20131216 Stat Journal
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This document describes a new algorithm called GRAph ALigner (GRAAL) for topological network alignment. GRAAL aims to provide a unique global alignment of nodes between two networks based solely on topological similarity, without using other a priori information. It works by first finding a dense core between the networks to seed the alignment, then expanding outwards in spheres of increasing radius to align additional nodes. The alignment score is based on the percentage of edges from the first network that are correctly aligned to edges in the second network. The algorithm is tested on sample networks and achieves an edge correctness of 0.089.
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20131216 Stat Journal
- 3. Result G H G(V, E) H(U, F) EC = 0.089
- 4. Motivation large-scale networks such as interactome Yeast Human Are two networks the same or similar?
- 5. Theoretical background Network or Graph Collection of nodes (vertex) and connections between them (edges). Biology, social communication, and web pages
- 7. 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)
- 8. 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
- 9. 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
- 10. n-node graphlet and automorphism orbits
- 11. n-node graphlet and automorphism orbits orbit Topologically relevant graphlet Topologically relevant Topologically relevant
- 16. n-node graphlet and automorphism orbits
- 19. GRAph ALigner algorithm (GRAAL) density topology * G H G(V, E) H(U, F)
- 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. 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)
- 22. GRAAL Make spheres and align. G(V, E) H(U, F)
- 23. GRAAL Make spheres and align. G(V, E) H(U, F)
- 24. GRAAL Make spheres and align. G(V, E) H(U, F)
- 25. GRAAL Expand radii of spheres and align. Aligned node G(V, E) H(U, F)
- 26. GRAAL Expand radii of spheres and align. Aligned node G(V, E) H(U, F)
- 27. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F)
- 28. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F)
- 29. GRAAL Expand radii of spheres up to 3. Aligned node G(V, E) H(U, F) Some nodes are not aligned.
- 30. Aligned node
- 31. Aligned node
- 32. Aligned node New seed New seed
- 33. Aligned node New seed New seed
- 34. GRAAL Nodes in G are aligned to exactly one node in H. Aligned node G(V, E) H(U, F)
- 35. Alignment score G H G(V, E) GRAAL function The correct node mapping G to H H(U, F)
- 36. 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)
- 37. Result G H G(V, E) H(U, F) EC = 0.089