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Then any maximum-weight spanning tree of the clique graph is a junction tree. So, to construct a junction tree we just have to extract a maximum weight spanning tree out of the clique graph. This can be efficiently done by, for example, modifying Kruskal's algorithm. The last step is to apply belief propagation to the obtained junction tree. [10]
The tree decomposition of a graph is far from unique; for example, a trivial tree decomposition contains all vertices of the graph in its single root node. A tree decomposition in which the underlying tree is a path graph is called a path decomposition, and the width parameter derived from these special types of tree decompositions is known as ...
It is a key step of the junction tree algorithm, used in belief propagation on graphical models. A directed acyclic graph The corresponding moral graph, with newly added arcs shown in red
3 Spanning tree? 2 comments. 4 Jordan. 3 comments. Toggle the table of contents. Talk: Junction tree algorithm. Add languages. Page contents not supported in other ...
We define subset of minimum bottleneck spanning trees S′ such that for every T j ∈ S′ and T k ∈ S we have B(T j) ≤ B(T k) for all i and k. [2] The graph on the right is an example of MBST, the red edges in the graph form a MBST of G(V, E).
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Chow and Liu provide a simple algorithm for constructing the optimal tree; at each stage of the procedure the algorithm simply adds the maximum mutual information pair to the tree. See the original paper, Chow & Liu (1968), for full details. A more efficient tree construction algorithm for the common case of sparse data was outlined in Meilă ...
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