Find groups that contain all elements, but do not overlap [closed] - r

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I've been given a set of country groups and I'm trying to get a set of mutually exclusive regions so that I can compare them. The problem is that my data contains several groups, many of which overlap. How can I get a set of groups which contain all countries, but do not overlap with each other?
For example, assume that this is the list of countries in the world:
World <- c("Angola", "France", "Germany", "Australia", "New Zealand")
Assume that this is my set of groups:
df <- data.frame(group = c("Africa", "Western Europe", "Europe", "Europe", "Oceania", "Oceania", "Commonwealth Countries"),
element = c("Angola", "France", "Germany", "France", "Australia", "New Zealand", "Australia"))
group element
1 Africa Angola
2 Western Europe France
3 Europe Germany
4 Europe France
5 Oceania Australia
6 Oceania New Zealand
7 Commonwealth Countries Australia
How could I remove overlapping groups (in this case Western Europe) to get a set of groups that contains all countries like the following:
df_solved <- data.frame(group = c("Africa", "Europe", "Europe", "Oceania", "Oceania"),
element = c("Angola", "France", "Germany", "Australia", "New Zealand"))
group element
1 Africa Angola
2 Europe France
3 Europe Germany
4 Oceania Australia
5 Oceania New Zealand

Answer 1

One possible rule could be to minimize the number of groups, e.g. to associate an element with that group which includes the most elements.
library(data.table)
setDT(df)[, n.elements := .N, by = group][
order(-n.elements), .(group = group[1L]), by = element]
element group
1: Germany Europe
2: France Europe
3: Australia Oceania
4: New Zealand Oceania
5: Angola Africa
Explanation
setDT(df)[, n.elements := .N, by = group][]
returns
group element n.elements
1: Africa Angola 1
2: Western Europe France 1
3: Europe Germany 2
4: Europe France 2
5: Oceania Australia 2
6: Oceania New Zealand 2
7: Commonwealth Countries Australia 1
Now, the rows are ordered by decreasing number of elements and for each country the first, i.e., the "largest", group is picked. This should return a group for each country as requested.
In case of ties, i.e., one group contains equally many elements, you can add additional citeria when ordering, e.g., length of the group name, or just alphabetical order.

Answer 2

1) If you want to simply eliminate duplicate elements then use !duplicated(...) as shown. No packages are used.
subset(df, !duplicated(element))
giving:
group element
1 Africa Angola
2 Europe France
3 Europe Germany
5 Oceania Australia
6 Oceania New Zealand
2) set partitioning If each group must be wholly in or wholly out and each element may only appear once then this is a set partitioning problem:
library(lpSolve)
const.mat <- with(df, table(element, group))
obj <- rep(1L, ncol(const.mat))
res <- lp("min", obj, const.mat, "=", 1L, all.bin = TRUE)
subset(df, group %in% colnames(const.mat[, res$solution == 1]))
giving:
group element
1 Africa Angola
2 Europe France
3 Europe Germany
5 Oceania Australia
6 Oceania New Zealand
3) set covering Of course there may be no exact set partition so we could consider the set covering problem (same code exceept "=" is replaced by ">=" in the lp line.
library(lpSolve)
const.mat <- with(df, table(element, group))
obj <- rep(1L, ncol(const.mat))
res <- lp("min", obj, const.mat, ">=", 1L, all.bin = TRUE)
subset(df, group %in% colnames(const.mat[, res$solution == 1]))
giving:
group element
1 Africa Angola
2 Europe France
3 Europe Germany
5 Oceania Australia
6 Oceania New Zealand
and we could optionally then apply (1) to remove any duplicates in the cover.
4) Non-dominated groups Another approach is to remove any group whose elements form a strict subset of the elements of some other group. For example, every element in Western Europe is in Europe and Europe has more elements than Western Europe so the elements of Western Europe are a strict subset of the elements of Europe and we remove Western Europe. Using const.mat from above:
# returns TRUE if jth column of const.mat is dominated by some other column
is_dom_fun <- function(j) any(apply(const.mat[, j] <= const.mat[, -j], 2, all) &
sum(const.mat[, j]) < colSums(const.mat[, -j]))
is_dom <- sapply(seq_len(ncol(const.mat)), is_dom_fun)
subset(df, group %in% colnames(const.mat)[!is_dom])
giving:
group element
1 Africa Angola
3 Europe Germany
4 Europe France
5 Oceania Australia
6 Oceania New Zealand
If there are any duplicates left we can use (1) to remove them.

Answer 3

library(dplyr)
df %>% distinct(element, .keep_all=TRUE)
group element
1 Africa Angola
2 Europe France
3 Europe Germany
4 Oceania Australia
5 Oceania New Zealand
Shoutout to Axeman for beating me with this answer.
Update
Your question is ill-defined. Why is 'Europe' preferred over 'Western Europe'? Put another way, each country is assigned several groups. You want to reduce it to one group per country. How do you decide which group?
Here's one way, we always prefer the biggest:
groups <- df %>% count(group)
df %>% inner_join(groups, by='group') %>%
arrange(desc(n)) %>% distinct(elemenet, .keep_all=TRUE)
group element n
1 Europe France 2
2 Europe Germany 2
3 Oceania Australia 2
4 Oceania New Zealand 2
5 Africa Angola 1

Answer 4

Here is one option with data.table
library(data.table)
setDT(df)[, head(.SD, 1), element]
Or with unique
unique(setDT(df), by = 'element')
# group element
#1: Africa Angola
#2: Europe France
#3: Europe Germany
#4: Oceania Australia
#5: Oceania New Zealand
Packages are used and it is data.table

Answer 5

A completely different approach would be to ignore the given groups but to look up just the country names in the catalogue of UN regions which are available in the countrycodes or ISOcodes packages.
The countrycodes package seems to offer the simpler interface and it also warns about country names which can not be found in its database:
# given country names - note the deliberately misspelled last entry
World <- c("Angola", "France", "Germany", "Australia", "New Zealand", "New Sealand")
# regions
countrycode::countrycode(World, "country.name.en", "region")
[1] "Middle Africa" "Western Europe" "Western Europe" "Australia and New Zealand"
[5] "Australia and New Zealand" NA
Warning message:
In countrycode::countrycode(World, "country.name.en", "region") :
Some values were not matched unambiguously: New Sealand
# continents
countrycode::countrycode(World, "country.name.en", "continent")
[1] "Africa" "Europe" "Europe" "Oceania" "Oceania" NA
Warning message:
In countrycode::countrycode(World, "country.name.en", "continent") :
Some values were not matched unambiguously: New Sealand