R: Making a More "Efficient" Distance Function

Question

I am working with the R programming language.

I generated the following random data set that contains x and y points:

set.seed(123)

x_cor = rnorm(10,100,100)
y_cor = rnorm(10,100,100)

my_data = data.frame(x_cor,y_cor)

       x_cor     y_cor
1   43.95244 222.40818
2   76.98225 135.98138
3  255.87083 140.07715
4  107.05084 111.06827
5  112.92877  44.41589
6  271.50650 278.69131
7  146.09162 149.78505
8  -26.50612 -96.66172
9   31.31471 170.13559
10  55.43380  52.72086

I am trying to write a "greedy search" algorithm that shows which point is located the "shortest distance" from some starting point.

For example, suppose we start at -26.50612, -96.66172

distance <- function(x1,x2, y1,y2) {
  dist <- sqrt((x1-x2)^2 + (y1 - y2)^2)
  return(dist)
}

Then I calculated the distance between -26.50612, -96.66172 and each point:

results <- list()

for (i in 1:10){


distance_i <- distance(-26.50612, my_data[i,1], -96.66172, my_data[i,2]  )
index = i

my_data_i = data.frame(distance_i, index)

 results[[i]] <- my_data_i

}

results_df <- data.frame(do.call(rbind.data.frame, results))

However, I don't think this is working because the distance between the starting point -26.50612, -96.66172 and itself is not 0 (see 8th row):

  distance_i index
1    264.6443     1
2    238.7042     2
3    191.3048     3
4    185.0577     4
5    151.7506     5
6    306.4785     6
7    331.2483     7
8    223.3056     8
9    213.3817     9
10   331.6455    10

My Question:

• Can someone please show me how to write a function that correctly finds the nearest point from an initial point
• (Step 1) Then removes the nearest point and the initial point from "my_data"
• (Step 2) And then re-calculates the nearest point from "my_data" using the nearest point identified Step 1 (ie with the removed data)
• And in the end, shows the path that was taken (eg 5,7,1,9,3, etc)

Can someone please show me how to do this?

Thanks!

Answer 1

This could be helpful and I think you can solve the further tasks by yourself

start <- c(x= -26.50612, y= -96.66172)
library(dplyr)
my_data <- data.frame(x_cor,y_cor) %>% 
  rowwise() %>% 
  mutate(dist = distance(start["x"], x_cor, start["y"], y_cor))

Answer 2

The solution is implemented as a recursive function distmin , which finds the closest point between an input x and a dataframe Y and then calls itself with the closest point and the dataframe without the closest point as arguments.

EDIT: I reimplemented distmin to use dataframes.

my_data = data.frame(x_cor,y_cor) |>
  mutate(idx = row_number())


distmin <- function(x, Y) {
  if(nrow(Y) == 0)  {
    NULL
  } else {
    dst <-  sqrt((x$x_cor - Y$x_cor)^2 + (x$y_cor - Y$y_cor)^2)
    m <- which.min(dst)
    res <- data.frame(x, dist = dst[m], nearest = Y[m,"idx"])
    rbind(res, distmin(Y[m,], Y[-m,]))
}}

N <- 5

distmin(my_data[N,], my_data[-N,])

##>        x_cor     y_cor idx      dist nearest
##> 5  112.92877  44.41589   5  58.09169      10
##> 10  55.43380  52.72086  10  77.90211       4
##> 4  107.05084 111.06827   4  39.04847       2
##> 2   76.98225 135.98138   2  57.02661       9
##> 9   31.31471 170.13559   9  53.77858       1
##> 1   43.95244 222.40818   1 125.32571       7
##> 7  146.09162 149.78505   7 110.20762       3
##> 3  255.87083 140.07715   3 139.49323       6
##> 6  271.50650 278.69131   6 479.27176       8

The following shows the order in which points are called.

distmin(my_data[N,], my_data[-N,])  |>
  mutate(ord = row_number()) |>
  ggplot(aes(x = x_cor, y_cor)) +
  geom_text(aes(label = ord))