.. intro:

What is a Dendrogram?
=====================

In general, a dendrogram is simply a binary tree (i.e. a tree where
every node has 0 or 2 children). In the present context, dendrograms are
abstract representations of the hierarchical structures in a dataset.

Consider this cartoon, 2-dimensional cloud map:

.. image:: contour.png
   :scale: 50%
   :align: center

Imagine drawing several contour lines on this map. Each contour will
trace 1 or more closed figures. As we draw contours at increasingly
low intensities, these various shapes will grow larger and merge with
one another. We can use a dendrogram to represent how these different
contour lines merge with one another:

.. image:: tree.png
   :scale: 50%
   :align: center

Each point on a vertical line corresponds to a specific, closed
contour (the level of that contour is the height of the point). The
branching of the tree matches the merger of contours -- when two
branches join at a height "y", two contour lines merge at a contour
level "y".

The procedure works the same way for 3 (or N) dimensional data, but
the contour lines become (hyper) surfaces.