i,k:(k+1)])^2))
  }
}

How to calculate the euclidean distance in R between two matrices each with unequal dimensions

1 Answers