.. _book_fig_chapter6_fig_great_wall_MST:


Euclidean Minimum Spanning Tree
-------------------------------
Figure 6.15

An approximate Euclidean minimum spanning tree over the two-dimensional
projection of the SDSS Great Wall. The upper panel shows the input points, and
the middle panel shows the dendrogram connecting them. The lower panel shows
clustering based on this dendrogram, created by removing the largest 10% of the
graph edges, and keeping the remaining connected clusters with 30 or more
members.

Additional information
~~~~~~~~~~~~~~~~~~~~~~
This figure is based on the data presented in Figure 1 of Cowan & Ivezic
(2008). A similar figure appears in the book
"Statistics, Data Mining, and Machine Learning in Astronomy", by
Ivezic, Connolly, Vanderplas, and Gray (2013).

The three panels of this figure show a hierarchical clustering of a subset
of galaxies from the Sloan Digital Sky Survey (SDSS).  This region is known
as the "SDSS Great Wall", and contains an extended cluster of several thousand
galaxies approximately 300Mpc (about 1 billion light years) from earth.  The
top panel shows the positions of over 8,000 galaxies projected to a 2D plane
with Earth at the point (0, 0).  The middle panel shows a dendrogram
representation of a Euclidean Minimum Spanning Tree (MST) over the galaxy
locations.  By eliminating edges of a MST which are greater than a given
length, we can measure the amount of clustering at that scale: this is one
version of a class of models known as Hierarchical Clustering.  The bottom
panel shows the results of this clustering approach for an edge cutoff of
3.5Mpc, along with a Gaussian Mixture Model fit to the distribution within
each cluster.



.. image:: ../images/chapter6/fig_great_wall_MST_1.png
    :scale: 100
    :align: center


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