Calculating all distances between one point and a group of points efficiently in R

Question

First of all, I am new to R (I started yesterday).

I have two groups of points, data and centers, the first one of size n and

Answer 1

dist works fast because is't vectorized and call internal C functions.
You code in loop could be vectorized in many ways.

For example to compute distance between data and centers you could use outer:

diff_ij <- function(i,j) sqrt(rowSums((data[i,]-centers[j,])^2))
X <- outer(seq_len(n), seq_len(K), diff_ij)

This gives you n x K matrix of distances. And should be way faster than loop.

Then you could use max.col to find maximum in each row (see help, there are some nuances when are many maximums). X must be negate cause we search for minimum.

CL <- max.col(-X)

To be efficient in R you should vectorized as possible. Loops could be in many cases replaced by vectorized substitute. Check help for rowSums (which describe also rowMeans, colSums, rowSums), pmax, cumsum. You could search SO, e.g. https://stackoverflow.com/search?q=[r]+avoid+loop (copy&paste this link, I don't how to make it clickable) for some examples.

Answer 2

rdist() is a R function from {fields} package which is able to calculate distances between two sets of points in matrix format quickly.

https://www.image.ucar.edu/~nychka/Fields/Help/rdist.html

Usage :

library(fields)
#generating fake data
n <- 5
m <- 10
d <- 3

x <- matrix(rnorm(n * d), ncol = d)
y <- matrix(rnorm(m * d), ncol = d)

rdist(x, y)
          [,1]     [,2]      [,3]     [,4]     [,5]
 [1,] 1.512383 3.053084 3.1420322 4.942360 3.345619
 [2,] 3.531150 4.593120 1.9895867 4.212358 2.868283
 [3,] 1.925701 2.217248 2.4232672 4.529040 2.243467
 [4,] 2.751179 2.260113 2.2469334 3.674180 1.701388
 [5,] 3.303224 3.888610 0.5091929 4.563767 1.661411
 [6,] 3.188290 3.304657 3.6668867 3.599771 3.453358
 [7,] 2.891969 2.823296 1.6926825 4.845681 1.544732
 [8,] 2.987394 1.553104 2.8849988 4.683407 2.000689
 [9,] 3.199353 2.822421 1.5221291 4.414465 1.078257
[10,] 2.492993 2.994359 3.3573190 6.498129 3.337441

Answer 3

My solution:

# data is a matrix where each row is a point
# point is a vector of values
euc.dist <- function(data, point) {
  apply(data, 1, function (row) sqrt(sum((point - row) ^ 2)))
}

You can try it, like:

x <- matrix(rnorm(25), ncol=5)
euc.dist(x, x[1,])

Answer 4

You may want to have a look into the apply functions.

For instance, this code

for (j in 1:K)
    {
    d[j] <- sqrt(sum((centers[j,] - data[i,])^2))
    }

Can easily be substituted by something like

dt <- data[i,]
d <- apply(centers, 1, function(x){ sqrt(sum(x-dt)^2)})

You can definitely optimise it more but you get the point I hope

Answer 5

Rather than iterating across data points, you can just condense that to a matrix operation, meaning you only have to iterate across K.

# Generate some fake data.
n <- 3823
K <- 10
d <- 64
x <- matrix(rnorm(n * d), ncol = n)
centers <- matrix(rnorm(K * d), ncol = K)

system.time(
  dists <- apply(centers, 2, function(center) {
    colSums((x - center)^2)
})
)

Runs in:

utilisateur     système      écoulé 
      0.100       0.008       0.108 

on my laptop.