Understand the `Reduce` function

Reduce takes a binary function and a list of data items and successively applies the function to the list elements in a recursive fashion. For example:

Reduce(intersect,list(a,b,c))

is the same as

intersect((intersect(a,b),c)

However, I don't think that construct will help you here as it will only return those elements that are common to all vectors.

To count the number of vectors that a gene appears in you could do the following:

vlist <- list(v1,v2,v3,v4,v5)addmargins(table(gene=unlist(vlist), vec=rep(paste0("v",1:5),times=sapply(vlist,length))),2,list(Count=function(x) sum(x[x>0])))       vecgene    v1 v2 v3 v4 v5 Count  geneA  1  1  0  1  0     3  geneB  1  0  0  0  1     2  geneC  0  1  0  0  1     2  geneD  0  0  1  0  0     1  geneE  0  0  1  1  0     2

A nice way to see what Reduce() is doing is to run it with its argument accumulate=TRUE. When accumulate=TRUE, it will return a vector or list in which each element shows its state after processing the first n elements of the list in x. Here are a couple of examples:

Reduce(`*`, x=list(5,4,3,2), accumulate=TRUE)# [1]   5  20  60 120i2 <- seq(0,100,by=2)i3 <- seq(0,100,by=3)i5 <- seq(0,100,by=5)Reduce(intersect, x=list(i2,i3,i5), accumulate=TRUE)# [[1]]#  [1]   0   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34  36# [20]  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68  70  72  74# [39]  76  78  80  82  84  86  88  90  92  94  96  98 100# # [[2]]#  [1]  0  6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96# # [[3]]# [1]  0 30 60 90

Assuming the input values given at the end of this answer, the expression

Reduce(intersect,list(a,b,c,d,e))## character(0)

gives the genes that are present in all vectors, not the genes that are present in at least two vectors. It means:

intersect(intersect(intersect(intersect(a, b), c), d), e)## character(0)

If we want the genes that are in at least two vectors:

L <- list(a, b, c, d, e)u <- unlist(lapply(L, unique)) # or:  Reduce(c, lapply(L, unique))tab <- table(u)names(tab[tab > 1])## [1] "geneA" "geneB" "geneC" "geneE"

or

sort(unique(u[duplicated(u)]))## [1] "geneA" "geneB" "geneC" "geneE"

Note: We used:

a <- c("geneA","geneB")b <- c("geneA","geneC")c <- c("geneD","geneE")d <- c("geneA","geneE")e <- c("geneB","geneC")