def construct_junction_tree(cliques):
"Construct a junction tree from a sequence of cliques."
# construct a complete graph which has the clique intersections as edge weights
g = bgl.Graph()
clusters = g.add_vertex_property(type='object')
for clique in cliques:
clusters[g.add_vertex()] = set(clique)
weights = g.add_edge_property(type='float')
separators = g.add_edge_property(type='object')
for v1 in g.vertices:
for v2 in g.vertices:
if v1 != v2 and None == g.edge(v1, v2):
intersection = clusters[v1].intersection(clusters[v2])
if intersection:
e = g.add_edge(v1, v2)
separators[e] = intersection
weights[e] = 1.0 / len(intersection)
maximal_tree_edges = bgl.kruskal_minimum_spanning_tree(g, weights)
# remove edges not in maximal tree
for e in g.edges:
if e not in maximal_tree_edges:
g.remove_edge(e)
return g, clusters, separators
# Copyright 2005 The Trustees of Indiana University.
# Use, modification and distribution is subject to the Boost Software
# License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
# http:#www.boost.org/LICENSE_1_0.txt)
# Authors: Douglas Gregor
# Andrew Lumsdaine
import boost.graph as bgl
# Load a graph from the GraphViz file 'mst.dot'
graph = bgl.read_graphviz('mst.dot')
# Compute the minimum spanning tree of the graph
mst_edges = bgl.kruskal_minimum_spanning_tree(graph, graph.edge_properties['weight'])
# Compute the weight of the minimum spanning tree
print 'MST weight =',sum([e.weight for e in mst_edges])
# Put the weights into the label. Make MST edges solid while all other
# edges remain dashed.
for e in graph.edges:
e.label = e.weight
if e in mst_edges:
e.style = 'solid'
else:
e.style = 'dashed'
# Write out the graph in GraphViz DOT format
graph.write_graphviz('mst-out.dot')
def build_tree(self, mi_threshold = 0.0):
"""
Builds a tree from the mutual information between the base distributions
"""
import boost.graph as bgl
# first build an (undirected) graph of the (negative) mutual informations
g = bgl.Graph()
vertices = [ g.add_vertex() for i in xrange(self.K) ]
weight_map = g.add_edge_property('weight', 'float')
joint_probabilities = g.add_edge_property('joints')
marginal_probabilities = g.add_vertex_property('marginals')
# add the edges and marginal probs
for i in xrange(self.K):
marginal_probabilities[vertices[i]] = self.marginal[i]
# add the edges and conditional probs
for i in xrange(self.K):
for j in xrange(i+1,self.K):
if self.mutual_information[i,j] > mi_threshold:
e = g.add_edge(vertices[i],vertices[j])
weight_map[e] = -self.mutual_information[i,j]
joint_probabilities[e] = self.joint[i,j]
# find the minimum spanning tree and remove those edges not in it
spanning_tree = bgl.kruskal_minimum_spanning_tree(g,weight_map)
for e in g.edges:
if e not in spanning_tree:
g.remove_edge(e)
def index_of(v):
for i in xrange(self.K):
if vertices[i] == v:
return i
raise RuntimeError( 'Could not find vertex: ' + v )
# build a directed forest from the (undirected) graph
def build_forest(g, root_idx = None):
"Take a forest and build an isomorphic Digraph"
import boost.graph as bgl
vertices_visited = set()
diforest = bgl.Digraph()
edge_label = diforest.add_edge_property( 'label', 'string' )
di_conditionals = diforest.add_edge_property( 'conditionals' )
di_marginals = diforest.add_vertex_property( 'marginals' )
di_vertices = [ diforest.add_vertex() for i in xrange(self.K) ]
def visit(i):
if i in vertices_visited: return
vertices_visited.add(i)
v = vertices[i]
di_v = di_vertices[i]
di_marginals[di_v] = marginal_probabilities[v]
for neighbour in g.adjacent_vertices(v):
j = index_of(neighbour)
if j not in vertices_visited:
e = diforest.add_edge(di_v, di_vertices[j])
edge_label[e] = '%.3f' % (-weight_map[g.edge(v,vertices[j])])
joint = joint_probabilities[g.edge(v,neighbour)]
if index_of(neighbour) < index_of(v): joint = joint.T # make sure we have correct orientation of joint
di_conditionals[e] = joint_to_conditional(joint)
visit(j) # recurse
# visit all the vertices - starting with root if given
if None != root_idx: visit(root_idx)
for i in xrange(self.K): visit(i)
# check each node has max one parent
for v in diforest.vertices: assert diforest.in_degree(v) < 2
return diforest
# set the root to have the highest MI
root_idx = self.mutual_information.argmax() % self.mutual_information.shape[0]
self.d = build_forest(g, root_idx = root_idx)
def build_tree(self, mi_threshold=0.0):
"""
Builds a tree from the mutual information between the base distributions
"""
import boost.graph as bgl
# first build an (undirected) graph of the (negative) mutual informations
g = bgl.Graph()
vertices = [g.add_vertex() for i in xrange(self.K)]
weight_map = g.add_edge_property('weight', 'float')
joint_probabilities = g.add_edge_property('joints')
marginal_probabilities = g.add_vertex_property('marginals')
# add the edges and marginal probs
for i in xrange(self.K):
marginal_probabilities[vertices[i]] = self.marginal[i]
# add the edges and conditional probs
for i in xrange(self.K):
for j in xrange(i + 1, self.K):
if self.mutual_information[i, j] > mi_threshold:
e = g.add_edge(vertices[i], vertices[j])
weight_map[e] = -self.mutual_information[i, j]
joint_probabilities[e] = self.joint[i, j]
# find the minimum spanning tree and remove those edges not in it
spanning_tree = bgl.kruskal_minimum_spanning_tree(g, weight_map)
for e in g.edges:
if e not in spanning_tree:
g.remove_edge(e)
def index_of(v):
for i in xrange(self.K):
if vertices[i] == v:
return i
raise RuntimeError('Could not find vertex: ' + v)
# build a directed forest from the (undirected) graph
def build_forest(g, root_idx=None):
"Take a forest and build an isomorphic Digraph"
import boost.graph as bgl
vertices_visited = set()
diforest = bgl.Digraph()
edge_label = diforest.add_edge_property('label', 'string')
di_conditionals = diforest.add_edge_property('conditionals')
di_marginals = diforest.add_vertex_property('marginals')
di_vertices = [diforest.add_vertex() for i in xrange(self.K)]
def visit(i):
if i in vertices_visited: return
vertices_visited.add(i)
v = vertices[i]
di_v = di_vertices[i]
di_marginals[di_v] = marginal_probabilities[v]
for neighbour in g.adjacent_vertices(v):
j = index_of(neighbour)
if j not in vertices_visited:
e = diforest.add_edge(di_v, di_vertices[j])
edge_label[e] = '%.3f' % (
-weight_map[g.edge(v, vertices[j])])
joint = joint_probabilities[g.edge(v, neighbour)]
if index_of(neighbour) < index_of(v):
joint = joint.T # make sure we have correct orientation of joint
di_conditionals[e] = joint_to_conditional(joint)
visit(j) # recurse
# visit all the vertices - starting with root if given
if None != root_idx: visit(root_idx)
for i in xrange(self.K):
visit(i)
# check each node has max one parent
for v in diforest.vertices:
assert diforest.in_degree(v) < 2
return diforest
# set the root to have the highest MI
root_idx = self.mutual_information.argmax(
) % self.mutual_information.shape[0]
self.d = build_forest(g, root_idx=root_idx)
# which will be converted into Boost.Graph property maps.
# In this case, we're only interested in the edge weights.
bgl_graph, translation_map = graphviz_graph.to_bgl(edge_properties = ['weight'])
# the returned translation_map is used to translate between the two
# graph formats:
# translation_map[boost_vertex] => corresponding yapgvb node
# translation_map[boost_edge] => corresponding yapgvb edge
# translation_map[yapgvb_node] => corresponding boost vertex
# translation_map[yapgvb_edge] => corresponding boost edge
weight_map = bgl_graph.edge_properties['weight']
# Compute the minimum spanning tree of the graph
# Returns a list of boost edges
mst_edges = bgl.kruskal_minimum_spanning_tree(bgl_graph, weight_map)
# Color the minimum spanning tree edges red in the graphviz representation
for bgl_edge in mst_edges:
# Get the yapgvb edge corresponding to the boost edge
graphviz_edge = translation_map[bgl_edge]
graphviz_edge.color = yapgvb.colors.red
print "Using dot for layout..."
graphviz_graph.layout(yapgvb.engines.dot)
print "Rendering mst.png..."
graphviz_graph.render('mst.png')
