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NeMoFinder: Dissecting genome-wide protein-protein intractions with meso-scale network motifs

NeMoFinder: Dissecting genome-wide protein-protein intractions with meso-scale network motifs. Mike Yuan. Outline of this presentation. Introduction to PPI Introduction to Graph Mining Related work Problem statement Details of the NeMoFinder algorithm Summary References .

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NeMoFinder: Dissecting genome-wide protein-protein intractions with meso-scale network motifs

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  1. NeMoFinder: Dissecting genome-wide protein-protein intractions with meso-scale network motifs Mike Yuan

  2. Outline of this presentation • Introduction to PPI • Introduction to Graph Mining • Related work • Problem statement • Details of the NeMoFinder algorithm • Summary • References

  3. Protein Interactions A Protein may interact with: • Other proteins • Nucleic Acids • Small molecules

  4. Finding Protein Partners

  5. Motivation • Important for biological functions • To understand the function of a protein, we need to find its interacting partners

  6. Graph Theory Vertex (node) Cycle Edge -5 Directed Edge (Arc) Weighted Edge 10 7 Molecular interaction networks are mapped as graphs

  7. The protein protein interaction network…

  8. Graph mining • Methods for Mining Frequent Subgraphs • Mining Variant and Constrained Substructure Patterns • Applications: • Graph Indexing • Similarity Search • Classification and Clustering

  9. Why Graph Mining? • Graphs are ubiquitous • Chemical compounds (Cheminformatics) • Protein structures, biological pathways/networks (Bioinformactics) • Program control flow, traffic flow, and workflow analysis • XML databases, Web, and social network analysis • Graph is a general model • Trees, lattices, sequences, and items are degenerated graphs • Complexity of algorithms: many problems are of high complexity

  10. Graph, Graph, Everywhere from H. Jeong et al Nature 411, 41 (2001) Aspirin Yeast protein interaction network Co-author network Internet

  11. Graph Pattern Mining • Frequent subgraphs • A (sub)graph is frequent if its support (occurrence frequency) in a given dataset is no less than a minimum support threshold • Applications of graph pattern mining • Mining biochemical structures • Program control flow analysis • Mining XML structures or Web communities • Building blocks for graph classification, clustering, compression, comparison, and correlation analysis

  12. Example: Frequent Subgraphs GRAPH DATASET (A) (B) (C) FREQUENT PATTERNS (MIN SUPPORT IS 2) (1) (2)

  13. Frequent Subgraph Mining Approaches • Apriori-based approach: if a graph is frequent, all of its subgraphs are frequent ─ the Apriori property • AGM/AcGM: Inokuchi, et al. (PKDD’00) • FSG: Kuramochi and Karypis (ICDM’01) • PATH#: Vanetik and Gudes (ICDM’02, ICDM’04) • FFSM: Huan, et al. (ICDM’03) • Pattern growth approach • MoFa, Borgelt and Berthold (ICDM’02) • gSpan: Yan and Han (ICDM’02) • Gaston: Nijssen and Kok (KDD’04)

  14. Problem Statement • PPI network G=(V,E) _ each vertex represents a unique protein _ each edge between vA and vB indicates there is an interaction between A and B • Network motif _frequently occurring subgraph pattern in a network • fg is the number of occurrences of a subgraph g, g is repeated if fg>F. • fg_randi is the frequency of g in a randomized network Grandi, for 1 ≤ i ≤ N, N is the number of the randomized networks. sg is the number of times fg≥fg_randi, g is unique if its sg >S. • Network motif discovery algorithm

  15. Problem Statement (cont) • Motivation of NeMoFinder- existing research has following limitations: _Number of network motifs candidates increases exponentially _Interesting network motifs are repeated and unique and Apirori algorithms are not applicable _The graph isomorphism problem is an NP problem • NeMoFinder _ a network motif discovery algorithm to discover repeated and unique meso-scale network motifs in a large PPI network

  16. Key procedures • Example graph G • Find repeated trees • Use repeated trees to partition a network into a set of graphs • Introduce graph cousins to facilitate the candidate generation and frequency counting processes.

  17. Step1. Discover Repeated Subgraphs • Step1.1 find repeated size-k trees • Eg. Size 2 to size 5 trees t2 t3 t4_1 t4_2 t5_1 t5_2 t5_3

  18. Step1. discover repeated subgraphs (cont) • ft2 = 7, ft3 = 13, ft4_1 = 6, ft4_2 =17, ft5_1=1, ft5_2 = 5, ft5_3 = 7. • T2 = {t2}, T3 = {t3}, T4 ={t4_1, t4_2} and T5 = {t5_2, t5_3}.

  19. Step 1.2 Use repeated size-k trees to partition graph • Occurrences of t4_1 in G.

  20. Step 1.2 Use repeated size-k trees to partition graph (cont) • Occurrences of t4_2 in G.

  21. Step1.2 Use repeated size-k trees to partition graph (cont) • Set of graphs GD4 G4_1 G4_2 G4_3 G4_4 G4_5

  22. Step 1.3: perform graph join operation to find repeated size-k graphs • Generate 3-edge subgraphs from size-4 trees t4_1 h1 h2 t4_2 h3 h4 h5

  23. Step 1.3: perform graph join operation to find repeated size-k graphs (cont) • Examples for graph join operations for subgraphs t4_1 h2 g1_2 t4_2 h3 g1_1 • fg1_1 = 2 and fg1_2 = 5

  24. Step 1.3: perform graph join operation to find repeated size-k graphs (cont) • Use subgraphs obtained to generate subgraphs g1_2 h6 h7 • Graph join operations for subgraphs g1_2 h6 g2 • f(g2)<2, algorithm stops

  25. Algorithm1 NeMoFinder 1: Input: G - PPI network;N - Number of randomized networks;K - Maximal network motif size;F - Frequency threshold;S - Uniqueness threshold; 2: Output: U - Repeated and unique network motif set; 3: D ← ∅; 4: for motif-size k from 3 to K do 5: T ← FindRepeatedTrees(k); 6: GDk ← GraphPartition(G, T) 7: D ← D  T; 8: D’ ← T; 9: i ← k; 10: while D’≠∅ and i ≤ k × (k − 1)/2 do 11: D’ ← FindRepeatedGraphs(k,i,D’); 12: D ← D D’; 13: i ← i + 1; 14: end while 15: end for Step1: Discover repeated subgraphs Step 1.1: Find repeated size-k trees Step 1.2: use repeated size-k trees to partition graph Step 1.3: perform graph join operation to find repeated size-k graphs

  26. Algorithm1 NeMoFinder (cont) 16: for counter i from 1 to N do 17: Grand ← RandomizedNetworkGeneration(); 18: for each g  D do 19: GetRandFrequency(g,Grand); 20: end for 21: end for 22: U ← ∅; 23: for each g D do 24: s ← GetUniqunessValue(g); 25: if s ≥ S then 26: U ← U  {g}; 27: end if 28: end for 29: return U; Step 2: Determine subgraph frequency in randomized networks Step 3: Compute uniqueness of subgraphs

  27. Algorithm Steps (cont) • Step 2: Determine subgraph frequency in randomized networks _Generate randomized networks Grandi(1≤i≤N) _check the frequency of the subgraphs in each of the randomized networks Grandi • Step 3: Compute uniqueness of subgraphs _ Based on frequencies in the input PPI network and the randomized networks _fg_randiis the frequency of g in a randomized network Grandi, for 1 ≤ i ≤ N, N is the number of the randomized networks. sg is the number of times fg≥fg_randi, g is unique if its sg >S.

  28. Find repeated subgraphs Algorithm 2 FindRepeatedGraphs(k, i,D’) 1: Input: D’ - Set of repeated subgraphs with k vertices and i − 1 edges; 2: Output: D’’ - Set of repeated subgraphs with k vertices and i edges; 3: C ← CandidateGeneration(k, i, D’); 4: D’’ ← FrequencyCounting(k, i, C); 5: return D’’;

  29. Candidate generation using graph cousins • Represent subgraphs by adjacency matrices • Code(M): a sequence formed by linking the lower triangular entries of M in the following order: m1,1m2,1m2,2…mn,1mn,2…mn,n • Transform adjancy matrix into canonical adjacency matrix (CAM) which has the maximal code • Definition of subCAM of a graph _ A matrix obtained by setting the last edge entry in CAM(g) to 0.

  30. Candidate generation using graph cousins (cont) • Definition of cousin _ Given two subgraphs g and h, if subCAM(g) = subCAM(h), then h is a cousin of g. • Three types of cousin relationship between g and h: _ Type I: Direct Cousin h is isomorphic to a subgraph g’ which has the same number of vertices and edges as g, and g’ ≠g; _ Type II: Twin Cousin h is isomorphic to subgraph g; _Type III: Distant Cousin h is a disconnected subgraph.

  31. 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 Candidate generation using graph cousins (cont) • Adjacency matrices for the graphs in figure 6 t4_1 h1 h2

  32. Candidate generation using graph cousins (cont) • Adjacency matrices for the graphs in figure 6 t4_2 h3 h4h5

  33. Candidate generation using graph cousins (cont) • Observations of above example _h1 is a type 1 direct cousin of t4_1 _h2 is a type 3 distant cousin of t4_1 _h3 is a type 2 twin cousin of t4_2 _h4 is a type 1 direct cousin of t4_2 _h5 is a type 3 distant cousin of t4_2

  34. Candidate generation using graph cousins (cont) Algorithm 3 CandidateGeneration(k, i,D’) 1: Input: D’ - Set of repeated subgraphs with k vertices and i − 1 edges; 2: Output: C - Set of candidates with k vertices and i edges; 3: C ← ∅; 4: for each g  D do 5: H ← GetCousin(g); 6: for each h  H do 7: g’ ← join(g, h); 8: C ← C  {g}; 9: end for 10: end for 11: return C; Step 1: Find set of cousins Step2: join g with cousins to form new subgraph

  35. Frequency counting • Leveraging properties of the different types of cousins _Lx: set of graphs in GDk embedding x _If type of h=type I direct cousin of g, g’ is subgraph obtained by g and h, then Lg’= Lg ∩ Lh, fg’= |Lg ∩ Lh| _if type of h = Type III distant cousin,then fg’= |Lg ∩ Lh| _if type of h = Type II twin cousin then fg’ =CheckAllOccurances(g) _Lt4_1 ={G4_1,G4_2,G4_3,G4_5}, Lh2 = {G4_1,G4_2,G4_3,G4_4,G4_5} Lg1_2= Lt4_1∩ Lh2 ={G4_1,G4_2,G4_3,G4_5}, fg1_2=4>2

  36. Frequency counting Algorithm 4 FrequencyCounting(k, i,C) 1: Input: GDk - Set of graphs generated by partitioning G with size-k repeated trees; C - Set of subgraph candidates with k vertices and i edges; F - Frequency threshold; 2: Output: D’’ - Set of repeated subgraphs with k vertices and i edges; 3: D’’ ← ∅; 4: for each g’  C do 5: Get the join parameter of g’: g and h; 6: Lg ← set of graphs in GDk embedding g; 7: Lh ← set of graphs in GDk embedding h; 8: if fg < F or fh < F then 9: fg’ ← 0; 10: else if type of h = Type I direct cousin then 11: fg’ ← |Lg ∩ Lh| 12: else if type of h = Type III distant cousin then 13: fg’ ← |Lg ∩ Lh| 14: else if type of h = Type II twin cousin then 15: fg’ ← CheckAllOccurances(g); 16: end if 17: if fg’ > F then 18: D’’ ← D’’  {g’}; 19: end if 20: end for 21: return D’’; Case h is direct cousin Case h is distant cousin Case h is twin cousin

  37. Summary • NemoFinder-an efficient network motif discovery algorithm to discover larger-sized repeated and unique network motifs in PPI networks. • Use repeated trees to partition network into graphs • Graph cousins for candidate generation and frequency counting

  38. References (1) • T. Asai, et al. “Efficient substructure discovery from large semi-structured data”, SDM'02 • C. Borgelt and M. R. Berthold, “Mining molecular fragments: Finding relevant substructures of molecules”, ICDM'02 • D. Cai, Z. Shao, X. He, X. Yan, and J. Han, “Community Mining from Multi-Relational Networks”, PKDD'05. • J.Chen, W.Hsu, M.Lee,NeMoFinder: Dissecting genome wide protein-protein interactions with repeated and unique network motifs, Seekiong Ng, SIGKDD 2006 • M. Deshpande, M. Kuramochi, and G. Karypis, “Frequent Sub-structure Based Approaches for Classifying Chemical Compounds”, ICDM 2003 • M. Deshpande, M. Kuramochi, and G. Karypis. “Automated approaches for classifying structures”, BIOKDD'02 • C. Faloutsos, K. McCurley, and A. Tomkins, “Fast Discovery of 'Connection Subgraphs”, KDD'04 • H. Fröhlich, J. Wegner, F. Sieker, and A. Zell, “Optimal Assignment Kernels For Attributed Molecular Graphs”, ICML’05

  39. References (2) • L. Holder, D. Cook, and S. Djoko. “Substructure discovery in the subdue system”, KDD'94 • J. Huan, W. Wang, D. Bandyopadhyay, J. Snoeyink, J. Prins, and A. Tropsha. “Mining spatial motifs from protein structure graphs”, RECOMB’04 • J. Huan, W. Wang, and J. Prins. “Efficient mining of frequent subgraph in the presence of isomorphism”, ICDM'03 • H. Hu, X. Yan, Yu, J. Han and X. J. Zhou, “Mining Coherent Dense Subgraphs across Massive Biological Networks for Functional Discovery”, ISMB'05 • A. Inokuchi, T. Washio, and H. Motoda. “An apriori-based algorithm for mining frequent substructures from graph data”, PKDD'00 • C. James, D. Weininger, and J. Delany. “Daylight Theory Manual Daylight Version 4.82”. Daylight Chemical Information Systems, Inc., 2003. • G. Jeh, and J. Widom, “Mining the Space of Graph Properties”, KDD'04 • H. Kashima, K. Tsuda, and A. Inokuchi, “Marginalized Kernels Between Labeled Graphs”, ICML’03

  40. References (3) • M. Koyuturk, A. Grama, and W. Szpankowski. “An efficient algorithm for detecting frequent subgraphs in biological networks”, Bioinformatics, 20:I200--I207, 2004. • T. Kudo, E. Maeda, and Y. Matsumoto, “An Application of Boosting to Graph Classification”, NIPS’04 • M. Kuramochi and G. Karypis. “Frequent subgraph discovery”, ICDM'01 • M. Kuramochi and G. Karypis, “GREW: A Scalable Frequent Subgraph Discovery Algorithm”, ICDM’04 • C. Liu, X. Yan, H. Yu, J. Han, and P. S. Yu, “Mining Behavior Graphs for ‘Backtrace'' of Noncrashing Bugs’'', SDM'05 • P. Mahé, N. Ueda, T. Akutsu, J. Perret, and J. Vert, “Extensions of Marginalized Graph Kernels”, ICML’04 • S. Nijssen and J. Kok. A quickstart in frequent structure mining can make a difference. KDD'04 • J. Prins, J. Yang, J. Huan, and W. Wang. “Spin: Mining maximal frequent subgraphs from graph databases”. KDD'04

  41. References (4) • D. Shasha, J. T.-L. Wang, and R. Giugno. “Algorithmics and applications of tree and graph searching”, PODS'02 • J. R. Ullmann. “An algorithm for subgraph isomorphism”, J. ACM, 23:31--42, 1976. • N. Vanetik, E. Gudes, and S. E. Shimony. “Computing frequent graph patterns from semistructured data”, ICDM'02 • C. Wang, W. Wang, J. Pei, Y. Zhu, and B. Shi. “Scalable mining of large disk-base graph databases”, KDD'04 • T. Washio and H. Motoda, “State of the art of graph-based data mining”, SIGKDD Explorations, 5:59-68, 2003 • X. Yan and J. Han, “gSpan: Graph-Based Substructure Pattern Mining”, ICDM'02 • X. Yan and J. Han, “CloseGraph: Mining Closed Frequent Graph Patterns”, KDD'03 • X. Yan, P. S. Yu, and J. Han, “Graph Indexing: A Frequent Structure-based Approach”, SIGMOD'04 • X. Yan, X. J. Zhou, and J. Han, “Mining Closed Relational Graphs with Connectivity Constraints”, KDD'05 • X. Yan, P. S. Yu, and J. Han, “Substructure Similarity Search in Graph Databases”, SIGMOD'05 • X. Yan, F. Zhu, J. Han, and P. S. Yu, “Searching Substructures with Superimposed Distance”, ICDE'06 • M. J. Zaki. “Efficiently mining frequent trees in a forest”, KDD'02

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