Cluster Analysis

Q: For an arbitrary matrix of non-negative integers, how can I obtain the sum of those matrix elements that are surrounded by zeros? As a concrete example, for the following matrix an output of is required.

The order in which the groups surrounded by zero is summed does not matter.

A: Carl Woll (carlw@wolfram.com) answers: First, use SparseArray to get the positions of non-zero elements.

Next, define a distance function yielding 0 for identical elements, 1 for adjacent elements, and a big number, say 10, for nonadjacent elements.

Then, load the Statistics`ClusterAnalysis` package and use FindClusters with the Agglomerate method.

Finally, total the cluster values.

Here is a function to do all the steps.

Check that ClusterSums works on mat.

As a bonus, this approach can be extended to handle higher dimensional arrays.