20131216 Stat Journal

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http://www.ncbi.nlm.nih.gov/pubmed/20236959
J R Soc Interface. 2010 Sep 6;7(50):1341-54. doi: 10.1098/rsif.2010.0063. Epub 2010 Mar 17.
Topological network alignment uncovers biological function and phylogeny.
Kuchaiev O, Milenkovic T, Memisevic V, Hayes W, Przulj N.

http://www.ncbi.nlm.nih.gov/pubmed/19259413
Cancer Inform. 2008;6:257-73. Epub 2008 Apr 14.
Uncovering biological network function via graphlet degree signatures.
Milenković T, Przulj N.

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20131216 Stat Journal

  1. 1. Topological network alignment 20131216 Statistics journal
  2. 2. Result G H G(V, E) H(U, F) EC = 0.089
  3. 3. Motivation large-scale networks such as interactome Yeast Human Are two networks the same or similar?
  4. 4. Theoretical background Network or Graph Collection of nodes (vertex) and connections between them (edges). Biology, social communication, and web pages
  5. 5. Theoretical background G H G(V, E) H(U, F)
  6. 6. Theoretical background Graph comparison Subgraph isomorphism Is G an exact subgraph of H? NP-complete Efficient algorithms are not known. G H G(V, E) Graph alignment Fitting G into H Edge correctness (EC): the % of E aligned to F NP-hard H(U, F)
  7. 7. Previous approaches Local alignment : ambiguous, different pairing Mapping are chosen independently for local regions of similarity. PathBLAST : homology information NetworkBLAST : conserved protein clusters with likelihood method MaWISh : evolution (sequence alignment) GRAEMLIN : dense conserved subgraph with phylogeny Global alignment Provide unique alignment from each node in smaller graph to exactly one node in larger graph ISORANK : maximize overall match GRAEMLIN : training from known graph alignments and phylogeny
  8. 8. New approaches Never use a priori information Sequence, Homology, Clusters, Phylogeny ,and Known alignments Topological similarity Orbit, graphlet, and signature similarity Of course, a priori information can be used. そう、GRAAL ならね
  9. 9. n-node graphlet and automorphism orbits
  10. 10. n-node graphlet and automorphism orbits orbit Topologically relevant graphlet Topologically relevant Topologically relevant
  11. 11. Graphlet Degree Vector
  12. 12. Graphlet Degree Vector
  13. 13. Graphlet Degree Vector
  14. 14. Graphlet Degree Vector
  15. 15. n-node graphlet and automorphism orbits
  16. 16. Signature similarity
  17. 17. Signature similarity
  18. 18. GRAph ALigner algorithm (GRAAL) density topology * G H G(V, E) H(U, F)
  19. 19. GRAAL Search the densest part and align. Search the minimal cost nodes pair (seed). If multi-minimal cost pairs, chosen randomly. G(V, E) H(U, F)
  20. 20. GRAAL Search the densest part and align. Search the minimal cost nodes pair (seed). If multi-minimal cost pairs, chosen randomly. G(V, E) H(U, F)
  21. 21. GRAAL Make spheres and align. G(V, E) H(U, F)
  22. 22. GRAAL Make spheres and align. G(V, E) H(U, F)
  23. 23. GRAAL Make spheres and align. G(V, E) H(U, F)
  24. 24. GRAAL Expand radii of spheres and align. Aligned node G(V, E) H(U, F)
  25. 25. GRAAL Expand radii of spheres and align. Aligned node G(V, E) H(U, F)
  26. 26. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F)
  27. 27. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F)
  28. 28. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F) Some nodes are not aligned.
  29. 29. Aligned node
  30. 30. Aligned node
  31. 31. Aligned node New seed New seed
  32. 32. Aligned node New seed New seed
  33. 33. GRAAL Nodes in G are aligned to exactly one node in H. Aligned node G(V, E) H(U, F)
  34. 34. Alignment score G H G(V, E) GRAAL function The correct node mapping G to H H(U, F)
  35. 35. Statistical significance The number of node pairs in H. Edge correctness The number of edges from G that are aligned to edges in H. G H G(V, E) H(U, F)
  36. 36. Result G H G(V, E) H(U, F) EC = 0.089

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