Matrix of distances from two separate data frames

Question

I would like to create a matrix containing the Euclidean distance of rows from one data frame compared to rows from another. For example, let's say I have the following data frames:

a <- c(1,2,3,4,5)
b <- c(5,4,3,2,1)
c <- c(5,4,1,2,3)
df1 <- data.frame(a,b,c)

a2 <- c(2,7,1,2,3)
b2 <- c(7,6,5,4,3)
c2 <- c(1,2,3,4,5)
df2 <- data.frame(a2,b2,c2)

I would like to create a matrix with the distances of each row in df1 compared to the rows of df2.

So, the matrix [2,1] should be the Euclidean distance between df1 [2,] and df2 [1,]. matrix [3,2] the distance between df [3,] and df2 [2,] etc.

Does anyone know how this can be achieved?

Answer 1

Perhaps you can use a package fields: a function rdistcan do what you want:

rdist:
  : .

> rdist(df1, df2)
     [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 4.582576 6.782330 2.000000 1.732051 2.828427
[2,] 4.242641 5.744563 1.732051 0.000000 1.732051
[3,] 4.123106 5.099020 3.464102 3.316625 4.000000
[4,] 5.477226 5.000000 4.358899 3.464102 3.316625
[5,] 7.000000 5.477226 5.656854 4.358899 3.464102

pdist

pdist:
  : X Y.

> pdist(df1, df2)
An object of class "pdist"
Slot "dist":
[1] 4.582576 6.782330 2.000000 1.732051 2.828427 4.242640 5.744563 1.732051
[9] 0.000000 1.732051 4.123106 5.099020 3.464102 3.316625 4.000000 5.477226
[17] 5.000000 4.358899 3.464102 3.316625 7.000000 5.477226 5.656854 4.358899
[25] 3.464102
attr(,"Csingle")
[1] TRUE

Slot "n":
[1] 5

Slot "p":
[1] 5

Slot ".S3Class":
[1] "pdist"

#

. , :

a <- c(1,2,3,4,5)
b <- c(5,4,3,2,1)
c <- c(5,4,1,2,3)
df1 <- rbind(a, b, c)

a2 <- c(2,7,1,2,3)
b2 <- c(7,6,5,4,3)
c2 <- c(1,2,3,4,5)
df2 <- rbind(a2,b2,c2)

rdist(df1, df2)

:

> rdist(df1, df2)
         [,1]     [,2]     [,3]
[1,] 6.164414 7.745967 0.000000
[2,] 5.099020 4.472136 6.324555
[3,] 4.242641 5.291503 5.656854

Answer 2

.

n - ( R, ):

square_dist(b,a) = sum_i(b[i]*b[i]) + sum_i(a[i]*a[i]) - 2*inner_prod(b,a)

a b i=[1,n]. a b - df1 df2, . , df1 df2.

:

d <- sqrt(matrix(rowSums(expand.grid(rowSums(df1*df1),rowSums(df2*df2))),
                 nrow=nrow(df1)) - 
          2. * as.matrix(df1) %*% t(as.matrix(df2)))

:

• rowSums sum_i(a[i]*a[i]) sum_i(b[i]*b[i]) a df1 b df2 .
• expand.grid df1 df2.
• rowSums sum_i(a[i]*a[i]) + sum_i(b[i]*b[i]) .
• matrix. , - df1.
• . df1 %*% t(df2), .
• , .

:

print(d)
##         [,1]     [,2]     [,3]     [,4]     [,5]
##[1,] 4.582576 6.782330 2.000000 1.732051 2.828427
##[2,] 4.242641 5.744563 1.732051 0.000000 1.732051
##[3,] 4.123106 5.099020 3.464102 3.316625 4.000000
##[4,] 5.477226 5.000000 4.358899 3.464102 3.316625
##[5,] 7.000000 5.477226 5.656854 4.358899 3.464102

, n > 1. n=3.