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TopK Interesting Subgraph Discovery in Information Networks. Manish Gupta Jing Gao Xifeng Yan Hasan Cam Jiawei Han. Real World Problems. Network Bottlenecks Discovery. Computer Networks. Organization Networks. Team Selection.
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TopK Interesting Subgraph Discovery in Information Networks Manish Gupta Jing GaoXifeng Yan Hasan Cam Jiawei Han gmanish@microsoft.com
Real World Problems Network Bottlenecks Discovery Computer Networks Organization Networks Team Selection Interestingness = Highest Historical Compatibility Interestingness = Lowest Bandwidth Suspicious Relationships Discovery Battlefield Networks Resource Allocation Social Networks Interestingness = Highest Negative Association Strength of Attribute Values Interestingness = Lowest Distance between Entities gmanish@microsoft.com
The Basic Underlying Problem Team Selection Network Bottlenecks Discovery Interestingness = Lowest Bandwidth Interestingness = Highest Historical Compatibility Suspicious Relationships Discovery Resource Allocation Interestingness = Highest Negative Association Strength Interestingness = Lowest Distance • Given • Edge-weighted Typed Network G • Typed Subgraph Query Q • Edge Interestingness measure • Find • TopK matching subgraphs gmanish@microsoft.com
Naïve Solution: Ranking After Matching 4 3 2 1 A A A B 0.8 0.7 0.2 12 13 0.2 Network G Query Q C C 0.4 0.5 0.4 0.3 6 5 4 3 2 1 2 3 6 5 4 4 3 3 2 B A A A A A A B Ranking 0.6 0.8 0.8 0.7 0.2 B A A A A A A Why compute all matches? We need only top-2! 0.6 0.8 0.8 0.8 0.7 0.9 0.1 0.7 0.1 10 9 8 7 0.7 11 1 4 10 9 8 7 B C A A A B A 0.3 0.6 0.5 0.2 A A A B B 0.3 0.6 0.5 Matching 4 3 2 6 5 A A A B A 0.8 0.7 0.6 0.1 0.9 7 10 9 5 B 6 5 A A 0.3 4 5 A A A B A 0.8 0.6 0.9 0.9 0.1 0.9 9 8 7 9 7 9 8 A A B A B 7 A A 0.6 0.5 0.6 gmanish@microsoft.com
Our Contributions • New notion: TopK interesting subgraph detection in information networks • Three new low-cost indexes • Graph topology index • Sorted edge lists • Graph maximum metapath weight index • Novel top-K algorithm to answer interestingness queries on large graphs • Detailed effectiveness and efficiency validation on several synthetic and real datasets gmanish@microsoft.com
Relationship with Previous Work • Subgraph matching • Approximate: fuzzy node/edge similarity • Exact: Matching without ranking • RDF graphs, probabilistic graphs, temporal graphs • TopK querying on graphs • H-hop aggregate queries • Keyword queries on RDF graphs • K most frequent patterns • Twig queries gmanish@microsoft.com
System Overview 2 Network G Breadth First Traversal from each Node up to Distance D Graph Topology Index Offline Index Construction Distance D Sort Edges 3 Graph Maximum MetaPathWeight Index 1 Sorted Edge Lists Find Candidate Nodes Query Q Candidate Nodes Top-K Computation Online Query Processing Top-K Subgraphs gmanish@microsoft.com
G=(V,E), B=avg #neighbors, T=#types Index Structures 12 13 0.2 Network G C C 0.4 0.5 0.4 0.3 6 5 4 3 2 1 B A A A A B 0.6 0.8 0.8 0.7 0.2 0.9 0.1 0.7 0.1 10 9 8 7 11 C A A A B 0.3 0.6 0.5 0.2 gmanish@microsoft.com
Find Candidate Nodes Graph Topology Index Query Q Query Q Graph Topology Index 2 3 A A 1 4 B A Query Topology gmanish@microsoft.com
Finding and Scoring MatchesKey Idea Query Q Top-K Computation 2 3 Start Y Generate a Size-1 Candidate A A More valid edges? N 1 4 Y B A TopK Quit? Compute Actual and UB Score N Y N Candidate Size==|Q|? B A A A Grow Candidates N Y Y Top-K Heap TopK Quit? Compute Actual and UB Score Update Heap Compute Max UB Score N Y TopK Quit? Done! gmanish@microsoft.com
Finding and Scoring MatchesGenerating Size-1 Candidates Size-1 Candidates Query Q 9 9 2 9 5 5 9 9 9 9 3 5 5 5 5 5 5 9 A A A A A A A A A A A A A A A A A A A A 5 1 9 4 B B B B B B B B B B A A A A A A A A A A Query Edge with both endpoints of same type Multiple query edges of the same type Candidate Growth B A A A Order (5,9) (3,4) (4,5) (2,3) (2,7) … Heapify? Discard? Prune? Grow? 8 6 6 10 Prune? Grow? 8 10 Heapify? Discard? Prune? Grow? gmanish@microsoft.com
Finding and Scoring MatchesActual Score and Upper Bound Score Candidate Growth 9 9 9 9 5 5 5 5 Prune? Grow? Prune? Grow? Heapify? Discard? 6 8 8 A A A A A A A A B B B B A A A A Actual Score= 0.9 B A A A UB Score = 0.9+ UB(NonConsidered Edges) = 0.9+ (0.6+0.6) = 2.1 • Partially grown candidate • Prune if UBScore< min(heap) • Grow otherwise • Fully grown candidate • Discard if UBScore< min(heap) • Update heap otherwise Useful Edge Lists gmanish@microsoft.com
Finding and Scoring MatchesGlobal Top-K Quit 12 13 0.2 Network G C C Query Q 0.4 0.5 0.4 0.3 6 5 4 3 2 1 2 3 B A A A A A A B 0.6 0.8 0.8 0.7 0.2 0.9 0.1 0.7 1 4 0.1 10 9 8 7 11 B A C A A A B 0.3 0.6 0.5 0.2 B A A A K=2 TopK Heap (4,3,2,7): 2.2 (3,4,5,6): 2.2 Stop 0.7+0.6+0.7 = 2 <2.2 gmanish@microsoft.com
Faster Query Processing using Graph Maximum MetaPath Weight Index Slight complication 1 1 1 4 3 5 C 4 3 5 C C A B C A B C 2 2 2 C C C Query 6 7 1 B C Query Partial Instantiation UB Score = Actual Score(1-2) + UB(1-3) + UB(2-3) + UB(3-4) + UB(4-5) C 1 4 3 5 C 2 C 4 A B C B Partial Candidate 7 3 6 7 C A UB Score = Actual Score(1-2) + UB(1-3-4-5) + UB(2-3) 2 B C 1 C 4 3 5 C Paths to cover Non-Considered Edges Edges to Consider Separately A B C 3 Paths to cover Non-Considered Edges A UB Score = Actual Score(1-2) + UB(1-3-4-5-7) + UB(2-3) + UB(4-6) +UB(6-7) 2 Using MMW Index! C gmanish@microsoft.com
Faster Query Processing using Graph Maximum MetaPathWeight Index 5 A A Prune? Grow? 9 B A Edge-based UBScore 0.9+0.8+0.7 =2.4 > 2.0 B A A A Grow K=2 TopK Heap (8,9,5,6): 2.1 (5,9,8,7): 2.0 Path-based UBScore 0.9+UB(5-A-B) =0.9+0.9 =1.8 < 2.0 Prune MMW Index gmanish@microsoft.com
Discussions • Queries with multiple edge semantics • Directed graphs • Homogeneous networks • Weighted query edges • Weights signify expected amount of interestingness • Weights signify importance of query edge • Faster computations versus index size gmanish@microsoft.com
Low-cost Index Structures gmanish@microsoft.com
Faster Query Execution Query Execution Time (msec) for Clique Queries (Graph G2 and indexes with D=2) Query Execution Time (msec) for Path Queries (Graph G2 and indexes with D=2) RAM: Ranking After Matching baseline RWM0: without using the candidate node filtering RWM1: without using the MMW index RWM2: same as RWM1 without the pruning any partially grown candidates RWM3: same as RWM1 without the global top-K quit check RWM4: same as RWM1 with the MMW index Query Execution Time (msec) for Subgraph Queries (Graph G2 and indexes with D=2) gmanish@microsoft.com
Good Scalability Good Scalability thanks to Effective Pruning Running time (msec) for different Query Sizes and Graph Sizes (D=2) Number of Candidates as Percentage of Total Matches for Different Query Sizes and Candidate Sizes Query Execution Time for Different Values of K gmanish@microsoft.com
Real Dataset Case Studies 2 2 4 1 1 Author Conf Author Conf Keyword 3 3 Author Author Q1 Q2 2 2 4 1 1 Person Film Person Company Settlement 3 3 Person Person Q3 Q4 gmanish@microsoft.com
Real Dataset Case Studies • DBLP • 1: Rohit Gupta, 2: BICoB, 3: Vipin Kumar • Rohit Gupta -- computer networking • Vipin Kumar -- Data and Information Systems • BICoB -- International Conference on Bioinformatics and Computational Biology • 1: Jimeng Sun, 2: Operating Systems Review (SIGOPS), 3: Christos Faloutsos, 4: mining • Jimeng Sun and Christos Faloutsos -- Data and Information Systems, Artificial intelligence, and Computational biology • "mining" -- Data and Information Systems • "Operating Systems Review (SIGOPS)" -- Operating systems, Computer architecture, Computer networking gmanish@microsoft.com
Real Dataset Case Studies • Wikipedia • 1: Stacy Keach, 2: The Biggest Battle, 3: John Huston • Stacy Keach and John Huston starred in the movie “The Biggest Battle” • Stacy Keach (American), John Huston (American), movie is Italian • Stacy (narration, comedy, music), John (drama, documentary, adventure), movie (war) • 1: Medha Patkar, 2: BBC, 3: Felix D’Alviella, 4: Mogilino • Medha Patkar -- Indian social activist -- won Best International Political Campaigner by BBC • Felix D’Alviella -- Belgian actor in the BBC soap opera Doctors • Mogilino -- village in Bulgaria -- BBC showed the popular film "Bulgaria’s Abandoned Children" in 2007 • British company rewarding an Indian woman, covering a place in Bulgaria or linked to a person from Belgium is rare gmanish@microsoft.com
Related Work (1) Theory literature on subgraph isomorphism [Cordella et al., 2004; McKay, 1981; Ullmann, 1976] Exact subgraph matching [Cheng et al., 2008; He and Singh, 2008; Sun et al., 2012; Zhang et al., 2007; Zhang et al., 2009; Zhao and Han, 2010; Zou et al., 2009] Approximate subgraph matching [Zou et al., 2007; Zeng et al., 2012; Tian et al., 2007; Zhang et al., 2010] gmanish@microsoft.com
Related Work (2) • Matching in graph databases [Ranu and Singh, 2009; Yan et al., 2005; Zhu et al., 2012] • Matching for RDF graphs [Liu et al., 2012], probabilistic graphs [Yuan et al., 2012] and temporal graphs [Bogdanov et al., 2011] • Top-K queries • h-hop aggregate queries [Yan et al., 2010] • K most frequent patterns [Yang et al., 2012; Zhu et al., 2011] • Top-K keyword queries on RDF graphs [Tran et al., 2009] • Top-K similarity queries [Zou et al., 2007] • Twig queries [Gou and Chirkova, 2008] gmanish@microsoft.com
Conclusion • Given • Typed unweighted query • A heterogeneous edge-weighted information network • Edge interestingness measure • Find • Top-K interesting subgraphs • Investigated ranking after matching baseline • Proposed three new graph indexes and exploited them for building a top-K solution • Showed efficiency, scalability and effectiveness on multiple synthetic and real datasets gmanish@microsoft.com
Thanks! gmanish@microsoft.com