How to display separate disconnected trees in MATLAB when doing hierarchical clustering and producing dendrograms?

Question

I am working with MATLAB, and I have an adjacency matrix:

mat =

 0     1     0     0     0     0
 1     0     0     0     1     0
 0     0     0     1     0     0
 0     0     1     0     0     1
 0     1     0     0     0     0
 0     0     0     1     0     0

which is not fully connected. Nodes {1,2,5} are connected, and {3,4,6} are connected (the edges are directed).

I would like to see the separate clusters in a dendrogram on a single plot. Since there is not path from one cluster to the next, I would like to see separate trees with separate roots for each cluster. I am using the commands:

mat=zeros(6,6)
mat(1,2)=1;mat(2,1)=1;mat(5,2)=1;mat(2,5)=1;
mat(6,4)=1;mat(4,6)=1;mat(3,4)=1;mat(4,3)=1;
Y=pdist(mat)
squareform(Y)
Z=linkage(Y)
figure()
dendrogram(Z)

These commands are advised from Hierarchical Clustering. And the result is attached: imageDendrogram. Other than that the labels don't make sense, the whole tree is connected, and I connect figure out how to have several disconnected trees which reflect the disconnected nature of the data. I would like to avoid multiple plots as I wish to work with larger datasets that may have many disjoint clusters.

Answer 1

I see this was asked a while ago, but in case you're still interested, here's something to try:

First extract the values above the diagonal from the adjacency matrix, like so:

>> matY = [];
>> for n = 2:6
for m = n:6
matY = [matY mat(n,m)];
end
end
>> matY

matY =

  Columns 1 through 13

     0     0     0     1     0     0     1     0     0     0     0     1     0

  Columns 14 through 15

     0     0

Now you have something that looks like the Y vector pdist would have produced. But the values here are the opposite of what you probably want; the unconnected vertices have a "distance" of zero and the connected ones are one apart. Let's fix that:

>> matY(matY == 0) = 10

matY =

  Columns 1 through 13

    10    10    10     1    10    10     1    10    10    10    10     1    10

  Columns 14 through 15

    10    10

Better. Now we can compute a regular cluster tree, which will represent connected vertices as "close together" and non-connected ones as "far apart":

>> linkage(matY)

ans =

     3     6     1
     1     5     1
     2     4     1
     7     8    10
     9    10    10

>> dendrogram(ans)

The resulting diagram:

Hope this is a decent approximation of what you're looking for.