Use `dplyr` to avoid `for` loop: calculate distance to observations - r

Question

I have two data sets A and B and for each observation in A I want to calculate a distance distance (e.g. an euclidean distance, L1 distance, or something else) to each observation in B (the calculation of the distance is based on the variables in the data sets). An observation from A should then be related to an observation in B for which this distance is minimal.
For example, if A has 5000 observations and B has 10000 observations then
for(i in 1:5000)
{
x = data.frame(x = numeric(), y = numeric())
for(j in 1:10000)
{
x[j,] = distance(A[i,], B[j,])
}
A[i,]$associated_row_B = x[which.min(x[1,]),1]
}
does basically what I want (I still have to solve if observations have the same distance). But since I am using dplyr I hardly ever had to use a for loop. My solution needs even two loops so I wonder if there is a possibility to avoid the for loop using a solution from dplyr/tidyverse.
A very basic example:
A:
i a b
1 -0.5920377 a
2 0.4263199 b
3 0.6737029 a
4 1.3063658 c
5 0.1314103 d
B:
i a b
1 -0.30201541 a
2 -0.07093386 b
3 0.96317764 c
4 -0.33303061 d
5 -1.00834895 d
and the distance function:
distance = function(x,y) return(c((x[2] - y[2])^2 + abs(x[3] - y[3]), y[1])
The first element of the return value is the actual distance, the second value is the identifier from B.

Answer 1

Fair warning: this is going to be pretty inefficient for large datasets!
You can accomplish this using crossing from tidyr and slice from dplyr.
First, let's create two dummy dataframes, A_df and B_df
A_df <- data.frame(
observation_A = runif(100),
id_A = 1:100
)
B_df <- data.frame(
observation_B = runif(50),
id_B = 1:50
)
For clarity, I've kept the column names unique between A_df and B_df. Next, we'll use tidyr::crossing to find every combination of rows between the two dataframes. Next, we use mutate to calculate the distance (here I arbitrarily took the absolute value of their difference, but you can apply your custom distance function here). Finally, we group by id_A, and keep only the minimum using slice (and base R which.max).
library(tidyverse)
full_df <- A_df %>%
crossing(B_df) %>%
mutate(distance = abs(observation_A-observation_B)) %>%
group_by(id_A) %>%
slice(which.min(distance))
Looking at full_df, we get what we were hoping for:
> full_df
# A tibble: 100 x 5
# Groups: id_A [100]
observation_A id_A observation_B id_B distance
<dbl> <int> <dbl> <int> <dbl>
1 0.826 1 0.851 44 0.0251
2 0.903 2 0.905 3 0.00176
3 0.371 3 0.368 18 0.00305
4 0.554 4 0.577 34 0.0232
5 0.656 5 0.654 10 0.00268
6 0.120 6 0.110 37 0.0101
7 0.991 7 0.988 6 0.00244
8 0.983 8 0.988 6 0.00483
9 0.325 9 0.318 45 0.00649
10 0.860 10 0.864 40 0.00407
# ... with 90 more rows