Learning Data Mining with Python

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In graph theory, a spanning tree is a set of edges on a graph that connects all of the
nodes together. The Minimum Spanning Tree (MST) is simply the spanning tree
with the lowest total weight. For our application, the nodes in our graph are samples
from our dataset, and the edge weights are the number of times those two samples
were clustered together—that is, the value from our coassociation matrix.
In the following figure, a MST on a graph of six nodes is shown. Nodes on the graph
can be used more than once in the MST. The only criterion for a spanning tree is that
all nodes should be connected together.
To compute the MST, we use SciPy's minimum_spanning_tree function, which is
found in the sparse package:
from scipy.sparse.csgraph import minimum_spanning_tree
The mst function can be called directly on the sparse matrix returned by our
coassociation function:
mst = minimum_spanning_tree(C)
However, in our coassociation matrix C, higher values are indicative of
samples that are clustered together more often—a similarity value. In contrast,
minimum_spanning_tree sees the input as a distance, with higher scores penalized.
For this reason, we compute the minimum spanning tree on the negation of the
coassociation matrix instead:
mst = minimum_spanning_tree(-C)
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