Find the minimum distance between two data frames, for each element in the second data frame

Question

I have two data frames ev1 and ev2, describing timestamps of two types of events collected over many tests. So, each data frame has columns "test_id", and "timestamp". What I need to find is the minimum distance of ev1 for each ev2, in the same test.

I have a working code that merges the two datasets, calculates the distances, and then uses dplyr to filter for the minimum distance:

ev1 = data.frame(test_id = c(0, 0, 0, 1, 1, 1), time=c(1, 2, 3, 2, 3, 4))
ev2 = data.frame(test_id = c(0, 0, 0, 1, 1, 1), time=c(6, 1, 8, 4, 5, 11))

data <- merge(ev2, ev1, by=c("test_id"), suffixes=c(".ev2", ".ev1"))

data$distance <- data$time.ev2 - data$time.ev1

min_data <- data %>%
  group_by(test_id, time.ev2) %>%
  filter(abs(distance) == min(abs(distance)))

While this works, the merge part is very slow and feels inefficient -- I'm generating a huge table with all combinations of ev2->ev1 for the same test_id, only to filter it down to one. It seems like there should be a way to "filter on the fly", during the merge. Is there?

Update: The following case with two "group by" columns fails when data.table approach outlined by akrun is used:

ev1 = data.frame(test_id = c(0, 0, 0, 1, 1, 1), time=c(1, 2, 3, 2, 3, 4), group_id=c(0, 0, 0, 1, 1, 1))
ev2 = data.frame(test_id = c(0, 0, 0, 1, 1, 1), time=c(5, 6, 7, 1, 2, 8), group_id=c(0, 0, 0, 1, 1, 1))
setkey(setDT(ev1), test_id, group_id)
DT <- ev1[ev2, allow.cartesian=TRUE][,distance:=abs(time-i.time)]

Error in eval(expr, envir, enclos) : object 'i.time' not found

Answer 1

Here's how I'd do it using data.table:

require(data.table)
setkey(setDT(ev1), test_id)
ev1[ev2, .(ev2.time = i.time, ev1.time = time[which.min(abs(i.time - time))]), by = .EACHI]
#    test_id ev2.time ev1.time
# 1:       0        6        3
# 2:       0        1        1
# 3:       0        8        3
# 4:       1        4        4
# 5:       1        5        4
# 6:       1       11        4

In joins of the form x[i] in data.table, the prefix i. is used to refer the columns in i, when both x and i share the same name for a particular column.

Please see this SO post for an explanation on how this works.

This is syntactically more straightforward to understand what's going on, and is memory efficient (at the expense of little speed¹) as it doesn't materialise the entire join result at all. In fact, this does exactly what you say in your post - filter on the fly, while merging.

1. On speed, it doesn't matter in most of the cases really. If there are a lot of rows in i, it might be a tad slower as the j-expression will have to be evaluated for each row in i. In contrast, @akrun's answer does a cartesian join followed by one filtering. So while it's high on memory, it doesn't evaluate j for each row in i. But again, this shouldn't even matter unless you work with really large i which is not often the case.

HTH

Answer 2

May be this helps:

library(data.table)
setkey(setDT(ev1), test_id)
DT <- ev1[ev2, allow.cartesian=TRUE][,distance:=time-i.time]
DT[DT[,abs(distance)==min(abs(distance)), by=list(test_id, i.time)]$V1]
#    test_id time i.time distance
#1:       0    3      6        3
#2:       0    1      1        0
#3:       0    3      8        5
#4:       1    4      4        0
#5:       1    4      5        1
#6:       1    4     11        7

Or

 ev1[ev2, allow.cartesian=TRUE][,distance:= time-i.time][,
      .SD[abs(distance)==min(abs(distance))], by=list(test_id, i.time)]

Update

Using the new grouping

setkey(setDT(ev1), test_id, group_id)
setkey(setDT(ev2), test_id, group_id)
DT <- ev1[ev2, allow.cartesian=TRUE][,distance:=i.time-time]
DT[DT[,abs(distance)==min(abs(distance)), by=list(test_id, 
                                group_id,i.time)]$V1]$distance
#[1]  2  3  4 -1  0  4

Based on the code you provided

min_data$distance
#[1]  2  3  4 -1  0  4