Frequent Subgraph Discovery

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Frequent Subgraph Discovery

• Michihiro Kuramochi and George Karypis
• ICDM 2001

2
Outline

• Introduction
• FSG algo.
• Canonical Labeling
• Conclusion

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Introduction

• n Most of existing data mining algorithms assume
  that the data is
• represented via
• n Transactions (set of items)
• n Sequence of items or events
• n Multi-dimensional vectors
• n Time series
• n Scientific datasets with layers, hierarchy,
  geometry,
• and arbitrary relations can not be
  accurately modeled using
• such frameworks.
• n e.g. chemical compounds

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• Graphs can
• accurately model
• and represent
• scientific data sets
• Graphs are suitable
• for capturing
• arbitrary relations
• between the various
• elements

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Example
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FSG(Frequent Subgraph Discovery Algorithm)

• Level-by-level approach Incremental on the number
  of edges of the frequent subgraphs(like Apriori)
• Counting of frequent single and double edge
  subgraphs
• For finding frequent size k-subgraphs(k3)
• Candidate generation
• Joining two size (k-1) subgraphs similar to each
  other
• Candidate pruning by downward closure property
• Frequency counting
• Check if a subgraph is contained in a transaction
• Repeat the steps for k k 1
• Increase the size of subgraphs by one edge

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FSG ApproachCandidate Generation

• Generate a size k-subgraph by merging two size
  (k-1) subgraphs

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FSG ApproachCandidate Pruning

• Pruning of size k-candidates
• For all the (k-1)-subgraphs
• of a size k-canidate,
• check if downward
• closure property
• holds

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FSG ApproachFrequency Counting

• For each subgraph to scan each one of the
  transaction graphs and determine if it is
  contained or not using subgraph isomorphism
• In Apriori,the frequency counting is performed
  substantially faster by building a hash-tree of
  candidate itemsets
• To scan each transaction to determine which of
  the itemsets in the hash-tree it supports

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FSG ApproachFrequency Counting

• Keep track of the TID-List
• Perform subgraph isomorphism only on the
  intersection of the TID lists of the parent
  frequent subgraphs of size k-1

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FSG ApproachFrequency Counting

• Perform only subgraph_isomorphism(c, T1)

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Key to PerformanceCanonical Labeling

• Given a graph, we want to find a unique order of
  vertices, by permuting rows and columns of its
  adjacency matrix

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Canonical Labeling

• Find the vertex order so that the matrix becomes
  lexicographically the Largest when we compare in
  the column-wise way

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Conclusion

• During both candidate generation and frequency
  counting, what FSG essentially does is to solve
  subgraph isomorphism
• Canonical Labeling can reduce our search space
• Using TID List
• Reduce the number of subgraph isomorphism checks
• Suitable for sparse graph transactions