Find closest points (lat / lon) from one data set to a second data set

Question

I have two data sets, A and B, which give locations of different points in the UK as such:

A = data.frame(reference = c(C, D, E), latitude = c(55.32043, 55.59062, 55.60859), longitude = c(-2.3954998, -2.0650243, -2.0650542))

B = data.frame(reference = c(C, D, E), latitude = c(55.15858, 55.60859, 55.59062), longitude = c(-2.4252843, -2.0650542, -2.0650243))

A has 400 rows and B has 1800 rows.
For all the rows in A, I would like to find the shortest distance in kilometers between a point in A and each of the three closest points in B, as well as the reference and coordinates in lat and long of these points in B.

I tried using this post

R - Finding closest neighboring point and number of neighbors within a given radius, coordinates lat-long

However, even when I follow all the instructions, mainly using the command distm from the package geosphere , the distance comes up in a unit that can't possibly be kilometers. I don't see what to change in the code, especially since I am not familiar at all with the geo packages.

Answer 1

I add below a solution using the spatialrisk package. The key functions in this package are written in C++ (Rcpp), and are therefore very fast.

The function spatialrisk::points_in_circle calculates the observations within radius from a center point. Note that distances are calculated using the Haversine formula. Since each element of the output is a data frame, purrr::map_dfr is used to row-bind them together:

purrr::map2_dfr(A$latitude, A$longitude, 
                  ~spatialrisk::points_in_circle(B, .y, .x, 
                                                 lon = longitude, 
                                                 lat = latitude, 
                                                 radius = 1e6)[1:3,], 
                .id = "id_A")

  id_A reference latitude longitude distance_m
1    1         C 55.15858 -2.425284  18115.958
2    1         E 55.59062 -2.065024  36603.447
3    1         D 55.60859 -2.065054  38260.562
4    2         E 55.59062 -2.065024      0.000
5    2         D 55.60859 -2.065054   2000.412
6    2         C 55.15858 -2.425284  53219.597
7    3         D 55.60859 -2.065054      0.000
8    3         E 55.59062 -2.065024   2000.412
9    3         C 55.15858 -2.425284  55031.092

Answer 2

geosphere library has several functions to help you. distGeo returns meters.

Note the data must be arranged Lon then Lat .

library(geosphere)

A = data.frame(longitude = c(-2.3954998, -2.0650243, -2.0650542), latitude = c(55.32043, 55.59062, 55.60859))

B = data.frame(longitude = c(-2.4252843, -2.0650542, -2.0650243), latitude = c(55.15858, 55.60859, 55.59062))

geosphere::distGeo(A, B)

# > geosphere::distGeo(A, B)
# [1] 18117.765  2000.682  2000.682

Vector of distances in meters

Answer 3

Here is solution using a single loop and vectorizing the distance calculation (converted to km).
The code is using base R's rank function to order/sort the list of calculated distances.
The indexes and the calculated distances of the 3 shortest values are store back in data frame A.

library(geosphere)

A = data.frame(longitude = c(-2.3954998, -2.0650243, -2.0650542), latitude = c(55.32043, 55.59062, 55.60859))
B = data.frame(longitude = c(-2.4252843, -2.0650542, -2.0650243), latitude = c(55.15858, 55.60859, 55.59062))

for(i in 1:nrow(A)){
  #calucate distance against all of B
  distances<-geosphere::distGeo(A[i,], B)/1000
  #rank the calculated distances
  ranking<-rank(distances, ties.method = "first")

  #find the 3 shortest and store the indexes of B back in A
  A$shortest[i]<-which(ranking ==1) #Same as which.min()
  A$shorter[i]<-which(ranking==2)
  A$short[i]<-which(ranking ==3)

  #store the distances back in A
  A$shortestD[i]<-distances[A$shortest[i]] #Same as min()
  A$shorterD[i]<-distances[A$shorter[i]]
  A$shortD[i]<-distances[A$short[i]]
}
A

  longitude latitude shortest shorter short shortestD  shorterD   shortD
1 -2.395500 55.32043        1       3     2  18.11777 36.633310 38.28952
2 -2.065024 55.59062        3       2     1   0.00000  2.000682 53.24607
3 -2.065054 55.60859        2       3     1   0.00000  2.000682 55.05710

As M Viking pointed out, for the geosphere package the data must be arranged Lon then Lat.

Answer 4

I know this is a long way but, in this question, there exists a formula for calculation the distance on your own. So if we convert those codes into the R we can do the same by just using base R .

Function :

rad = function(x) {
    return(x * pi / 180)

}   

getDistance = function(p1, p2) {

        R = 6378137 #  Earth’s mean radius in meter
        dLat = rad(p2[1] - p1[1])
        dLong = rad(p2[2] - p1[2])


        a = ( sin(dLat / 2) * sin(dLat / 2) +
        cos(rad(p1[1])) * cos(rad(p2[1])) *
            sin(dLong / 2) * sin(dLong / 2)  )


        c = 2 * atan2(sqrt(a),sqrt(1 - a))
        d = R * c
  return(d)  # returns the distance in meter
}

Example :

p1 <- c(55.32043 , -2.395500)
p3 <- c(55.15858 , -2.425284)

getDistance(p1,p3)
18115.96

Thus, once we can call those two functions, we can calculate any distance between two locations. So,

output <-lapply( 1:nrow(A), function(i) 
         lapply(1:nrow(B), function(j) 
             cbind(A[i,],B[j,],Distance=getDistance(as.numeric(A[i,-1]),as.numeric(B[j,-1])))

           ))

do.call(rbind,lapply(1:3,function(i) do.call(rbind,output[[i]])))

gives,

   reference latitude longitude reference latitude longitude  Distance
1          C 55.32043 -2.395500         C 55.15858 -2.425284 18115.958
2          C 55.32043 -2.395500         D 55.60859 -2.065054 38260.562
3          C 55.32043 -2.395500         E 55.59062 -2.065024 36603.447
23         D 55.59062 -2.065024         C 55.15858 -2.425284 53219.597
21         D 55.59062 -2.065024         D 55.60859 -2.065054  2000.412
22         D 55.59062 -2.065024         E 55.59062 -2.065024     0.000
33         E 55.60859 -2.065054         C 55.15858 -2.425284 55031.092
31         E 55.60859 -2.065054         D 55.60859 -2.065054     0.000
32         E 55.60859 -2.065054         E 55.59062 -2.065024  2000.412