Finding the complete adjacency matrix in R

问题

I have an adjacency matrix from the package 'bnlearn' using the function amat (the matrix is acyclical). For example:

    +---+-------------------------------+               
    |   |   1     2     3     4     5   |               
    +---+-------------------------------+               
    | 1 |   0     1     0     0     0   |               
    | 2 |   0     0     1     0     0   |               
    | 3 |   0     0     0     1     0   |               
    | 4 |   0     0     0     0     1   |               
    | 5 |   0     0     0     0     0   |               
    +---+-------------------------------+

I need to find the complete dependency matrix from this. For one lag dependency matrix I can use:

New_matrix<- if(old_matrix+old_matrix*old_matrix)>0 then 1 else 0

For two lag dependency matrix I can use:

New_matrix_2<- if(new_matrix+new_matrix*old_matrix)>0 then 1 else 0

The problem is I don't know where the adjacency is complete, that is for how many iterations do I run this to get to the final matrix with all interdependencies incorporated?

    +---+-------------------------------+               
    |   |   1     2     3     4     5   |               
    +---+-------------------------------+               
    | 1 |   0     1     1     1     1   |               
    | 2 |   0     0     1     1     1   |               
    | 3 |   0     0     0     1     1   |               
    | 4 |   0     0     0     0     1   |               
    | 5 |   0     0     0     0     0   |               
    +---+-------------------------------+

For this, the answer is 3 iterations. But the matrix that I need to solve this for is 500x500. Is there a direct way to arrive at the complete adjacency matrix?

回答1:

To find the paths from all nodes, it is probably easier to use the igraph package.

Using your example,

library(bnlearn)
library(igraph)

# Create BN in your example
g <- empty.graph(LETTERS[1:5])
amat(g) <- rbind(cbind(0, diag(4)),0)
amat(g)
#   A B C D E
# A 0 1 0 0 0
# B 0 0 1 0 0
# C 0 0 0 1 0
# D 0 0 0 0 1
# E 0 0 0 0 0

# Convert to igraph object using BN adj. matrix as input
g1 <- graph_from_adjacency_matrix(amat(g))

# You can find all ancestors for each node by using 
# the mode="in" argument, and order to specify the depth of the search
neighborhood(g1, order=nrow(amat(g)), mode="in")

# Similarly, you can get the full connected graph 
# using the same options
ances <- connect(g1, order=nrow(amat(g)), mode="in" )
get.adjacency(ances, sparse=FALSE)
#   A B C D E
# A 0 1 1 1 1
# B 0 0 1 1 1
# C 0 0 0 1 1
# D 0 0 0 0 1
# E 0 0 0 0 0

Alternatively, you can use matrix exponential

m <- amat(g)
1* as.matrix((Matrix::expm(m) - diag(ncol(m))) > 0)

来源：https://stackoverflow.com/questions/35603398/finding-the-complete-adjacency-matrix-in-r

标签

adjacency-matrix