Efficient Algorithms for Association Finding and Frequent Association Pattern Mining
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The document presents efficient algorithms for association finding and frequent association pattern mining in large graph data. It describes the problems of finding all associations connecting a set of query entities within a diameter constraint and mining frequent association patterns. The basic solutions and optimizations for association finding using distance-based pruning and distance oracles are discussed. For frequent pattern mining, it addresses generating a canonical code to uniquely represent patterns and counting code occurrences to determine frequency. Experiments on real datasets demonstrate the efficiency and scalability of the approaches.
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Efficient Algorithms for Association Finding and Frequent Association Pattern Mining
- 1. Efficient Algorithms for Association Finding and Frequent Association Pattern Mining Gong Cheng, Daxin Liu, Yuzhong Qu Websoft Research Group National Key Laboratory for Novel Software Technology Nanjing University, China Websoft
- 2. Background and motivation • To suggest friends, recognize suspected terrorists, answer questions … based on massive graph data
- 3. Problem statement An association connecting a set of query entities is a minimal subgraph that • contains all the query entities, and • is connected. Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 4. Problem statement An association connecting a set of query entities is a minimal subgraph that • contains all the query entities, and • is connected. Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 5. Problem statement An association connecting a set of query entities is a minimal subgraph that • contains all the query entities, and • is connected. Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 6. Problem statement An association connecting a set of query entities is a minimal subgraph that • contains all the query entities, and • is connected. Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice • Tree-structured • Leaves ⊆ Query entities
- 7. Problem statement 1. How to efficiently find associations in a possibly very large graph? 2. How to help users explore a possibly large set of associations that have been found? Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 8. Problem statement 1. How to efficiently find associations in a possibly very large graph? 2. How to help users explore a possibly large set of associations that have been found? Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice Association finding Frequent association pattern mining
- 9. Association finding: Problem • To find all the associations having a limited diameter (Diameter = Greatest distance between any pair of vertices) Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 10. Association finding: Basic solution Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Chris attended Paper-AisAuthorOf acceptedAt ISWC Alice Bob reviewer ISWC ISWC An association A set of paths
- 11. Association finding: Basic solution Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Chris attended Paper-AisAuthorOf acceptedAt ISWC Alice Bob reviewer ISWC ISWC 1. Path finding 2. Path merging
- 12. Association finding: Optimization • Distance-based search space pruning Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice • DiameterConstraint ≤ 3 • Length(AliceDan) = 1 • Distance(Dan, Bob) = 4 Length+Distance > DiameterConstraint
- 13. Association finding: Optimization • Distance computation • Materializing offline computed results: O(V2) space • Online computing: O(E) time per pair • Using distance oracle: a space-time trade-off Chris Bob Paper-A Paper-B Dan isAuthorOf knows correspondingAuthor acceptedAt Ellen knows ISWC isAuthorOf COLD acceptedAt attended attended attended reviewer reviewer Frank knows Alice
- 14. Association finding: Deduplication Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Chris attended Paper-AisAuthorOf acceptedAt ISWC Alice Bob reviewer ISWC ISWC An association A set of paths
- 15. Association finding: Deduplication Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Chris attended Paper-AisAuthorOf Alice Bob reviewer ISWC ISWC A duplicate association Another set of paths Paper-A acceptedAt Paper-A acceptedAt
- 16. Association finding: Deduplication • Canonical code Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice code(Tree(Alice)) = Alice,isAuthorOf,code(Tree(Paper-A))$ = … Paper-A,acceptedAt,code(Tree(ISWC))$ … = … ISWC,reviewer,code(Tree(Bob)),~attended,code(Tree(Chris))$ … = … Bob$ … (Assuming Bob precedes Chris)
- 17. Frequent association pattern mining • Association pattern: A conceptual abstract that summarizes a group of associations Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Association Association pattern (Intermediate entity Class) Chris Bob PaperisAuthorOf acceptedAt Conference attended reviewer Alice
- 18. Frequent association pattern mining • Problem: To mine all the association patterns matched by more than a threshold proportion of associations Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Association Association pattern (Intermediate entity Class) Chris Bob PaperisAuthorOf acceptedAt Conference attended reviewer Alice
- 19. Frequent association pattern mining • Basic solution: Chris Bob Paper-AisAuthorOf acceptedAt ISWC attended reviewer Alice Association Association pattern (Intermediate entity Class) Chris Bob PaperisAuthorOf acceptedAt Conference attended reviewer Alice Calculating the frequency of an association pattern = Counting the occurrence of its canonical code
- 20. Frequent association pattern mining • Canonical code Chris Bob PaperisAuthorOf acceptedAt Conference attended reviewer Alice Paper isAuthorOf acceptedAt Conference code(Tree(Alice)) = Alice,isAuthorOf,code(Tree(Paper)),isAuthorOf,code(Tree(Paper))$ Paper equals Paper. So which subtree should go first? (Canonical code may not be unique!)? ?
- 21. Frequent association pattern mining • Canonical code Chris Bob PaperisAuthorOf acceptedAt Conference attended reviewer Alice Paper isAuthorOf acceptedAt Conference code(Tree(Alice)) = Alice,isAuthorOf,code(Tree(Paper)),isAuthorOf,code(Tree(Paper))$ Smallest leaf as its proxy to be compared Equality would never happen. (Canonical code is now unique!) (Assuming Bob precedes Chris)
- 22. Experiments • Datasets • LinkedMDB: 1M vertices and 2M arcs • DBpedia (2015-04): 4M vertices and 15M arcs • Parameter settings • Diameter constraint (λ): 2, 4 • Number of query entities (n): 2, 3, 4, 5 • Test queries • 1,000 random sets of query entities under each setting of λ and n • Hardware configuration • 3.3GHz CPU, 24GB memory • Data graphs: in memory • Distance oracles: on disk
- 23. Experiments • Results: Association finding BSC: Basic solution (not pruning) PRN: Optimized solution (distance-based pruning) PRN-1: Optimized solution (distance-based pruning except for the last level of search)
- 24. Experiments • Results: Frequent association pattern mining • LinkedMDB • <10,000 associations: <21ms • 13,531 associations: 68ms • DBpedia • <10,000 associations: <65ms • 1,198,968 associations: 2909ms
- 25. Takeaway messages • Subgraph finding and mining are faster than what we expected. • Consider distance oracle and canonical code in your own research.
- 26. Takeaway messages • Subgraph finding and mining are faster than what we expected. • Consider distance oracle and canonical code in your own research.