Hyper Hyper

1
Hyper Hyper

• Mining Frequent Hypergraphs
• 07.03.2005Tamas Horvath, Björn Bringmann,His
  Royal Highness Professor Doctor Luc De Raedt

2
A Hypergraph(or set system)
A

• HG (V, E, S, ?)
• Set V of Nodes v
• Set E of Edges eEach edge e is a subset of
  V(i.e. E ? 2V )

B
D
E
C
3
Subhypergraphs

• H (V, E, S, ?) and H (V, E, S, ?)with V
  Í V anda mapping ? E ? E such that e ?(e)

Í
injective
partial
strict
subhypergraph
A
A
B
D
E
B
D
E
C
C
F
4
Living on the EDGE

• ? Edges in proper subhypergraphs
• ? Edges in partial subhypergraphs

e1 e2
A
B
C
A
B
C
e1 ? e2
A
B
A
B
C
5
4 Reductions
itemset mining
itemset mining
IP
Good news
- OP
bipartite graphs
bipartite graphs (strict partial)
- OP
3 uniform ß-acyclic Hypergraphsdeciding if H is
Freq is NP-Hard
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Itemset Mining (proper)

• Transaction Hypergraph
• Items Hyperedges (set of vertice)
• ? A set of Hypergraphs is a Database

A

• A,B,C, B,D,E

B
D
E
C
can be enumerated in incremental polynomial time
7
Itemset Mining (partial)

• Transaction Hypergraph
• Items Powersets of Hyperedges
• ? A set of Hypergraphs is a Database

A

• A,B,C, B,D,E

A,B, A,C, B,C,, B,D, B,E, D,E,
B
D
E
A, B, C, D, E
C
IP for bounded rank
8
Bipartite Graphs

• Idea Every Hypergraph HG can be represented as
  a Graph
• HG (V, E) ? G (V ? E, E)E ? (v, e) v
  ? e, e ? E, v ? V

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How our Hypergraph transforms
U
R
M
e
M
S
U
R
F
S
M
R
e
F
e
U
e

• Nodes stay nodes
• Edges become nodes
• Each node is connected with its edges

S
F
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Bi Partite
proper
partial
S
e
M
MSU
M
U
U
R
F
e
R
FRU
S
F
Cant be enumerated in output polynomial time
11
Mining Hypergraphs
Hypergraphs
injective

• gSpan
• closeGraph
• AGM

Use anyItemsetminer
Use anyGraphminer
Frequent Hypergraphs
12
Mining the Hype

• Mining KDD Bibliographies
• Reference lists modeled as hypergraphs

• R. Agrawal, H. Mannila, R. Srikant, H. Toivonen
• H. Mannila, H. Toivonen
• R. Agrawal, L. De Raedt
• L. De Raedt, T. Horvath

, B. Bringmann
Argawal
Mannila
Srikant
Toivonen
De Raedt
Horvath
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Citation Datasets
14
Speed
15
Search and Find
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Conclusions

• Using reductions to mine Hypergraphs
• Positive and negative complexity results
• Experiments show that it is useful
• If you write a KDD Paper,cite Agrawal and Srikant

( or break the tradition )
17
?
Questions
ideas
comments
valuable insights
coffee ?
18
Thanks!