Identification of "clusters" or "groups" in the matrix

Question

I have a matrix filled with discrete elements, and I need to group them into intact groups. So, for example, take this matrix:

[A B B C A]
[A A B A A]
[A B B C C]
[A A A A A]

There would be two separate clusters for A, two separate clusters for C and one cluster for B.

The result I'm looking for would ideally assign a unique identifier to each client, something like this:

[1 2 2 3 4]
[1 1 2 4 4]
[1 2 2 5 5]
[1 1 1 1 1]

Right now I have an R code that does this recursively, just iteratively checking the closest neighbor, but it quickly overflows when the matrix gets large (i.e. 100x100).

Is there a built-in function in R that can do this? I looked at bitmaps and image processing, but no luck. I am convinced that this should be there.

Thank!

Answer 1

, , , , :

# Build initial matrix and lattice graph
library(igraph)
mat <- matrix(c(1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 1, 1, 1, 3, 1), nrow=4)
labels <- as.vector(mat)
g <- graph.lattice(dim(mat))
lyt <- layout.auto(g)

# Remove edges between elements of different types
edgelist <- get.edgelist(g)
retain <- labels[edgelist[,1]] == labels[edgelist[,2]]
g <- delete.edges(g, E(g)[!retain])

# Take a look at what we have
plot(g, layout=lyt)

. , , , :

matrix(clusters(g)$membership, nrow=nrow(mat))
#      [,1] [,2] [,3] [,4] [,5]
# [1,]    1    2    2    3    4
# [2,]    1    1    2    4    4
# [3,]    1    2    2    5    5
# [4,]    1    1    1    1    1

, 2, , . :

[A B C B]
[B A A A]

, 4 , 6, - :

# Build initial matrix and lattice graph (neighborhood size 2)
mat <- matrix(c(1, 2, 2, 1, 3, 1, 2, 1), nrow=2)
labels <- as.vector(mat)
rows <- (seq(length(labels)) - 1) %% nrow(mat)
cols <- ceiling(seq(length(labels)) / nrow(mat))
g <- graph.lattice(dim(mat), nei=2)

# Remove edges between elements of different types or that aren't diagonal
edgelist <- get.edgelist(g)
retain <- labels[edgelist[,1]] == labels[edgelist[,2]] &
  abs(rows[edgelist[,1]] - rows[edgelist[,2]]) <= 1 &
  abs(cols[edgelist[,1]] - cols[edgelist[,2]]) <= 1
g <- delete.edges(g, E(g)[!retain])

# Cluster to obtain final groups
matrix(clusters(g)$membership, nrow=nrow(mat))
#      [,1] [,2] [,3] [,4]
# [1,]    1    2    3    4
# [2,]    2    1    1    1

Answer 2

, , , , .. . dist(). , .

N * 4, ( Prim Tree Alg); (x0, y0, x1, y1), . 1. treelist . , (, ), .

treelist<-list()
 treecnt<-1
 #kill edge walls, i.e. wall segments on the border of the maze.
 #  edges<- which(dowalls[,1]==dowalls[,3] | dowalls[,2]==dowalls[,4])
 vedges <- which( (dowalls[,1]==dowalls[,3]) & (dowalls[,1]==1 | dowalls[,1]==dimx+1) )
 hedges <- which( (dowalls[,2]==dowalls[,4]) & (dowalls[,2]==1 | dowalls[,1]==dimy+1) )
 dowalls<-dowalls[-c(vedges,hedges),,drop=FALSE]
 # now sort into trees 
 while(nrow(dowalls)>0 ) {
     tree <- matrix(dowalls[1,],nr=1) #force dimensions 
     dowalls<-dowalls[-1,,drop=FALSE]
     treerow <- 1 #current row of tree we're looking at
     while ( treerow <= nrow(tree) ) {
         #only examine the first 'column' of the dist() matrix 'cause those are the
         # distances from the tree[] endpoints
         touch <- c( which(dist(rbind(tree[treerow,1:2],dowalls[,1:2]) )[1:nrow(dowalls)]==0),  which(dist(rbind(tree[treerow,1:2],dowalls[,3:4]) )[1:nrow(dowalls)]==0), which(dist(rbind(tree[treerow,3:4],dowalls[,1:2]) )[1:nrow(dowalls)]==0), which(dist(rbind(tree[treerow,3:4],dowalls[,3:4]) )[1:nrow(dowalls)]==0) )
         if(length(touch) ) {
            tree <- rbind(tree,dowalls[c(touch),])
            dowalls <- dowalls[-c(touch),,drop=FALSE] 
            }
    # now be careful: want to track the row of tree[] we're working with AND
    # track how many rows there currently are in tree[]
        treerow <- treerow + 1 
    } #end of while treerow <= nrow 
    treelist[[treecnt]]<-tree
    treecnt <- treecnt + 1 
} #end ; all walls have been classified