Post on 11-Feb-2017
transcript
Compression-based Graph Mining Exploiting
Structure Primitives
Seminar explorative DatenanalyseWerner Hoffmann
19.06.2015
Jing Feng, Xiao He, Nina Hubig, Christian Böhm and Claudia Plant
Outline
- What?- Why?- How?- Conclusion!
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Context [1]
Graphs:unweightedundirectedmodelled as adjacency matrixsparse
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Social Media DataIs Facebook sparse?-> 1.4 x 10^9 nodes ¹-> on average 340 friends² per node-> 478 x 10^9 edges-> possible edges: 0.9 x 10^18 => only 0,000000156% of all possible edges existYes Facebook is very sparse¹https://en.wikipedia.org/wiki/Facebook ²http://www.statista.com/statistics/232499/americans-who-use-social-networking-sites-several-times-per-day/
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Why
spa
rse?
http://www.twolfanger.de/wp-content/uploads/2013/06/Degree-Network.png 5
Instagram network Werner
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51 friends13 edges[4]
Goal
Find values for
transitivity [2] and
hubness of a graph
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Outline
- What?- Why?- How?- Conclusion!
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What is the benefit of knowing the structure of a graph?- deeper insights in Graph
- lossless compression is possible
- link prediction
- number of clusters
- graph partitioning9
Outline
- What?- Why?- How?- Conclusion!
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Basic regular substructures
Trianglestransitivity
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Starshubness
Characteristics of CXprime(Compression-based eXploiting Primitives)
Minimum Description Length - based [3]¹
no Input parameters (unsupervised)
Clustering is k-means like
¹https://en.wikipedia.org/wiki/Minimum_description_length 12
Three different ways of coding
- edge
- hub (or star)
- mesh (or triangle)
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Coding Example Hub
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G={(A,B);(A,C);(A,D);(A,E);(A,F)}
Coding Example Hub
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G={(A,B);(A,C);(A,D);(A,E);(A,F)}
G={HUB(A|B,C,D,E,F}
Coding Example Mesh
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G={(A,B);(A,C);(A,D);(A,E);(B,C);(B,D);(B,E);(C,D);(C,E);(D,E)}
Coding Example Mesh
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G={(A,B);(A,C);(A,D);(A,E);(B,C);(B,D);(B,E);(C,D);(C,E);(D,E)}
G={HUB(A|B,C,D,E);HUB(B|C,D,E);HUB(C|D,E);HUB(D|E)}
Coding Example Mesh
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G={(A,B);(A,C);(A,D);(A,E);(B,C);(B,D);(B,E);(C,D);(C,E);(D,E)}
G={HUB(A|B,C,D,E);HUB(B|C,D,E);HUB(C|D,E);HUB(D|E)}
G={M(A,B,C,D,E)}
Coding Example Hub
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G={(A,B);(A,C);(A,D);(A,E);(A,F)}
G={HUB(A|B,C,D,E,F}
G={M(A,B);M(A,C);M(A,D);M(A,E);M(A,F);M(A,G)}
Outcomes 1
After coding the graph in a star-coding and in a
triangle-coding you can see which one is the
smallest, so which basic structure is most
common.
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all possible connections of Three nodes
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Outcomes 2
If you always use the minimum of the three
possible codings you get an overall minimum
graph. This graph is now clustered in areas of
hubs and triangles.
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Outline
- What?- Why?- How?- Conclusion!
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Critics
- No example how the coding
actually looks like
- given probabilities are not
replicable
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Summary
The mentioned results in the paper are really good. The compression rate is extremely high compared to other graph compression algorithms. The clustering results look really good.
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Thanks for your attention[1] FENG JING , XIAO HE , NINA HUBIG , CHRISTIAN BÖHM, CLAUDIA PLANT: Compression-based Graph Mining Exploiting Structure Primitives. Data Mining (ICDM), 2013 IEEE 13th International Conference on, 181–190. IEEE, 2013
[2] T. Schank and D. Wagner, “Approximating clustering coefficient and transitivity,” J. Graph Algorithms Appl., vol. 9, no. 2, pp. 265–275, 2005.
[3] J. Rissanen, “An introduction to the mdl principle,” Helsinki Institute for Information Technology, Tech. Rep., 2005.
[4] Python, Pyplot, Instagram API
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