R: data.table compare sets of rows - r

Question

I am working in R with data.tables. I have the following data.table encoding a set of points with coordinates A,B,C,D and index encoding a set the point belongs to.
library(data.table)
A B C D set
1: 0 0 0 0 1
2: 1 0 1 0 2
3: 1 1 1 0 2
4: 0 1 0 0 2
5: 1 0 1 1 2
6: 0 1 0 0 3
7: 1 1 0 0 3
8: 0 0 1 0 4
9: 1 0 1 0 4
10: 0 1 0 1 4
11: 0 0 0 0 5
12: 1 0 0 0 5
13: 1 1 1 0 5
14: 1 1 1 1 5
dt = setDT(structure(list(A = c(0L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L,
0L, 1L, 1L, 1L), B = c(0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L,
0L, 0L, 1L, 1L), C = c(0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L,
0L, 0L, 1L, 1L), D = c(0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L,
0L, 0L, 0L, 1L), set = c(1L, 2L, 2L, 2L, 2L, 3L, 3L, 4L, 4L,
4L, 5L, 5L, 5L, 5L)), .Names = c("A", "B", "C", "D", "set"), row.names = c(NA,
-14L), class = "data.frame"))
I have another table encoding e.g. probability of each set.
set mass
1: 1 0.27809187
2: 2 0.02614841
3: 3 0.36890459
4: 4 0.28975265
5: 5 0.03710247
wt = setDT(structure(list(set = 1:5, mass = c(0.27809187, 0.02614841, 0.36890459,
0.28975265, 0.03710247)), .Names = c("set", "mass"), row.names = c(NA,
-5L), class = "data.frame"))
I would like to have a procedure to create a projection to a subspace e.g. C,D. (Note that original points 1,4,6,7,11,12 coincide in this case, sets 1 and 3 are the same in this subspace as well as sets 2 and 5.
unique(dt[,c("C","D", "set")])
> C D set
1: 0 0 1
2: 1 0 2
3: 0 0 2
4: 1 1 2
5: 0 0 3
6: 1 0 4
7: 0 1 4
8: 0 0 5
9: 1 0 5
10: 1 1 5
and to identify the same sets, keep just unique ones and sum the corresponding masses. I.e. in this case:
> C D set
1: 0 0 1
2: 1 0 2
3: 0 0 2
4: 1 1 2
5: 1 0 4
6: 0 1 4
set mass
1: 1 0.6469965 % set 1 + set 3
2: 2 0.06325088 % set 2 + set 5
3: 4 0.36890459
Thank you for your ideas.

Answer 1

Similar in concept to Frank's, we can map the binary values of each set to a decimal with x * 2 ^ ((length(x) - 1):0). Subsetting, also, for "C" and "D", we get:
coords = c("C", "D")
d = data.frame(set = dt$set,
val = Reduce("+", Map("*", list(dt$C, dt$D), 2 ^ ((length(coords) - 1):0))))
d
Then, we can group identical sets following the same idea:
tab = table(d$val, d$set) > 0L ## `table(d) > 0` to ignore the duplicates
gr = colSums(tab * (2 ^ ((nrow(tab) - 1):0)))
gr
# 1 2 3 4 5
# 8 11 8 6 11
## another (pre-edit) alternative with unnecessary overhead
#gr = cutree(hclust(dist(table(d) > 0L)), h = 0)
#gr
#1 2 3 4 5
#1 2 1 3 2
and aggregate based on this group:
rowsum(wt$mass[match(names(gr), wt$set)], gr, reorder = FALSE)
# [,1]
#8 0.64699646
#11 0.06325088
#6 0.28975265

Answer 2

A somewhat clunky option: make a unique string for each set, and then group on that.
coords = c("C", "D")
gDT = setorder(unique(dt[,c(coords, "set"), with=FALSE]))[,
.(s = paste(do.call(paste, c(.SD, .(sep="_"))), collapse="."))
, by=set, .SDcols = coords][,
g := .GRP
, by=s][]
# set s g
# 1: 1 0_0 1
# 2: 2 0_0.1_0.1_1 2
# 3: 3 0_0 1
# 4: 5 0_0.1_0.1_1 2
# 5: 4 0_1.1_0 3
gDT[wt, on=.(set), mass := i.mass ]
gDT[, .(set = first(set), mass = sum(mass)), by=g]
# g set mass
# 1: 1 1 0.64699646
# 2: 2 2 0.06325088
# 3: 3 4 0.28975265
Comments
You can get rid of the g by chaining on [, g := NULL][] in the last line.
setorder is just sorting the data so that the unique string turns out the same in set sets that are the same.
Grouped first and sum operations are optimized, as you can see if you add verbose = TRUE to the final line, like gDT[, .(set = first(set), mass = sum(mass)), by=g, verbose=TRUE].