Lei Shi

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Seminar 2009
Frequent Subgraph/ Substructure Mining

• Lei Shi
• Department of Computer Science and Engineering
• State University of New York at Buffalo

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Outline

• Introduction
• Apriori-based Subgrah Mining
• Pattern Growth Subgraph Mining
• Summary

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Graphs are everywhere
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Graph Mining Problems

• Graph Pattern Mining
• Frequent subgraph pattern mining
• Pattern summarization
• Optimal graph patterns
• Graph patterns with constraints
• Approximate graph patterns .
• Graph Classification
• Graph clustering
• Important node identification
• Bridge and hub identification
• Other Important Topics
• Graph compression
• Graph model
• Social network analysis.

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Subgraph pattern Mining

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

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Frequent Subgraph Example
(1) (2) (3)
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Key Challenges in Subgraph Mining

• Graph isomorphism
• to detect if two graphs are identical in
  structure
• Graph representation (Canonical Labeling)
• A canonical label is a unique code of a given
  graph.
• Canonical label should be the same no matter how
  graphs are represented, as long as graphs have
  the same topological structure and the same
  labeling of edges and vertices.
• Subgraph candidate generation
• generate candidate frequent subgraphs from
  datasets

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Subgraph Mining Approaches

• Apriori-based
• AGM/AcGM Inokuchi, et al. (PKDD00)
• FSG Kuramochi and Karypis (ICDM01)
• M. Kuramochi and G. Karypis. Frequent subgraph
  discovery. In ICDM01, pages 313-320, Nov. 2001
• PATH Vanetik and Gudes (ICDM02, ICDM04)
• FFSM Huan, et al. (ICDM03) and SPIN Huan et
  al. (KDD04)
• FTOSM Horvath et al. (KDD06)
• Pattern growth based
• Subdue Holder et al. (KDD94)
• MoFa Borgelt and Berthold (ICDM02)
• gSpan Yan and Han (ICDM02)
• Yan, X. and Han, J. 2002. gSpan Graph-Based
  Substructure Pattern Mining. In Proceedings of
  the 2002 IEEE international Conference on Data
  Mining (Icdm02) (December 09-12, 2002). ICDM.
  IEEE Computer Society, Washington, DC, 721
• Gaston Nijssen and Kok (KDD04)
• CMTreeMiner Chi et al. (TKDE05)
• LEAP Yan et al. (SIGMOD08)

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Outline

• Introduction and Background
• Apriori-based Subgrah Mining
• Pattern Growth Subgraph Mining
• Summary

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Apriori-based Approach

• FSG Frequent subgraph discovery. In ICDM01,
  Nov. 2001 M.Kuramochi and G. Karypis.
• Flattened Representation as Canonical Labeling
• Apriori-based method to generate subgraph
  candidate

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Graph Representation in FSG

• Flattened Representation

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Graph Representation in FSG

• Flatterned Representation

Lexicographic order or dictionary order
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Apriori-based method

• Apriori Property
• If a graph is frequent, all of its subgraphs are
  frequent.
• Candidate Generation
• Create a set of candidate size k1
• -from given two frequent k-subgraphs
• -containing the same (k-1)-subgraph
• -Result in several candidates size k1

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Apriori-based method

• Graph candidate generated Example

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Apriori-based method

• FlowChart

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Apriori-based method

• Experiment Result
• -Chemical Compound Dataset, which contains 340
  compounds,24 different atoms (vertices)

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Outline

• Introduction
• Apriori-based Subgrah Mining
• Pattern Growth Subgraph Mining
• Summary

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Motivation of gSpan

• Weakness of Apriori-based approach
• The generation of size (k1) subgraph candidates
  from size k frequent subgraph too complicated and
  complex.
• Pruning false positive subgraph isomorphism is
  an NP complete problem which is costly.
• gSpan Graph-Based Substructure Pattern Mining
• Change the way to represent a graph (DFS Depth
  First Search)
• Using pattern growth to generate new subgraph
  candidate.

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gSpan Graph-Based Substructure Pattern Mining

• DFS (Depth First Search) Code
• First Step DFS the graph and use edges on the
  path to represent the graph.
• Second Step DFS Lexicographic Order
• Pattern Growth subgraph generation

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DFS code
An edge is presented by 5 tuples.
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DFS code

• Second Step DFS Lexicographic Order

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Pattern Growth Approach

• Pattern Growth (free extension)

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Pattern Growth Approach

• Duplicate Graphs

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Pattern Growth Approach

• Free extension

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Pattern Growth Approach

• Right most extension

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Pattern Growth Approach

• Exmaples (cont.)

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gSpan
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gSpan
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Pattern Growth Approach

• Experimental result using Chemical data

• 340 molecules
• 66 atom types and
• 4 bond types as labels
• On average only 27 vertices with 28 edges

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Summary

• Graph representation
• Flattern representation vs. DFS code
• Generation of Candidate Patterns
• apriori vs. pattern growth

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Pattern-Growth Approach
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Frequent Graph Pattern

• Given a graph dataset D, find subgraph g, s.t.
• Where is the percentage of graphs
  in D that contain g.
• Problem 1 Exponential Pattern Set
• Problem 2 Threshold Setting

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Difference between frequent itemset and frequent
subgraph discovery
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Frequent itemset discovery
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subgraph Mining Algorithms

• Apriori-based approach
• AGM/AcGM Inokuchi, et al. (PKDD00)
• FSG Kuramochi and Karypis (ICDM01)
• PATH Vanetik and Gudes (ICDM02, ICDM04)
• FFSM Huan, et al. (ICDM03) and SPIN Huan et
  al. (KDD04)
• FTOSM Horvath et al. (KDD06)
• Pattern growth approach
• Subdue Holder et al. (KDD94)
• MoFa Borgelt and Berthold (ICDM02)
• gSpan Yan and Han (ICDM02)
• Gaston Nijssen and Kok (KDD04)
• CMTreeMiner Chi et al. (TKDE05)
• LEAP Yan et al. (SIGMOD08)

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Framework of subraph Mining Algorithms

• Search Order
• breadth vs. depth
• complete vs. incomplete
• Generation of Candidate Patterns
• apriori vs. pattern growth
• Discovery Order of Patterns
• DFS order
• path tree graph
• Elimination of Duplicate Subgraphs
• passive vs. active
• Support Calculation
• embedding store or not

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Frequent Subgraph
Examples
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Example (cont.)
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Subgraph Mining Approaches

• Apriori-based approach
• AGM/AcGM Inokuchi, et al. (PKDD00)
• FSG Kuramochi and Karypis (ICDM01)
• M. Kuramochi and G. Karypis. Frequent subgraph
  discovery. In ICDM01, pages 313-320, Nov. 2001
• PATH Vanetik and Gudes (ICDM02, ICDM04)
• FFSM Huan, et al. (ICDM03) and SPIN Huan et
  al. (KDD04)
• FTOSM Horvath et al. (KDD06)
• Pattern growth approach
• Subdue Holder et al. (KDD94)
• MoFa Borgelt and Berthold (ICDM02)
• gSpan Yan and Han (ICDM02)
• Yan, X. and Han, J. 2002. gSpan Graph-Based
  Substructure Pattern Mining. In Proceedings of
  the 2002 IEEE international Conference on Data
  Mining (Icdm02) (December 09-12, 2002). ICDM.
  IEEE Computer Society, Washington, DC, 721
• Gaston Nijssen and Kok (KDD04)
• CMTreeMiner Chi et al. (TKDE05)
• LEAP Yan et al. (SIGMOD08)

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Outline

• Introduction and Background
• Apriori-based Subgrah Mining
• Pattern Growth Subgraph Mining
• Summary
• DFS code
• Yan, X. and Han, J. 2002. gSpan Graph-Based
  Substructure Pattern Mining. In Proceedings of
  the 2002 IEEE international Conference on Data
  Mining (Icdm02) (December 09-12, 2002). ICDM.
  IEEE Computer Society, Washington, DC, 721

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Pattern Growth Approach