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Junction Tree Construction

Junction Tree Construction. Practice exercise. Example 1: Junction Tree Construction . Step1: Insert link between parents of common child. A. B. D. E. C. G. F. H. Example 1: Junction Tree Construction. Step2: C onvert into undirected graph. A. B. A. B. D. E. D. E. C. C. G.

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Junction Tree Construction

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  1. Junction Tree Construction Practice exercise

  2. Example 1: Junction Tree Construction Step1: Insert link between parents of common child A B D E C G F H

  3. Example 1: Junction Tree Construction Step2: Convert into undirected graph A B A B D E D E C C G G F H F H

  4. Example 1: Junction Tree Construction Step3: Triangulate a graph if it has circle of length>3 A B D E C G F H Note : No need of triangulation in this example.

  5. Example 1: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 2 A B 4 5 3 D E C 8 6 7 G F H

  6. Example 1: Junction Tree Construction Definition: A Clique in a graph is set of adjacent vertices which is a complete graph. • Five cliques are found in Example 1: • One clique of four nodes • Four cliques of three nodes Step4: Ordered the node by max cardinality search. ABCDE 4 1 ACD 5 2 A B CDF 6 4 5 3 D E C CEH 7 8 6 7 G EHG 8 F H

  7. Example 1: Junction Tree Construction Construct Tree ABCDE 4 ACD 5 ABCDE CDF 6 CEH CEH 7 ACD EHG 8 CDF EHG

  8. Example 2: Junction Tree Construction Step1: Insert link between parents of common child A B C D E F G H I

  9. Example 2: Junction Tree Construction Step2: Convert into undirected graph A A B C D B C D E F G E F G H I H I

  10. Example 2: Junction Tree Construction Step3: Triangulate a graph if it has circle of length>3 A B C D E F G H I

  11. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 F has three numbered neighbour B, C and D where B and D are not connected therefore add link between B and D and restart numbering again from beginning. B C D 5 E F G H I

  12. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 B C D 5 6 7 E F G H I 8 9

  13. Example 2: Junction Tree Construction • Five cliques are found in Example 2: • Two cliques of four nodes • Four cliques of three nodes Step4: Ordered the node by max cardinality search. Clique Nodes Max Cardinality 1 A ABCD 4 BCDF 5 2 4 3 B C D BEF 6 DFG 5 7 6 7 E F G EFH 8 H I FGI 8 9 9

  14. Example 2: Junction Tree Construction Construct Tree ABCD 4 ABCD BCDF 5 BEF 6 BCDF DFG 7 DFG EFH 8 BEF FGI 9 FGI EFH

  15. Example 2: Junction Tree Construction (with different triangulation ) Step1: Insert link between parents of common child A B C D E F G H I

  16. Example 2: Junction Tree Construction Step2: Convert into undirected graph A A B C D B C D E F G E F G H I H I

  17. Example 2: Junction Tree Construction Step3: Triangulate a graph if it has circle of length>3 A B C D E F G H I

  18. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 G has three numbered neighbour F, C and D where F and D are not connected therefore add link between F and D and restart numbering again from beginning. B C D 6 5 7 E F G H I

  19. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 F has three numbered neighbour E, C and D where E and D are not connected therefore add link between E and D and restart numbering again from beginning. B C D 6 5 E F G H I

  20. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 E has three numbered neighbour B, C and D where B and D are not connected therefore add link between B and D and restart numbering again from beginning. B C D 5 E F G H I

  21. Example 2: Junction Tree Construction Step3: Numbered the node if its numbered neighboured nodes are connected together. 1 A 2 4 3 B C D 6 5 7 E F G H 8 I 9

  22. Example 2: Junction Tree Construction • Cliques are found in Example 2: • Four cliques of four nodes. • Two cliques of three nodes. Step4: Ordered the node by max cardinality search. 1 A Clique Nodes Max Cardinality 2 4 3 ABCD 4 B C D BCDE 5 6 CDEF 5 6 7 E F G CDFG 7 EFH 8 H 8 I 9 FGI 9

  23. Example 2: Junction Tree Construction Construct Tree ABCD 4 ABCD BCDE 5 CDEF 6 BCDE CDFG 7 CDEF EFH 8 FGI 9 EFH CDFG FGI

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