Determine what is the closest x,y point to the center of a cluster

Question

I have the following data with random clusters:

iris$cluster = sample(0:1, nrow(iris), replace=TRUE)

Now I calculate the centers of the two clusters using the following code:

centers=iris %>% 
 group_by(cluster) %>% 
 summarise_at(vars(matches("Sepal")), mean)

Now I would like to calculates for each row in the dataset whether they are closer to the center of cluster 1 of the center of cluster 2. So basically the euclidean distance of center 0 vs 1 for row 1,2,3 etc....

Any thoughts on what is the most efficient what to do this is R?

The problem of finding the distance of points to the center has been solved here (remember Pythagaros): [https://stackoverflow.com/questions/5559384/euclidean-distance-of-two-vectors](https://stackoverflow.com/questions/5559384/euclidean-distance-of-two-vectors) and [https://stackoverflow.com/questions/35099730/calculating-the-distance-from-center-to-each-data-points](https://stackoverflow.com/questions/35099730/calculating-the-distance-from-center-to-each-data-points) — Manuel Bickel, Feb 26 '18 at 09:08
Possible duplicate of [calculating the distance from center to each data points](https://stackoverflow.com/questions/35099730/calculating-the-distance-from-center-to-each-data-points) — Manuel Bickel, Feb 26 '18 at 09:08

score 1 · Accepted Answer · answered Feb 26 '18 at 09:19

Depending on the dimensionality of your problem, one method is to create a permutation of centers with each row and then find the minimum for each row

library(data.table)
library(microbenchmark)

#create data
DT <- setDT(copy(iris))
set.seed(0L)
cols <- grep("^Sepal", names(DT), value=TRUE)
centers <- DT[, lapply(.SD, mean), 
    by=.("cluster"=sample(0:1, nrow(iris), replace=TRUE)), 
    .SDcols=cols]
setnames(centers, cols, paste0("mean_", cols))

CJ.dft <- function(...) {
    Reduce(f=function(x, y) cbind(x[rep(1:nrow(x), times=nrow(y)),], y[rep(1:nrow(y), each=nrow(x)),]),
        x=list(...)[-1],
        init=..1)
} #CJ.dft

crossJoinMtd <- function() {
    #cross join data with centers
    ans <- CJ.dft(DT[, rn:=.I], centers)

    #find the closest cluster
    ans[,
        .(ClosestCluster=cluster[which.min((Sepal.Length - mean_Sepal.Length)^2 + (Sepal.Width - mean_Sepal.Width)^2)]), 
        by=.(rn)]
}

Sample usage:

crossJoinMtd()
#      rn ClosestCluster
#  1:   1              1
#  2:   2              0
#  3:   3              0
#  4:   4              0
#  5:   5              1
# ---                   
#146: 146              1
#147: 147              0
#148: 148              1
#149: 149              1
#150: 150              0

some timings:

microbenchmark(crossJoinMtd(),
    times=100L)

# Unit: milliseconds
#           expr    min      lq     mean  median      uq     max neval
# crossJoinMtd() 2.7325 3.03085 3.558447 3.26885 3.58805 14.6075   100

If OP can provide more details on the number of clusters or dimensionalities, it probably can be further optimized.

Determine what is the closest x,y point to the center of a cluster

1 Answers1