annotate toolboxes/FullBNT-1.0.7/graph/best_first_elim_order.m @ 0:e9a9cd732c1e tip

first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 function order = best_first_elim_order(G, node_sizes, stage)
wolffd@0 2 % BEST_FIRST_ELIM_ORDER Greedily search for an optimal elimination order.
wolffd@0 3 % order = best_first_elim_order(moral_graph, node_sizes)
wolffd@0 4 %
wolffd@0 5 % Find an order in which to eliminate nodes from the graph in such a way as to try and minimize the
wolffd@0 6 % weight of the resulting triangulated graph. The weight of a graph is the sum of the weights of each
wolffd@0 7 % of its cliques; the weight of a clique is the product of the weights of each of its members; the
wolffd@0 8 % weight of a node is the number of values it can take on.
wolffd@0 9 %
wolffd@0 10 % Since this is an NP-hard problem, we use the following greedy heuristic:
wolffd@0 11 % at each step, eliminate that node which will result in the addition of the least
wolffd@0 12 % number of fill-in edges, breaking ties by choosing the node that induces the lighest clique.
wolffd@0 13 % For details, see
wolffd@0 14 % - Kjaerulff, "Triangulation of graphs -- algorithms giving small total state space",
wolffd@0 15 % Univ. Aalborg tech report, 1990 (www.cs.auc.dk/~uk)
wolffd@0 16 % - C. Huang and A. Darwiche, "Inference in Belief Networks: A procedural guide",
wolffd@0 17 % Intl. J. Approx. Reasoning, 11, 1994
wolffd@0 18 %
wolffd@0 19
wolffd@0 20 % Warning: This code is pretty old and could probably be made faster.
wolffd@0 21
wolffd@0 22 n = length(G);
wolffd@0 23 if nargin < 3, stage = { 1:n }; end % no constraints
wolffd@0 24
wolffd@0 25 % For long DBNs, it may be useful to eliminate all the nodes in slice t before slice t+1.
wolffd@0 26 % This will ensure that the jtree has a repeating structure (at least away from both edges).
wolffd@0 27 % This is why we have stages.
wolffd@0 28 % See the discussion of splicing jtrees on p68 of
wolffd@0 29 % Geoff Zweig's PhD thesis, Dept. Comp. Sci., UC Berkeley, 1998.
wolffd@0 30 % This constraint can increase the clique size significantly.
wolffd@0 31
wolffd@0 32 MG = G; % copy the original graph
wolffd@0 33 uneliminated = ones(1,n);
wolffd@0 34 order = zeros(1,n);
wolffd@0 35 t = 1; % Counts which time slice we are on
wolffd@0 36 for i=1:n
wolffd@0 37 U = find(uneliminated);
wolffd@0 38 valid = myintersect(U, stage{t});
wolffd@0 39 % Choose the best node from the set of valid candidates
wolffd@0 40 min_fill = zeros(1,length(valid));
wolffd@0 41 min_weight = zeros(1,length(valid));
wolffd@0 42 for j=1:length(valid)
wolffd@0 43 k = valid(j);
wolffd@0 44 nbrs = myintersect(neighbors(G, k), U);
wolffd@0 45 l = length(nbrs);
wolffd@0 46 M = MG(nbrs,nbrs);
wolffd@0 47 min_fill(j) = l^2 - sum(M(:)); % num. added edges
wolffd@0 48 min_weight(j) = prod(node_sizes([k nbrs])); % weight of clique
wolffd@0 49 end
wolffd@0 50 lightest_nbrs = find(min_weight==min(min_weight));
wolffd@0 51 % break ties using min-fill heuristic
wolffd@0 52 best_nbr_ndx = argmin(min_fill(lightest_nbrs));
wolffd@0 53 j = lightest_nbrs(best_nbr_ndx); % we will eliminate the j'th element of valid
wolffd@0 54 %j1s = find(score1==min(score1));
wolffd@0 55 %j = j1s(argmin(score2(j1s)));
wolffd@0 56 k = valid(j);
wolffd@0 57 uneliminated(k) = 0;
wolffd@0 58 order(i) = k;
wolffd@0 59 ns = myintersect(neighbors(G, k), U);
wolffd@0 60 if ~isempty(ns)
wolffd@0 61 G(ns,ns) = 1;
wolffd@0 62 G = setdiag(G,0);
wolffd@0 63 end
wolffd@0 64 if ~any(logical(uneliminated(stage{t}))) % are we allowed to the next slice?
wolffd@0 65 t = t + 1;
wolffd@0 66 end
wolffd@0 67 end
wolffd@0 68