Find the intersection of all combination of list of list

Question

My ultimate goal is to have alluvial plots in R. However, my data is big and is not stored in a way that can be used for direct input, I have:

1. 4 groups (they will be axes of the alluvial plot)
2. In each of these groups consist of a list of a list of vector

My thought is to use length(intersect()) to get the frequency of each combination of the list of list of vectors.

To get the combination of the list of list, I used cross() from the purrr. I am not sure if this is the right way to get this combination matrix, and I am open to other methods. Similarly, I am open to other pipelines that can accomplish the goal. The main reason is that I am stuck at this point and cannot find a good way to find the intersection of the list of list of vectors.

Below is a toy dataset and the expected output I would like to get (I type the result manually):

library(tidyverse)
group1 <- list(module1 = c("test1", "test2", "test3", "test4", "test5", "test6"),
               module2 = c("test7", "test8", "test9", "test10"),
               module3 = c("test11", "test12", "test13"))

group2 <- list(module1 = c("test3", "test4", "test5", "test7", "test8"),
               module2 = c("test1", "test12", "test13"),
               module3 = c("test2", "test6", "test11"))

group3 <- list(module1 = c("test3", "test5", "test6", "test8"),
               module2 = c("test1", "test7", "test9", "test10"),
               module3 = c("test13", "test14", "test15"))

list_combination <- list(group1 = names(group1), group2 = names(group2), group3 = names(group3)) %>% 
  cross() %>% 
  bind_rows()

expected_result_intersect <- list_combination %>%  #below are the results
  mutate(intersect_result = list(
    c("test3", "test5"), #intersect(group1_module1, intersect(group2_module1, group3_module1))
    c("test8"), #intersect(group1_module2, intersect(group2_module1, group3_module1))
    NULL, #intersect(group1_module3, intersect(group2_module1, group3_module1))
    NULL, #intersect(group1_module1, intersect(group2_module2, group3_module1))
    NULL, #intersect(group1_module2, intersect(group2_module2, group3_module1))
    NULL, #intersect(group1_module3, intersect(group2_module3, group3_module1))
    c("test6"), #intersect(group1_module1, intersect(group2_module3, group3_module1))
    NULL, #intersect(group1_module2, intersect(group2_module3, group3_module1))
    NULL, #intersect(group1_module3, intersect(group2_module3, group3_module1))
    c("test5"), #intersect(group1_module1, intersect(group2_module1, group3_module2))
    c("test7"), #intersect(group1_module2, intersect(group2_module1, group3_module2))
    NULL, #intersect(group1_module3, intersect(group2_module1, group3_module2))
    c("test1"), #intersect(group1_module1, intersect(group2_module2, group3_module2))
    NULL, #intersect(group1_module2, intersect(group2_module2, group3_module2))
    NULL, #intersect(group1_module3, intersect(group2_module2, group3_module2))
    NULL, #intersect(group1_module1, intersect(group2_module3, group3_module2))
    NULL, #intersect(group1_module2, intersect(group2_module3, group3_module2))
    NULL, #intersect(group1_module3, intersect(group2_module3, group3_module2))
    NULL, #intersect(group1_module1, intersect(group2_module1, group3_module3))
    NULL, #intersect(group1_module2, intersect(group2_module1, group3_module3))
    NULL, #intersect(group1_module3, intersect(group2_module1, group3_module3))
    NULL, #intersect(group1_module1, intersect(group2_module2, group3_module3))
    NULL, #intersect(group1_module2, intersect(group2_module2, group3_module3))
    c("test13"), #intersect(group1_module3, intersect(group2_module2, group3_module3))
    NULL, #intersect(group1_module1, intersect(group2_module3, group3_module3))
    NULL, #intersect(group1_module2, intersect(group2_module3, group3_module3))
    NULL #intersect(group1_module3, intersect(group2_module3, group3_module3))
    ))

expected_result_counts <- expected_result_intersect %>% 
  rowwise() %>% 
  mutate(Freq = length(intersect_result))


library(ggalluvial)
ggplot(expected_result_counts,
       aes(y = Freq, axis1 = group1, axis2 = group2)) +
  geom_alluvium(aes(fill = group3), width = 1/12) +
  geom_stratum(width = 1/12, fill = "black", color = "grey") +
  geom_label(stat = "stratum", aes(label = after_stat(stratum))) +
  scale_x_discrete(limits = c("Group1", "Group2"), expand = c(.05, .05)) +
  scale_fill_brewer(type = "qual", palette = "Set1") +
  ggtitle("test plot")

Something to note:

• I am not trying to get any combination within the group, i.e. I do not need intersect(group1_module1, group1_module2) as the character vectors within the group are having distinct elements.
• In the real dataset, I have over 50 modules per group. Therefore, it would be great if the proposed method is computation/RAM efficient.

I am open to other languages to process the data but prefer using R to plot the graph as I am more familiar with ggplot.

Thanks!

Answer 1

map(cross(lst(group1, group2, group3)), ~reduce(.x, intersect))

is what you are looking for

my_list <- lst(group1, group2, group3)

list_combination%>%
  mutate(result = map(cross(my_list),~reduce(.x,intersect)))

# A tibble: 27 × 4
   group1  group2  group3  result   
   <chr>   <chr>   <chr>   <list>   
 1 module1 module1 module1 <chr [2]>
 2 module2 module1 module1 <chr [1]>
 3 module3 module1 module1 <chr [0]>
 4 module1 module2 module1 <chr [0]>
 5 module2 module2 module1 <chr [0]>
 6 module3 module2 module1 <chr [0]>
 7 module1 module3 module1 <chr [1]>
 8 module2 module3 module1 <chr [0]>
 9 module3 module3 module1 <chr [0]>
10 module1 module1 module2 <chr [0]>
# … with 17 more rows

---

In base R:

 apply(expand.grid(my_list),1, Reduce,f=intersect)