R: Grouping data within cetrain range - r

Question

I have a data frame with two columns, let's call them X and Y. Here's an example of it:
df <- data.frame(X = LETTERS[1:8],
Y = c(14, 12, 12, 11, 9, 6, 4, 1),
stringsAsFactors = FALSE)
which produces this:
X Y
A 14
B 12
C 12
D 11
E 9
F 6
G 4
H 1
Note that the data frame will always be ordered in a descending order based on Y. I want to group together cases where the Y values lie within a certain range, while updating the X column to reflect the grouping too. For example, if the value is 2, I would like the final output to be:
X new_Y
A 14.00000
B C D 11.66667
E 9.00000
F G 5.00000
H 1.00000
Let me explain how I got that. From the starting df data frame, the closest values were B and C. Joining them would result in:
X new_Y
A 14
B C 12
D 11
E 9
F 6
G 4
H 1
The new_Y value for cases B and C is the average of the original values for B and C i.e. 12. From this second data frame, B C are within 2 from D so they are the next to be grouped together:
X new_Y
A 14.00000
B C D 11.66667
E 9.00000
F 6.00000
G 4.00000
H 1.00000
Note that the Y value for B C D is 11.67 because the original values of B, C and D were 12, 12 and 11 respectively and their average is 11.667. I wouldn't want the code to return the average Y from the previous iteration (which in this case would be 11.5).
Finally, F and G can also be grouped together, producing the final output stated above.
I'm not sure of the code needed to achieve this. My only thoughts were to calculate the distance from the previous and following element, look for the minimum and check whether it exceeds the threshold value (of 2 in the example above). Based on where that minimum appears, join the X column while averaging the Y values from the original table. Repeat this until the minimum becomes larger than the threshold.
But I'm not sure how to write the necessary code to achieve this or whether there's a more efficient solution to the algorithm I'm suggesting above. Any help will be much appreciated.
P.S I forgot to mention that if the distance between the previous and the following Y value is the same, then the grouping should be done towards the larger Y value. So
X Y
A 10
B 8
C 6
would be returned as
X new_Y
A B 9
C 6
Thanks in advance for your patience. My apologies if I didn't explain this very well.

Answer 1

This sounds like hierarchical agglomerative clustering.
To get the groups, use dist, hclust and cutree.
Note that centroid clustering with hclust expects the distances as the square of the Euclidean distance.
df <- data.frame(X = LETTERS[1:8],
Y = c(14, 12, 12, 11, 9, 6, 4, 1),
stringsAsFactors = FALSE)
dCutoff <- 2
d2 <- dist(df$Y)^2
hc <- hclust(d2, method = "centroid")
group_id <- cutree(hc, h = dCutoff^2)
group_id
#> [1] 1 2 2 2 3 4 4 5
To munge the original table, we can use dplyr.
library('dplyr')
df %>%
group_by(group_id = group_id) %>%
summarise(
X = paste(X, collapse = ' '),
Y = mean(Y))
#> # A tibble: 5 x 3
#> group_id X Y
#> <int> <chr> <dbl>
#> 1 1 A 14.00000
#> 2 2 B C D 11.66667
#> 3 3 E 9.00000
#> 4 4 F G 5.00000
#> 5 5 H 1.00000

Answer 2

This gives the average of the previous iteration though. In any case I hope it helps
library(data.table)
df <- data.table(X = LETTERS[1:8],
Y = c(14, 12, 12, 11, 9, 6, 4, 1),
stringsAsFactors = FALSE)
differences <- c(diff(df$Y),NA) # NA for the last element
df$difference <- abs(differences) # get the differences of the consequent elements(since Y is sorted it works)
minimum <- min(df$difference[1:(length(df$difference)-1)]) # get the minimum
while (minimum < 2){
index <- which(df$difference==minimum) # see where the minimum occurs
check = FALSE
# because the last row cannot have a number since there is not an element after that
# we need to see if this element has the minimum difference with its previous
# if it does not have the minimum difference then we exclude it and paste it later
if(df[nrow(df)-1,difference]!=minimum){
last_row <- df[nrow(df)]
df <- df[-nrow(df)]
check = TRUE
}
tmp <- df[(index:(index+1))]
df <- df[-(index:(index+1))]
to_bind <- data.table(X = paste0(tmp$X, collapse = " "))
to_bind$Y <- mean(tmp$Y)
df <- rbind(df[,.(X,Y)],to_bind)
if(check){
df <- rbind(df,last_row[,.(X,Y)])
}
setorder(df,-Y)
differences <- c(diff(df$Y),NA) # NA for the last element
df$difference <- abs(differences) # get the differences of the consequent elements(since Y is sorted it works)
minimum <- min(df$difference[1:(length(df$difference)-1)]) # get the minimum
}