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SPIN: Mining Maximal Frequent Subgraphs from Graph Databases. Jun Huan, Wei Wang, Jan Prins, Jiong Yang KDD 2004. Introduction. Graphs model a relations among data Inter-disciplinary research Huge number of recurring patterns To mining only maximal frequent subgraphs.

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spin mining maximal frequent subgraphs from graph databases

SPIN: Mining Maximal Frequent Subgraphs from Graph Databases

Jun Huan, Wei Wang, Jan Prins, Jiong Yang

KDD 2004

introduction
Introduction
  • Graphs model a relations among data
    • Inter-disciplinary research
  • Huge number of recurring patterns
  • To mining only maximal frequent subgraphs.
    • None of its super graphs are frequent
advantages
Advantages
  • Reducing the total number of mined subgraphs
    • Saving space and analysis effort
  • Reducing mining time
  • Non-maximal frequent subgraph can be reconstructed.
  • Maximal frequent subgraphs are of most interest in some appliations.
algorithm
Algorithm
  • Mining all frequent trees from a general graph database.
    • Tree normalization is simpler than graph.
    • In certain applications, most of the frequent subgraphs are really trees.
    • Use current subgraph mining algorithm
    • Mining subtrees from a forest
algorithm1
Algorithm
  • Reconstruct all maximal subgraphs from the mined trees.
    • For each frequent tree T, find all frequent subgraphs whose canonical spanning tree are isomorphic to T
    • Enumerate the equvalence class of a tree T
    • Maximal subgraph mining
tree based equivalence classes
Tree-based Equivalence Classes
  • A subtree T is a spanning tree of G if T contains all nodes in G.
    • Maximal one: canonical spanning tree
  • Group all frequent subgraphs in to equivalence classes based on spanning trees.
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12 singletons group
enumerating graphs from trees
Enumerating Graphs from Trees
  • G C :{e1,e2,…,en}
    • If frequent -> edge C (candidate set)
  • Search space of G: G:C ={G+y|y 2C}

GO

optimizations
Optimizations
  • Removing a set of frequent subgraphs that can not be maximal from a search space
  • Locally maximal:frequent subgraph G is maximal in its equivalence class
  • Globally maximal:maximal frequent in a graph database
  • Avoid enumerating subgraphs which are notlocally maximal.
bottom up pruning
Bottom-up Pruning
  • G’ = G C
    • G’ is frequent : each graph in search space is a subgraph of G’ and not maximal
tail shrink
Tail Shrink
  • Embedding of G in G’ is a subgraph isomorphism f from G to G’
    • Two embeddings of L in P

l1->P1, l2->P2, l3->P3, l4->P4

l1->P1, l2->P3 ,l3->P2 ,l4->P4

go

tail shrink1
Tail Shrink
  • candidate edge (i, j, el) is associative to a graph G
    • It appears in every embedding of G in a graph databases
  • If a tree T contains a set of associative edges, any maximal frequent graph G, a superset of T, must contains all associative edges.
tail shrink2
Tail Shrink
  • Remove associative edges from candidate sets and augment them to T without missing any maximal ones
    • Reducing the search space
    • Prune the entire equivalences class in certain cases
  • A set of associative edges C of a tree T is lethal
    • G’ = T C has a canonical spanning treedifferent from that of T

go

external edge pruning
External-Edge Pruning
  • Remove one equivalence class without any knowledge about its candidate edges
  • External-edge for a graph G: it connects a node in G and a node not in G
  • (i, el, vl) is associative to a graph G
    • Every embedding f of G in a graph G’, G’ has a node v with the label vl
    • v connects to the node f(i) with an edge label el in G’
    • Not exist node j V[G] such that v = f(j)
experiments
Experiments
  • 2.8GHz Pentium Xeon,
  • 512KB L2 cache,2GB main memory
  • Red Hat Linux 7.3
  • C++ Programming language
synthetic dataset
Synthetic Dataset

D10KT30L200I11V4E4

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