content: """
  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.
  """
  # Author: Jake VanderPlas
  # License: BSD
  #   The figure produced by this code is published in the textbook
  #   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
  #   For more information, see http://astroML.github.com
  #   To report a bug or issue, use the following forum:
  #    https://groups.google.com/forum/#!forum/astroml-general
  
  from __future__ import print_function, division
  
  import numpy as np
  from matplotlib import pyplot as plt
  
  from scipy import sparse
  from sklearn.mixture import GMM
  
  from astroML.clustering import HierarchicalClustering, get_graph_segments
  from astroML.datasets import fetch_great_wall
  
  #----------------------------------------------------------------------
  # This function adjusts matplotlib settings for a uniform feel in the textbook.
  # Note that with usetex=True, fonts are rendered with LaTeX.  This may
  # result in an error if LaTeX is not installed on your system.  In that case,
  # you can set usetex to False.
  from astroML.plotting import setup_text_plots
  setup_text_plots(fontsize=8, usetex=True)
  
  #------------------------------------------------------------
  # get data
  X = fetch_great_wall()
  
  xmin, xmax = (-375, -175)
  ymin, ymax = (-300, 200)
  
  #------------------------------------------------------------
  # Compute the MST clustering model
  n_neighbors = 10
  edge_cutoff = 0.9
  cluster_cutoff = 10
  model = HierarchicalClustering(n_neighbors=10,
                                 edge_cutoff=edge_cutoff,
                                 min_cluster_size=cluster_cutoff)
  model.fit(X)
  print(" scale: %2g Mpc" % np.percentile(model.full_tree_.data,
                                          100 * edge_cutoff))
  
  n_components = model.n_components_
  labels = model.labels_
  
  #------------------------------------------------------------
  # Get the x, y coordinates of the beginning and end of each line segment
  T_x, T_y = get_graph_segments(model.X_train_,
                                model.full_tree_)
  T_trunc_x, T_trunc_y = get_graph_segments(model.X_train_,
                                            model.cluster_graph_)
  
  #------------------------------------------------------------
  # Fit a GMM to each individual cluster
  Nx = 100
  Ny = 250
  Xgrid = np.vstack(map(np.ravel, np.meshgrid(np.linspace(xmin, xmax, Nx),
                                              np.linspace(ymin, ymax, Ny)))).T
  density = np.zeros(Xgrid.shape[0])
  
  for i in range(n_components):
      ind = (labels == i)
      Npts = ind.sum()
      Nclusters = min(12, Npts // 5)
  
      gmm = GMM(Nclusters, random_state=0).fit(X[ind])
      dens = np.exp(gmm.score(Xgrid))
      density += dens / dens.max()
  
  density = density.reshape((Ny, Nx))
  
  #----------------------------------------------------------------------
  # Plot the results
  fig = plt.figure(figsize=(5, 6))
  fig.subplots_adjust(hspace=0, left=0.1, right=0.95, bottom=0.1, top=0.9)
  
  ax = fig.add_subplot(311, aspect='equal')
  ax.scatter(X[:, 1], X[:, 0], s=1, lw=0, c='k')
  ax.set_xlim(ymin, ymax)
  ax.set_ylim(xmin, xmax)
  ax.xaxis.set_major_formatter(plt.NullFormatter())
  ax.set_ylabel('(Mpc)')
  
  ax = fig.add_subplot(312, aspect='equal')
  ax.plot(T_y, T_x, c='k', lw=0.5)
  ax.set_xlim(ymin, ymax)
  ax.set_ylim(xmin, xmax)
  ax.xaxis.set_major_formatter(plt.NullFormatter())
  ax.set_ylabel('(Mpc)')
  
  ax = fig.add_subplot(313, aspect='equal')
  ax.plot(T_trunc_y, T_trunc_x, c='k', lw=0.5)
  ax.imshow(density.T, origin='lower', cmap=plt.cm.hot_r,
            extent=[ymin, ymax, xmin, xmax])
  
  ax.set_xlim(ymin, ymax)
  ax.set_ylim(xmin, xmax)
  ax.set_xlabel('(Mpc)')
  ax.set_ylabel('(Mpc)')
  
  plt.show()
  