comparison toolboxes/FullBNT-1.0.7/graph/cliques_to_jtree.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [jtree, root, B, w] = cliques_to_jtree(cliques, ns)
+% MK_JTREE Make an optimal junction tree.
+% [jtree, root, B, w] = mk_jtree(cliques, ns)
+% 
+% A junction tree is a tree that satisfies the jtree property, which says:
+% for each pair of cliques U,V with intersection S, all cliques on the path between U and V
+% contain S. (This ensures that local propagation leads to global consistency.)
+%
+% We can create a junction tree by computing the maximal spanning tree of the junction graph.
+% (The junction graph connects all cliques, and the weight of an edge (i,j) is
+% |C(i) intersect C(j)|, where C(i) is the i'th clique.)
+%
+% The best jtree is the maximal spanning tree which minimizes the sum of the costs on each edge,
+% where cost(i,j) = w(C(i)) + w(C(j)), and w(C) is the weight of clique C,
+% which is the total number of values C can take on.
+%
+% For details, see
+%  - Jensen and Jensen, "Optimal Junction Trees", UAI 94.
+%
+% Input:
+%  cliques{i} = nodes in clique i
+%  ns(i) = number of values node i can take on
+% Output:
+%  jtree(i,j) = 1 iff cliques i and j aer connected
+%  root = the clique that should be used as root
+%  B(i,j) = 1 iff node j occurs in clique i
+%  w(i) = weight of clique i
+
+
+
+num_cliques = length(cliques);
+w = zeros(num_cliques, 1); 
+B = sparse(num_cliques, 1);
+for i=1:num_cliques
+  B(i, cliques{i}) = 1;
+  w(i) = prod(ns(cliques{i}));
+end
+
+
+% C1(i,j) = length(intersect(cliques{i}, cliques{j})); 
+% The length of the intersection of two sets is the dot product of their bit vector representation.
+C1 = B*B';
+C1 = setdiag(C1, 0);
+
+% C2(i,j) = w(i) + w(j)
+num_cliques = length(w);
+W = repmat(w, 1, num_cliques);
+C2 = W + W';
+C2 = setdiag(C2, 0);
+
+jtree = sparse(minimum_spanning_tree(-C1, C2)); % Using -C1 gives *maximum* spanning tree
+
+% The root is arbitrary, but since the first pass is towards the root,
+% we would like this to correspond to going forward in time in a DBN.
+root = num_cliques;
+
+